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Convert the decimal below to a fraction in simplest form.

0.63

79 answers

To convert the decimal 0.63 to a fraction, we can follow these steps:

  1. Write the decimal as a fraction: \[ 0.63 = \frac{63}{100} \] This is because 0.63 means 63 hundredths.

  2. Simplify the fraction, if possible. We need to find the greatest common divisor (GCD) of the numerator and denominator. The numerator is 63 and the denominator is 100.

    • The factors of 63 are: 1, 3, 7, 9, 21, 63
    • The factors of 100 are: 1, 2, 4, 5, 10, 20, 25, 50, 100

    The GCD of 63 and 100 is 1, since they have no common factors other than 1.

  3. Since the GCD is 1, the fraction \(\frac{63}{100}\) is already in its simplest form.

Thus, the decimal 0.63 as a fraction in simplest form is \[ \frac{63}{100}. \]

Convert the decimal below to a fraction in simplest form.
0.77

To convert the decimal 0.77 to a fraction, we can follow these steps:

  1. Write the decimal as a fraction: \[ 0.77 = \frac{77}{100} \] This represents 77 hundredths.

  2. Simplify the fraction, if possible. We need to find the greatest common divisor (GCD) of the numerator and denominator. The numerator is 77 and the denominator is 100.

    • The factors of 77 are: 1, 7, 11, 77
    • The factors of 100 are: 1, 2, 4, 5, 10, 20, 25, 50, 100

    The only common factor is 1, meaning the GCD is 1.

  3. Since the GCD is 1, the fraction \(\frac{77}{100}\) is already in its simplest form.

Thus, the decimal 0.77 as a fraction in simplest form is \[ \frac{77}{100}. \]

Convert the decimal below to a fraction in simplest form.
0.49

To convert the decimal 0.49 to a fraction, we can follow these steps:

  1. Write the decimal as a fraction: \[ 0.49 = \frac{49}{100} \] This represents 49 hundredths.

  2. Simplify the fraction, if possible. To do this, we need to find the greatest common divisor (GCD) of the numerator and denominator. The numerator is 49 and the denominator is 100.

    • The factors of 49 are: 1, 7, 49
    • The factors of 100 are: 1, 2, 4, 5, 10, 20, 25, 50, 100

    The only common factor between 49 and 100 is 1, which means the GCD is 1.

  3. Since the GCD is 1, the fraction \(\frac{49}{100}\) is already in its simplest form.

Thus, the decimal 0.49 as a fraction in simplest form is \[ \frac{49}{100}. \]

Convert the decimal below to a fraction in simplest form.
0.52

To convert the decimal 0.52 to a fraction, follow these steps:

  1. Write the decimal as a fraction: \[ 0.52 = \frac{52}{100} \] This represents 52 hundredths.

  2. Simplify the fraction, if possible. First, we need to determine the greatest common divisor (GCD) of the numerator (52) and the denominator (100).

    • The factors of 52 are: 1, 2, 4, 13, 26, 52
    • The factors of 100 are: 1, 2, 4, 5, 10, 20, 25, 50, 100

    The common factors of 52 and 100 are: 1, 2, and 4. The greatest common divisor is 4.

  3. Divide both the numerator and denominator by their GCD (4): \[ \frac{52 \div 4}{100 \div 4} = \frac{13}{25} \]

Thus, the decimal 0.52 as a fraction in simplest form is \[ \frac{13}{25}. \]

convert the fraction below into a decimal 7/60 (Edit the repeating and non-repeating part of the decimal)

To convert the fraction \(\frac{7}{60}\) into a decimal, we can perform long division:

  1. Divide 7 by 60:

    • 60 goes into 7 zero times, so we write 0 and add a decimal point.
    • Add a zero, making it 70.
    • 60 goes into 70 once (1), so we write down 1.
    • Subtract \(60 \times 1 = 60\) from 70, leaving us with \(70 - 60 = 10\).

  2. Bring down another zero, making it 100:

    • 60 goes into 100 once (1), so we write down another 1.
    • Subtract \(60 \times 1 = 60\) from 100, leaving us with \(100 - 60 = 40\).

  3. Bring down another zero, making it 400:

    • 60 goes into 400 six times (6), so we write down 6.
    • Subtract \(60 \times 6 = 360\) from 400, leaving us with \(400 - 360 = 40\).

  4. Bring down another zero, making it 400 again:

    • We see we are back to 400. Thus, the next digit will again be 6, and this process will repeat.

The decimal representation of the fraction \(\frac{7}{60}\) is: \[ 0.116666... \] The part "666..." continues indefinitely.

Final Representation:

The decimal can be expressed as: \[ 0.11\overline{6} \] where \(0.11\) is the non-repeating part, and \(6\) is the repeating part.

convert the fraction below into a decimal 1/6 (Edit the repeating and non-repeating part of the decimal)

To convert the fraction \(\frac{1}{6}\) into a decimal, we can perform long division:

  1. Divide 1 by 6:

    • 6 goes into 1 zero times, so we write 0 and add a decimal point.
    • Add a zero to make it 10.
    • 6 goes into 10 one time (1), so we write down 1.
    • Subtract \(6 \times 1 = 6\) from 10, leaving \(10 - 6 = 4\).

  2. Bring down another zero, making it 40:

    • 6 goes into 40 six times (6), so we write down 6.
    • Subtract \(6 \times 6 = 36\) from 40, leaving \(40 - 36 = 4\).

  3. Bring down another zero, making it 40 again:

    • We see we are again left with 40, so the next digit will be 6, and this process will repeat.

The decimal representation of the fraction \(\frac{1}{6}\) is: \[ 0.166666... \] The part "666..." continues indefinitely.

Final Representation:

The decimal can be expressed as: \[ 0.1\overline{6} \] where \(0.1\) is the non-repeating part, and \(6\) is the repeating part.

convert the fraction below into a decimal 17/30 (Edit the repeating and non-repeating part of the decimal)

To convert the fraction \(\frac{17}{30}\) into a decimal, we can perform long division:

  1. Divide 17 by 30:

    • 30 goes into 17 zero times, so we write 0 and add a decimal point.
    • Add a zero to the 17, making it 170.
    • 30 goes into 170 five times (5), so we write down 5.
    • Subtract \(30 \times 5 = 150\) from 170, leaving us with \(170 - 150 = 20\).

  2. Bring down another zero, making it 200:

    • 30 goes into 200 six times (6), so we write down 6.
    • Subtract \(30 \times 6 = 180\) from 200, leaving us with \(200 - 180 = 20\).

  3. Bring down another zero, making it 200 again:

    • We see that we're repeating the process. Therefore, the next digit is again 6.

The decimal representation of the fraction \(\frac{17}{30}\) is: \[ 0.566666... \] The part "666..." continues indefinitely.

Final Representation:

The decimal can be expressed as: \[ 0.5\overline{6} \] where \(0.5\) is the non-repeating part, and \(6\) is the repeating part.

convert the fraction below into a decimal 31/40 (Edit the repeating and non-repeating part of the decimal)

To convert the fraction \(\frac{31}{40}\) into a decimal, we can perform long division:

  1. Divide 31 by 40:

    • 40 goes into 31 zero times, so we write 0 and add a decimal point.
    • Add a zero to 31, making it 310.
    • 40 goes into 310 seven times (7), so we write down 7.
    • Subtract \(40 \times 7 = 280\) from 310, leaving us with \(310 - 280 = 30\).

  2. Bring down another zero, making it 300:

    • 40 goes into 300 seven times (7) again, so we write down another 7.
    • Subtract \(40 \times 7 = 280\) from 300, leaving \(300 - 280 = 20\).

  3. Bring down another zero, making it 200:

    • 40 goes into 200 five times (5), so we write down 5.
    • Subtract \(40 \times 5 = 200\) from 200, leaving \(200 - 200 = 0\).

The division ends here, and we obtain a terminating decimal.

The decimal representation of the fraction \(\frac{31}{40}\) is: \[ 0.775 \]

Final Representation:

Since the decimal \(0.775\) does not have any repeating parts, we can simply write it as: \[ 0.775 \] In this case, there is no repeating part, and the entire number is the non-repeating decimal.

convert the fraction below into a decimal 31/50 (Edit the repeating and non-repeating part of the decimal)

To convert the fraction \(\frac{31}{50}\) into a decimal, we can perform long division or directly divide \(31\) by \(50\).

  1. Divide 31 by 50:

    • 50 goes into 31 zero times, so we write 0 and add a decimal point.
    • Add a zero to \(31\), making it \(310\).
    • 50 goes into \(310\) six times (6), so we write down \(6\).
    • Subtract \(50 \times 6 = 300\) from \(310\), leaving us with \(310 - 300 = 10\).

  2. Bring down another zero, making it \(100\):

    • 50 goes into \(100\) two times (2), so we write down \(2\).
    • Subtract \(50 \times 2 = 100\) from \(100\), leaving \(100 - 100 = 0\).

The division ends here, and we obtain a terminating decimal.

The decimal representation of the fraction \(\frac{31}{50}\) is: \[ 0.62 \]

Final Representation:

Since the decimal \(0.62\) does not have any repeating parts, we can simply write it as: \[ 0.62 \] In this case, there is no repeating part, and the entire number is the non-repeating decimal.

convert the fraction below into a decimal 21/50 (Edit the repeating and non-repeating part of the decimal)

To convert the fraction \(\frac{21}{50}\) into a decimal, we can perform long division or directly divide \(21\) by \(50\).

  1. Divide 21 by 50:

    • 50 goes into 21 zero times, so we write 0 and add a decimal point.
    • Add a zero to \(21\), making it \(210\).
    • 50 goes into \(210\) four times (4), so we write down \(4\).
    • Subtract \(50 \times 4 = 200\) from \(210\), leaving us with \(210 - 200 = 10\).

  2. Bring down another zero, making it \(100\):

    • 50 goes into \(100\) two times (2), so we write down \(2\).
    • Subtract \(50 \times 2 = 100\) from \(100\), leaving \(100 - 100 = 0\).

This means we have finished the division, and we obtain a terminating decimal.

The decimal representation of the fraction \(\frac{21}{50}\) is: \[ 0.42 \]

Final Representation:

Since the decimal \(0.42\) does not have any repeating parts, we can simply write it as: \[ 0.42 \] In this case, there is no repeating part, and the entire number is the non-repeating decimal.

convert the fraction below into a decimal 3/10 (Edit the repeating and non-repeating part of the decimal)

To convert the fraction \(\frac{3}{10}\) into a decimal, we can directly divide \(3\) by \(10\).

  1. Divide 3 by 10:
    • 10 goes into 3 zero times, so we write \(0\) and add a decimal point.
    • Add a zero to \(3\), making it \(30\).
    • 10 goes into \(30\) three times (3), so we write down \(3\).
    • Subtract \(10 \times 3 = 30\) from \(30\), leaving \(30 - 30 = 0\).

Since there is no remainder, we have finished the division.

The decimal representation of the fraction \(\frac{3}{10}\) is: \[ 0.3 \]

Final Representation:

Since the decimal \(0.3\) does not have any repeating parts, we can simply write it as: \[ 0.3 \] In this case, there is no repeating part, and the entire number is the non-repeating decimal.

convert the fraction below into a decimal 13/30 (Edit the repeating and non-repeating part of the decimal)

To convert the fraction \(\frac{13}{30}\) into a decimal, we can perform long division:

  1. Divide 13 by 30:

    • 30 goes into 13 zero times, so we write 0 and add a decimal point.
    • Add a zero to 13, making it 130.
    • 30 goes into 130 four times (4), so we write down 4.
    • Subtract \(30 \times 4 = 120\) from 130, leaving us with \(130 - 120 = 10\).

  2. Bring down another zero, making it 100:

    • 30 goes into 100 three times (3), so we write down 3.
    • Subtract \(30 \times 3 = 90\) from 100, leaving us with \(100 - 90 = 10\).

  3. Bring down another zero, making it 100 again:

    • We see we're back at 100, which means the next digit will also be 3, leading to a repeating pattern.

The decimal representation of the fraction \(\frac{13}{30}\) is: \[ 0.433333... \]

Final Representation:

The decimal can be expressed as: \[ 0.43\overline{3} \] where \(0.43\) is the non-repeating part, and \(3\) is the repeating part.

convert the fraction below into a decimal 13/20 (Edit the repeating and non-repeating part of the decimal)

To convert the fraction \(\frac{13}{20}\) into a decimal, we can perform long division or directly divide \(13\) by \(20\).

  1. Divide 13 by 20:

    • 20 goes into 13 zero times, so we write \(0\) and add a decimal point.
    • Add a zero to \(13\), making it \(130\).
    • 20 goes into \(130\) six times (6), so we write down \(6\).
    • Subtract \(20 \times 6 = 120\) from \(130\), leaving us with \(130 - 120 = 10\).

  2. Bring down another zero, making it \(100\):

    • 20 goes into \(100\) five times (5), so we write down \(5\).
    • Subtract \(20 \times 5 = 100\) from \(100\), leaving \(100 - 100 = 0\).

Since there is no remainder, we finish the division.

The decimal representation of the fraction \(\frac{13}{20}\) is: \[ 0.65 \]

Final Representation:

Since the decimal \(0.65\) does not have any repeating parts, we can simply write it as: \[ 0.65 \] In this case, there is no repeating part, and the entire number is the non-repeating decimal.

convert the fraction below into a decimal 1/10 (Edit the repeating and non-repeating part of the decimal)

To convert the fraction \(\frac{1}{10}\) into a decimal, we can directly divide \(1\) by \(10\).

  1. Divide 1 by 10:
    • 10 goes into 1 zero times, so we write \(0\) and add a decimal point.
    • Add a zero to \(1\), making it \(10\).
    • 10 goes into \(10\) one time (1), so we write down \(1\).
    • Subtract \(10 \times 1 = 10\) from \(10\), leaving \(10 - 10 = 0\).

Since there is no remainder, we finish the division.

The decimal representation of the fraction \(\frac{1}{10}\) is: \[ 0.1 \]

Final Representation:

Since the decimal \(0.1\) does not have any repeating parts, we can simply write it as: \[ 0.1 \] In this case, there is no repeating part, and the entire number is the non-repeating decimal.

convert the following repeating decimal to a fraction in simplest form
line above .98

To convert the repeating decimal \(0.\overline{98}\) (which means \(0.989898...\)) into a fraction, we can follow these steps:

  1. Let \(x\) represent the repeating decimal: \[ x = 0.\overline{98} \]

  2. Multiply both sides of the equation by 100 (since the repeating part is two digits long): \[ 100x = 98.\overline{98} \]

  3. Now, subtract the original equation from this new equation: \[ 100x - x = 98.\overline{98} - 0.\overline{98} \] This simplifies to: \[ 99x = 98 \]

  4. Now, solve for \(x\): \[ x = \frac{98}{99} \]

  5. Check if the fraction can be simplified: The GCD (Greatest Common Divisor) of \(98\) and \(99\) is \(1\), since \(98 = 2 \times 7^2\) and \(99 = 3^2 \times 11\) share no common factors.

Therefore, the fraction \(\frac{98}{99}\) is already in its simplest form.

Final Answer:

The repeating decimal \(0.\overline{98}\) can be expressed as the fraction: \[ \frac{98}{99} \]

convert the following repeating decimal to a fraction in simplest form
line above .32

To convert the repeating decimal \(0.\overline{32}\) (which means \(0.323232...\)) into a fraction, we can follow these steps:

  1. Let \(x\) represent the repeating decimal: \[ x = 0.\overline{32} \]

  2. Multiply both sides of the equation by 100 (since the repeating part is two digits long): \[ 100x = 32.\overline{32} \]

  3. Now subtract the original equation from this new equation: \[ 100x - x = 32.\overline{32} - 0.\overline{32} \] This simplifies to: \[ 99x = 32 \]

  4. Now solve for \(x\): \[ x = \frac{32}{99} \]

  5. Check if the fraction can be simplified: The GCD (Greatest Common Divisor) of 32 and 99 is 1, since:

    • \(32 = 2^5\)
    • \(99 = 3^2 \times 11\)

    They share no common factors.

Thus, the fraction \(\frac{32}{99}\) is already in its simplest form.

Final Answer:

The repeating decimal \(0.\overline{32}\) can be expressed as the fraction: \[ \frac{32}{99} \]

convert the following repeating decimal to a fraction in simplest form
line above .9

To convert the repeating decimal \(0.\overline{9}\) (which means \(0.999999...\)) into a fraction, we can use the following method:

  1. Let \(x\) represent the repeating decimal: \[ x = 0.\overline{9} \]

  2. Multiply both sides of the equation by 10 (since the repeating part is one digit long): \[ 10x = 9.\overline{9} \]

  3. Now subtract the original equation from this new equation: \[ 10x - x = 9.\overline{9} - 0.\overline{9} \] This simplifies to: \[ 9x = 9 \]

  4. Now solve for \(x\): \[ x = \frac{9}{9} = 1 \]

Final Answer:

The repeating decimal \(0.\overline{9}\) is equal to the fraction: \[ 1 \]

In other terms, \(0.999999...\) is mathematically equal to \(1\).

convert the following repeating decimal to a fraction in simplest form
line above .65

To convert the repeating decimal \(0.\overline{65}\) (which means \(0.656565...\)) into a fraction, we can follow these steps:

  1. Let \(x\) represent the repeating decimal: \[ x = 0.\overline{65} \]

  2. Multiply both sides of the equation by 100 (since the repeating part "65" has two digits): \[ 100x = 65.\overline{65} \]

  3. Now subtract the original equation from this new equation: \[ 100x - x = 65.\overline{65} - 0.\overline{65} \] This simplifies to: \[ 99x = 65 \]

  4. Now solve for \(x\): \[ x = \frac{65}{99} \]

  5. Check if the fraction can be simplified:

    • The numerator \(65 = 5 \times 13\).
    • The denominator \(99 = 3^2 \times 11\).

Since \(65\) and \(99\) have no common factors other than \(1\), the fraction \(\frac{65}{99}\) is already in its simplest form.

Final Answer:

The repeating decimal \(0.\overline{65}\) can be expressed as the fraction: \[ \frac{65}{99} \]

convert the following repeating decimal to a fraction in simplest form
line above .24

To convert the repeating decimal \(0.\overline{24}\) (which means \(0.242424...\)) into a fraction, follow these steps:

  1. Let \(x\) represent the repeating decimal: \[ x = 0.\overline{24} \]

  2. Multiply both sides of the equation by 100 (since the repeating part "24" has two digits): \[ 100x = 24.\overline{24} \]

  3. Now subtract the original equation from this new equation: \[ 100x - x = 24.\overline{24} - 0.\overline{24} \] This simplifies to: \[ 99x = 24 \]

  4. Now solve for \(x\): \[ x = \frac{24}{99} \]

  5. Check if the fraction can be simplified:

    • The numerator \(24 = 2^3 \times 3\).
    • The denominator \(99 = 3^2 \times 11\).

The GCD of \(24\) and \(99\) is \(3\). Therefore, we can simplify the fraction: \[ x = \frac{24 \div 3}{99 \div 3} = \frac{8}{33} \]

Final Answer:

The repeating decimal \(0.\overline{24}\) can be expressed as the fraction: \[ \frac{8}{33} \]

convert the following repeating decimal to a fraction in simplest form
line above .50

To convert the repeating decimal \(0.\overline{50}\) (which means \(0.505050...\)) into a fraction, follow these steps:

  1. Let \(x\) represent the repeating decimal: \[ x = 0.\overline{50} \]

  2. Multiply both sides of the equation by 100 (since the repeating part "50" has two digits): \[ 100x = 50.\overline{50} \]

  3. Now subtract the original equation from this new equation: \[ 100x - x = 50.\overline{50} - 0.\overline{50} \] This simplifies to: \[ 99x = 50 \]

  4. Now solve for \(x\): \[ x = \frac{50}{99} \]

  5. Check if the fraction can be simplified:

    • The numerator \(50 = 2 \times 5^2\).
    • The denominator \(99 = 3^2 \times 11\).

Since \(50\) and \(99\) have no common factors other than \(1\), the fraction \(\frac{50}{99}\) is already in its simplest form.

Final Answer:

The repeating decimal \(0.\overline{50}\) can be expressed as the fraction: \[ \frac{50}{99} \]

convert the following repeating decimal to a fraction in simplest form
line above .72

To convert the repeating decimal \(0.\overline{72}\) (which means \(0.727272...\)) into a fraction, we can follow these steps:

  1. Let \(x\) represent the repeating decimal: \[ x = 0.\overline{72} \]

  2. Multiply both sides of the equation by 100 (since the repeating part "72" has two digits): \[ 100x = 72.\overline{72} \]

  3. Now subtract the original equation from this new equation: \[ 100x - x = 72.\overline{72} - 0.\overline{72} \] This simplifies to: \[ 99x = 72 \]

  4. Now solve for \(x\): \[ x = \frac{72}{99} \]

  5. Check if the fraction can be simplified:

    • The numerator \(72 = 2^3 \times 3^2\).
    • The denominator \(99 = 3^2 \times 11\).

The GCD of \(72\) and \(99\) is \(9\). Therefore, we can simplify the fraction: \[ x = \frac{72 \div 9}{99 \div 9} = \frac{8}{11} \]

Final Answer:

The repeating decimal \(0.\overline{72}\) can be expressed as the fraction: \[ \frac{8}{11} \]

convert the following repeating decimal to a fraction in simplest form
line above .01

To convert the repeating decimal \(0.\overline{01}\) (which means \(0.010101...\)) into a fraction, follow these steps:

  1. Let \(x\) represent the repeating decimal: \[ x = 0.\overline{01} \]

  2. Multiply both sides of the equation by 100 (since the repeating part "01" has two digits): \[ 100x = 1.\overline{01} \]

  3. Now subtract the original equation from this new equation: \[ 100x - x = 1.\overline{01} - 0.\overline{01} \] This simplifies to: \[ 99x = 1 \]

  4. Now solve for \(x\): \[ x = \frac{1}{99} \]

Final Answer:

The repeating decimal \(0.\overline{01}\) can be expressed as the fraction: \[ \frac{1}{99} \]

Rational and irrational numbers are both part of the _________ rational numbers include ________________ the square root of a _______ is a rational number since it can be written as a whole number fractions written as a ratio of integers can be converted to ____________ decimals irrational numbers cannot be written as _________ irrational numbers include _________ the square root of imperfect squares _____________ in decimal form Pi is an example of _____________ (Explain the difference in rational and irrational numbers

Here's a comprehensive explanation of rational and irrational numbers, along with the details to fill in the blanks in your text.

**Rational and irrational numbers are both part of the real numbers. Rational numbers include integers, whole numbers, fractions, and terminating or repeating decimals. The square root of a perfect square is a rational number since it can be written as a whole number. Fractions written as a ratio of integers can be converted to terminating or repeating decimals. Irrational numbers cannot be written as simple fractions. Irrational numbers include non-repeating, non-terminating decimals and the square roots of imperfect squares. Irrational numbers in decimal form do not repeat or terminate. Pi is an example of an irrational number.

Explanation of the Difference Between Rational and Irrational Numbers:

  1. Rational Numbers:

    • Defined as any number that can be expressed as a fraction \(\frac{a}{b}\), where \(a\) and \(b\) are integers and \(b \neq 0\).
    • Include integers (e.g., -3, 0, 2), whole numbers (e.g., 0, 1, 2), proper and improper fractions (e.g., \(\frac{1}{2}, \frac{5}{3}\)), and decimal representations that either terminate (e.g., 0.75) or repeat (e.g., 0.333...).
    • Examples: \(1, -4.5, \frac{2}{3}, 0.25, 0.666...\).

  2. Irrational Numbers:

    • Defined as numbers that cannot be expressed as a fraction of two integers. Their decimal representation does not terminate or repeat.
    • Include numbers such as the square roots of non-perfect squares (e.g., \(\sqrt{2}, \sqrt{3}\)) and special numbers like \(\pi\) (the ratio of the circumference of a circle to its diameter) or \(e\) (the base of the natural logarithm).
    • Examples: \(\sqrt{2}, \pi, e, 0.1010010001...\) (a non-terminating, non-repeating decimal).

In summary, the main difference between rational and irrational numbers lies in their ability to be expressed as fractions. Rational numbers can, while irrational numbers cannot.

Determine if square root of 25 is rational or irrational and give a reason for your answer

the number square roof 25 is ______ because ___________

The number \(\sqrt{25}\) is rational because it can be expressed as the fraction \(\frac{5}{1}\) (or simply as the integer \(5\)), which is a ratio of two integers. Since rational numbers include integers, and all integers can be expressed as fractions, \(\sqrt{25}\) is classified as a rational number.

Complete statement:

The number \(\sqrt{25}\) is rational because \(5\) can be expressed as a ratio of integers, specifically \(\frac{5}{1}\).

Determine if square root of 25 is rational or irrational and give a reason for your answer

the number square roof 25 is ______ because ___________

A: it is a decimal that terminates
B: it is a decimal that repeats
C: it is a decimal that does not repeat or terminate
D: it is the square root of a perfect square
E: it is the square root of a non-perfect square

The number \(\sqrt{25}\) is rational because it is the square root of a perfect square.

Complete statement:

The number \(\sqrt{25}\) is rational because D: it is the square root of a perfect square.

This is because \(\sqrt{25} = 5\), which is an integer and can be expressed as the ratio \(\frac{5}{1}\).

Determine if 0.84375 is rational or irrational and give a reason for your answer

the number 0.84375 is ______ because ___________

A: it is a decimal that terminates
B: it is a decimal that repeats
C: it is a decimal that does not repeat or terminate
D: it is the square root of a perfect square
E: it is the square root of a non-perfect square

The number \(0.84375\) is rational because it can be expressed as a fraction and it is a decimal that terminates.

Complete statement:

The number \(0.84375\) is rational because A: it is a decimal that terminates.

This means that \(0.84375\) can be represented as \(\frac{84375}{100000}\) or simplified further as a fraction, confirming that it is indeed a rational number.

Determine if 0.625 is rational or irrational and give a reason for your answer

the number 0.625 is ______ because ___________

A: it is a decimal that terminates
B: it is a decimal that repeats
C: it is a decimal that does not repeat or terminate
D: it is the square root of a perfect square
E: it is the square root of a non-perfect square

The number \(0.625\) is rational because it can be expressed as a fraction and it is a decimal that terminates.

Complete statement:

The number \(0.625\) is rational because A: it is a decimal that terminates.

This means that \(0.625\) can be represented as \(\frac{625}{1000}\), which simplifies to \(\frac{5}{8}\), confirming that it is indeed a rational number.

Determine if square root of 16 is rational or irrational and give a reason for your answer

the number square root of 16 is ______ because ___________

A: it is a decimal that terminates
B: it is a decimal that repeats
C: it is a decimal that does not repeat or terminate
D: it is the square root of a perfect square
E: it is the square root of a non-perfect square

The number \(\sqrt{16}\) is rational because it is the square root of a perfect square.

Complete statement:

The number \(\sqrt{16}\) is rational because D: it is the square root of a perfect square.

This is because \(\sqrt{16} = 4\), which is an integer and can be expressed as the ratio \(\frac{4}{1}\).

Determine if 0.875 is rational or irrational and give a reason for your answer

the number 0.875 is ______ because ___________

A: it is a decimal that terminates
B: it is a decimal that repeats
C: it is a decimal that does not repeat or terminate
D: it is the square root of a perfect square
E: it is the square root of a non-perfect square

The number \(0.875\) is rational because it can be expressed as a fraction and it is a decimal that terminates.

Complete statement:

The number \(0.875\) is rational because A: it is a decimal that terminates.

This means that \(0.875\) can be represented as \(\frac{875}{1000}\), which simplifies to \(\frac{7}{8}\), confirming that it is indeed a rational number.

Determine if square root of 4 is rational or irrational and give a reason for your answer

the number square root of 4 is ______ because ___________

A: it is a decimal that terminates
B: it is a decimal that repeats
C: it is a decimal that does not repeat or terminate
D: it is the square root of a perfect square
E: it is the square root of a non-perfect square

The number \(\sqrt{4}\) is rational because it is the square root of a perfect square.

Complete statement:

The number \(\sqrt{4}\) is rational because D: it is the square root of a perfect square.

This is because \(\sqrt{4} = 2\), which is an integer and can be expressed as the ratio \(\frac{2}{1}\).

Determine if square root of 9 is rational or irrational and give a reason for your answer

the number square root of 9 is ______ because ___________

A: it is a decimal that terminates
B: it is a decimal that repeats
C: it is a decimal that does not repeat or terminate
D: it is the square root of a perfect square
E: it is the square root of a non-perfect square

The number \(\sqrt{9}\) is rational because it is the square root of a perfect square.

Complete statement:

The number \(\sqrt{9}\) is rational because D: it is the square root of a perfect square.

This is because \(\sqrt{9} = 3\), which is an integer and can be expressed as the ratio \(\frac{3}{1}\).

Determine if 0.69789978997899789 is rational or irrational and give a reason for your answer

the number 0.6978997899899789 is ______ because ___________

A: it is a decimal that terminates
B: it is a decimal that repeats
C: it is a decimal that does not repeat or terminate
D: it is the square root of a perfect square
E: it is the square root of a non-perfect square

The number \(0.69789978997899789\) is irrational because it does not have a repeating pattern and does not terminate.

Complete statement:

The number \(0.69789978997899789\) is irrational because C: it is a decimal that does not repeat or terminate.

In this case, the decimal appears to continue without repeating and does not end, indicating it cannot be expressed as a fraction of two integers.

Determine if 0.5 is rational or irrational and give a reason for your answer

the number 0.5 is ______ because ___________

A: it is a decimal that terminates
B: it is a decimal that repeats
C: it is a decimal that does not repeat or terminate
D: it is the square root of a perfect square
E: it is the square root of a non-perfect square

The number \(0.5\) is rational because it can be expressed as a fraction and it is a decimal that terminates.

Complete statement:

The number \(0.5\) is rational because A: it is a decimal that terminates.

This means that \(0.5\) can be represented as \(\frac{5}{10}\), which simplifies to \(\frac{1}{2}\), confirming that it is indeed a rational number.

Determine if 0.71875 is rational or irrational and give a reason for your answer

the number 0.71875 is ______ because ___________

A: it is a decimal that terminates
B: it is a decimal that repeats
C: it is a decimal that does not repeat or terminate
D: it is the square root of a perfect square
E: it is the square root of a non-perfect square

The number \(0.71875\) is rational because it can be expressed as a fraction and it is a decimal that terminates.

Complete statement:

The number \(0.71875\) is rational because A: it is a decimal that terminates.

This means that \(0.71875\) can be represented as \(\frac{71875}{100000}\), which simplifies to \(\frac{115}}{160}\) or similar fractions, confirming that it is indeed a rational number.

Determine if square root of 49 is rational or irrational and give a reason for your answer

the number square root of 49 is ______ because ___________

A: it is a decimal that terminates
B: it is a decimal that repeats
C: it is a decimal that does not repeat or terminate
D: it is the square root of a perfect square
E: it is the square root of a non-perfect square

The number \(\sqrt{49}\) is rational because it is the square root of a perfect square.

Complete statement:

The number \(\sqrt{49}\) is rational because D: it is the square root of a perfect square.

This is because \(\sqrt{49} = 7\), which is an integer and can be expressed as the ratio \(\frac{7}{1}\).

Determine if 0.1875 is rational or irrational and give a reason for your answer

the number 0.1875 is ______ because ___________

A: it is a decimal that terminates
B: it is a decimal that repeats
C: it is a decimal that does not repeat or terminate
D: it is the square root of a perfect square
E: it is the square root of a non-perfect square

The number \(0.1875\) is rational because it can be expressed as a fraction and it is a decimal that terminates.

Complete statement:

The number \(0.1875\) is rational because A: it is a decimal that terminates.

This means that \(0.1875\) can be represented as \(\frac{1875}{10000}\), which simplifies to \(\frac{3}{16}\), confirming that it is indeed a rational number.

Determine if square root of 16 is rational or irrational and give a reason for your answer

the number square root of 16 is______ because ___________

A: it is a decimal that terminates
B: it is a decimal that repeats
C: it is a decimal that does not repeat or terminate
D: it is the square root of a perfect square
E: it is the square root of a non-perfect square

The number \(\sqrt{16}\) is rational because it is the square root of a perfect square.

Complete statement:

The number \(\sqrt{16}\) is rational because D: it is the square root of a perfect square.

This is because \(\sqrt{16} = 4\), which is an integer and can be expressed as the ratio \(\frac{4}{1}\).

Determine if square root of 49 is rational or irrational and give a reason for your answer

the number square root of 49 is______ because ___________

A: it is a decimal that terminates
B: it is a decimal that repeats
C: it is a decimal that does not repeat or terminate
D: it is the square root of a perfect square
E: it is the square root of a non-perfect square

The number \(\sqrt{49}\) is rational because it is the square root of a perfect square.

Complete statement:

The number \(\sqrt{49}\) is rational because D: it is the square root of a perfect square.

This is because \(\sqrt{49} = 7\), which is an integer and can be expressed as the ratio \(\frac{7}{1}\).

Determine if square root of 53 is rational or irrational and give a reason for your answer

the number square root of 53 is______ because ___________

A: it is a decimal that terminates
B: it is a decimal that repeats
C: it is a decimal that does not repeat or terminate
D: it is the square root of a perfect square
E: it is the square root of a non-perfect square

The number \(\sqrt{53}\) is irrational because it is the square root of a non-perfect square.

Complete statement:

The number \(\sqrt{53}\) is irrational because E: it is the square root of a non-perfect square.

This is because \(53\) is not a perfect square (the integers closest to the square roots are \(7^2 = 49\) and \(8^2 = 64\)), and thus \(\sqrt{53}\) cannot be expressed as a fraction of two integers. Its decimal representation will be non-terminating and non-repeating.

Determine if square root of 43 is rational or irrational and give a reason for your answer

the number square root of 43 is______ because ___________

A: it is a decimal that terminates
B: it is a decimal that repeats
C: it is a decimal that does not repeat or terminate
D: it is the square root of a perfect square
E: it is the square root of a non-perfect square

The number \(\sqrt{43}\) is irrational because it is the square root of a non-perfect square.

Complete statement:

The number \(\sqrt{43}\) is irrational because E: it is the square root of a non-perfect square.

This is because \(43\) is not a perfect square (the integers closest to the square roots are \(6^2 = 36\) and \(7^2 = 49\)). Thus, \(\sqrt{43}\) cannot be expressed as a fraction of two integers, and its decimal representation will be non-terminating and non-repeating.