How to find the decimal equivalent of a fraction

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PSAT Math › How to find the decimal equivalent of a fraction

Questions 1 - 8

The ogre under the bridge eats $\frac{4}{5}$ of a pizza and then throws the rest of the pizza to the rats. The rats eat $\frac{3}{4}$ of what is left. What fraction of the pizza is left when the rats are done?

Explanation

1/5 of the pizza is left after the ogre eats his share. The rats eat 3/4 of that, so 1/4 of 1/5 of the pizza is left.

1/4 * 1/5 = 1/20 = 5%

Which of the following numbers is between 1/5 and 1/6?

0.25

0.22

0.19

0.16

0.13

Explanation

Long division shows that 1/5 = 0.20 and 1/6 = 0.16666... 0.13 < 0.16 < 1/6 < 0.19 < 1/5 < 0.22 < 0.25.

Trevor, James, and Will were each given a candy bar. Trevor ate 7/12 of his and Will ate 20% of his. If James ate more than Will and less than Trevor, what amount could James have eaten?

8/9

2/7

3/5

9/15

1/10

Explanation

Turn Trevor and Will’s amounts into decimals to compare: 20% = 0.20 and 7/12 = 0.5083 rounded. When the answer choices are converted into decimals, 2/7 = 0.2871 is the only value between 0.20 and 0.5083.

$\frac{1}{10}\times \frac{3}{5}\div \frac{6}{7}= {?}}$

0.01

0.04

0.05

0.07

0.10

Explanation

Multiply numerator by the other numerator and multiply the denominator by the other denominator for multiplication. To divide fractions, switch numerator and denominator and treat it as multiplication. The answer is 0.07.

How much less is $\frac{1}{16}$ than ?

$\frac{1}{250}$

$\frac{1}{16}$ is greater than .

$\frac{2}{250}$

$\frac{2}{25}$

$\frac{1}{25}$

Explanation

$\frac{1}{16}=.0625$

$.0665-.0625=.004=\frac{4}{1000}=\frac{1}{250}$

Express as a decimal: $\frac{16}{9}$

$1.\overline{7}$

$1.6\overline{7}$

$0.5\overline{6}$

Explanation

Divide 16 by 9:

Division

The "7" repeats forever, so

$\frac{16}{9} = 1.\overline{7}$

Express as a decimal: $\frac{9}{16}$

$1.\overline{7}$

$0.5\overline{6}$

$0.\overline{5}$

Explanation

Divide 9 by 16:

Division

$\frac{9}{16} = 0.5625$

Convert the fraction to a decimal.

$\frac{13}{25}$

Explanation

We can multiply our numerator and denominator by , which leads to $\frac{52}{100}$ . From here we divide by our denominator, moving the decimal two places to the left.

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