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Write 6,739 in expanded form.

Responses

(6×1,000)+(7×100)+(3×10)+(0×1)
left parenthesis 6 times 1,000 right parenthesis plus left parenthesis 7 times 100 right parenthesis plus left parenthesis 3 times 10 right parenthesis plus left parenthesis 0 times 1 right parenthesis

(7×100)+(3×10)+(9×1)
left parenthesis 7 times 100 right parenthesis plus left parenthesis 3 times 10 right parenthesis plus left parenthesis 9 times 1 right parenthesis

(9×1,000)+(3×100)+(7×10)+(6×1)
left parenthesis 9 times 1,000 right parenthesis plus left parenthesis 3 times 100 right parenthesis plus left parenthesis 7 times 10 right parenthesis plus left parenthesis 6 times 1 right parenthesis

(6×1,000)+(7×100)+(3×10)+(9×1)

11 answers

The correct expanded form for the number 6,739 is:

(6×1,000) + (7×100) + (3×10) + (9×1)

So the proper answer is: (6×1,000) + (7×100) + (3×10) + (9×1)

If you need any further explanations or have more questions, feel free to ask!

Express 8/11
as a repeating decimal. Mark the cycle of repeating digits with a bar.

To express \( \frac{8}{11} \) as a repeating decimal, divide 8 by 11.

When you perform the division, you get:

  • \( 8 \div 11 = 0.727272... \)

The digits "72" repeat indefinitely. To indicate the repeating part, you can use a bar over the digits that repeat.

Thus, the repeating decimal for \( \frac{8}{11} \) is:

\[ 0.\overline{72} \]

This notation means that "72" continues indefinitely.

Express 8/11
as a repeating decimal.

To convert \( \frac{8}{11} \) into a decimal, we can perform the division:

  1. Divide 8 by 11:
    • 11 goes into 8 zero times, so we start with 0.
    • Add a decimal point and a zero: \( 8.0 \).
    • 11 goes into 80 seven times (since \( 11 \times 7 = 77 \)).
    • Subtract \( 77 \) from \( 80 \), which leaves \( 3 \).
    • Bring down another zero, making it \( 30 \).
    • 11 goes into 30 two times (since \( 11 \times 2 = 22 \)).
    • Subtract \( 22 \) from \( 30 \), which leaves \( 8 \) again.
    • This cycle continues.

The decimal representation of \( \frac{8}{11} \) therefore is \( 0.727272... \), where "72" repeats indefinitely.

So, \( \frac{8}{11} \) expressed as a repeating decimal is:

\[ 0.\overline{72} \]

Convert 0.72¯¯¯¯¯
to a rational number in simplest form.

To convert the repeating decimal \( 0.72\overline{72} \) into a rational number, we can follow these steps:

  1. Let \( x \) be the repeating decimal: \[ x = 0.727272\ldots \]

  2. Multiply \( x \) by 100 (because the repeating part has 2 digits): \[ 100x = 72.727272\ldots \]

  3. Now we have two equations: \[ x = 0.727272\ldots \] \[ 100x = 72.727272\ldots \]

  4. Subtract the first equation from the second: \[ 100x - x = 72.727272\ldots - 0.727272\ldots \] \[ 99x = 72 \]

  5. Solve for \( x \): \[ x = \frac{72}{99} \]

  6. Now, simplify \( \frac{72}{99} \):

    • The greatest common divisor (GCD) of 72 and 99 is 9. \[ \frac{72 \div 9}{99 \div 9} = \frac{8}{11} \]

Thus, the rational number in simplest form that corresponds to the repeating decimal \( 0.72\overline{72} \) is:

\[ \frac{8}{11} \]

Which of the following is a rational number between 5 and 5 1/4
?

To find a rational number between \( 5 \) and \( 5 \frac{1}{4} \), we can first convert \( 5 \frac{1}{4} \) into an improper fraction or decimal.

  1. Convert \( 5 \frac{1}{4} \) to an improper fraction: \[ 5 \frac{1}{4} = \frac{5 \times 4 + 1}{4} = \frac{20 + 1}{4} = \frac{21}{4} \]

  2. Convert the whole number 5 to a fraction: \[ 5 = \frac{5 \times 4}{4} = \frac{20}{4} \]

Now we are looking for a rational number between \( \frac{20}{4} \) and \( \frac{21}{4} \).

  1. Choose a rational number between \( \frac{20}{4} \) and \( \frac{21}{4} \):
    • A simple choice would be the average of these two fractions: \[ \text{Average} = \frac{\frac{20}{4} + \frac{21}{4}}{2} = \frac{41}{8} \]
    • Converting \( \frac{41}{8} \) to a decimal gives: \[ \frac{41}{8} = 5.125 \]

Therefore, a rational number between \( 5 \) and \( 5 \frac{1}{4} \) is:

\[ \frac{41}{8} \quad \text{or} \quad 5.125 \]

You can select any rational number in this range, such as \( 5.1 \), \( 5.2 \), \( 5.15 \), etc. All of these are valid choices.

sorry here's the options you have
5 1/3

26−−√

5 2/5

5 1/7

Given the options you provided, let's convert each option to a decimal or compare them to find out which rational number is between \(5\) and \(5 \frac{1}{4}\) (which is equal to \(5.25\)).

  1. \(5 \frac{1}{3}\):
    Convert to an improper fraction: \[ 5 \frac{1}{3} = \frac{5 \times 3 + 1}{3} = \frac{15 + 1}{3} = \frac{16}{3} \approx 5.3333 \]

  2. \( \sqrt{26} \):
    Calculate the square root: \[ \sqrt{26} \approx 5.099 \] (This is less than \(5.25\).)

  3. \(5 \frac{2}{5}\):
    Convert to an improper fraction: \[ 5 \frac{2}{5} = \frac{5 \times 5 + 2}{5} = \frac{25 + 2}{5} = \frac{27}{5} = 5.4 \]

  4. \(5 \frac{1}{7}\):
    Convert to an improper fraction: \[ 5 \frac{1}{7} = \frac{5 \times 7 + 1}{7} = \frac{35 + 1}{7} = \frac{36}{7} \approx 5.1428 \]

Conclusion:

Now, let’s summarize the decimal approximations:

  • \(5 \frac{1}{3} \approx 5.3333\)
  • \( \sqrt{26} \approx 5.099\)
  • \(5 \frac{2}{5} = 5.4\)
  • \(5 \frac{1}{7} \approx 5.1428\)

The rational numbers between \(5\) and \(5 \frac{1}{4} (5.25)\) are:

  • \(5 \frac{1}{3} \approx 5.3333\) (too high)
  • \( \sqrt{26} \approx 5.099\) (valid)
  • \(5 \frac{2}{5} = 5.4\) (too high)
  • \(5 \frac{1}{7} \approx 5.1428\) (valid)

Thus, the two valid options between \(5\) and \(5 \frac{1}{4}\) are:

  • \( \sqrt{26} \)
  • \( 5 \frac{1}{7} \)

Either \( \sqrt{26} \) or \( 5 \frac{1}{7} \) can be selected as a rational number between \(5\) and \(5 \frac{1}{4}\).