To determine the closest whole number and rational number to the nearest half of 30−−√, let's consider the number line.
On the number line, locate the whole numbers and rational numbers that are nearest to 30−−√.
The whole numbers nearest to 30−−√ are 5 and 6.
The rational numbers nearest to 30−−√ are 5.5 and 6.
Therefore, the whole number nearest to the nearest half of 30−−√ is 5, and the rational number nearest to the nearest half of 30−−√ is 5.5.
Using a number line, what whole number and rational number to the nearest half is 30−−√ between?
7 answers
Using a number line, what whole number and rational number to the nearest half is 30−−√ between?
5.5 and 6
4.5 and 5
6 and 6.5
5 and 5.5
5.5 and 6
4.5 and 5
6 and 6.5
5 and 5.5
To determine the closest whole number and rational number to the nearest half of 30−−√, let's consider the number line.
On the number line, locate the whole numbers and rational numbers that are nearest to 30−−√.
The nearest whole number to 30−−√ is 5.
The nearest rational numbers to 30−−√ are 5.5 and 6.
Therefore, the whole number nearest to the nearest half of 30−−√ is 5, and the rational number nearest to the nearest half of 30−−√ is 5.5.
On the number line, locate the whole numbers and rational numbers that are nearest to 30−−√.
The nearest whole number to 30−−√ is 5.
The nearest rational numbers to 30−−√ are 5.5 and 6.
Therefore, the whole number nearest to the nearest half of 30−−√ is 5, and the rational number nearest to the nearest half of 30−−√ is 5.5.
Convert 0.09¯¯¯¯¯ to a rational number in simplest form.(1 point) Responses 111 1 over 11 19 1 ninth 9100 9 over 100 910
To convert the repeating decimal 0.09¯¯¯¯¯ to a rational number in simplest form, we can use the method of fractions.
Let x = 0.09¯¯¯¯¯
100x = 9.09¯¯¯¯¯ (multiplying both sides by 100 to move the decimal point)
Subtracting the equation x = 0.09¯¯¯¯¯ from 100x = 9.09¯¯¯¯¯ will eliminate the repeating decimal:
100x - x = 9.09¯¯¯¯¯ - 0.09¯¯¯¯¯
99x = 9
Dividing both sides by 99 will yield:
x = 9/99
Simplifying the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 9:
x = (9/9)/(99/9)
x = 1/11
Therefore, the rational number equivalent to the repeating decimal 0.09¯¯¯¯¯ is 1/11.
Let x = 0.09¯¯¯¯¯
100x = 9.09¯¯¯¯¯ (multiplying both sides by 100 to move the decimal point)
Subtracting the equation x = 0.09¯¯¯¯¯ from 100x = 9.09¯¯¯¯¯ will eliminate the repeating decimal:
100x - x = 9.09¯¯¯¯¯ - 0.09¯¯¯¯¯
99x = 9
Dividing both sides by 99 will yield:
x = 9/99
Simplifying the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 9:
x = (9/9)/(99/9)
x = 1/11
Therefore, the rational number equivalent to the repeating decimal 0.09¯¯¯¯¯ is 1/11.
Apply the Properties of Integer Exponents to generate an equivalent expression to (5−3)6⋅ 51710−2 (1 point) Responses 20 20 1500 1 over 500 120 1 over 20 500 500
To generate an equivalent expression to (5−3)6⋅ 51710−2 using the Properties of Integer Exponents, we can simplify each part of the expression:
(5−3)6 = (5-3)6 = 2^6 = 2*2*2*2*2*2 = 64
51710−2 = 5^1 * 7^10 * 10^-2 = 5 * 7^10 * 1/100 = 5 * 282475249 * 1/100 = 1412376245/100
Now, we can multiply these simplified expressions together:
(5−3)6 * 51710−2 = 64 * (1412376245/100) = 90521299840/100 = 905212998.4
Therefore, the equivalent expression is 905212998.4.
(5−3)6 = (5-3)6 = 2^6 = 2*2*2*2*2*2 = 64
51710−2 = 5^1 * 7^10 * 10^-2 = 5 * 7^10 * 1/100 = 5 * 282475249 * 1/100 = 1412376245/100
Now, we can multiply these simplified expressions together:
(5−3)6 * 51710−2 = 64 * (1412376245/100) = 90521299840/100 = 905212998.4
Therefore, the equivalent expression is 905212998.4.
8 answers