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PSAT Math : Decimals with Fractions

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Example Questions

Example Question #1512 : Act Math

How much less is $\frac{1}{16}$ than 0.0665 ?

Possible Answers:

$\frac{2}{250}$

$\frac{1}{25}$

$\frac{1}{250}$

$\frac{1}{16}$ is greater than 0.0665 .

$\frac{2}{25}$

Correct answer:

$\frac{1}{250}$

Explanation:

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

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

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Example Question #1513 : Act Math

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?

Possible Answers:

$10\%$

$5\%$

$1\%$

$2\%$

$7.5\%$

Correct answer:

$5\%$

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%

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Example Question #1 : Decimals With Fractions

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

Possible Answers:

$0.5\overline{6}$

0.5625

$1.6\overline{7}$

1.6

$1.\overline{7}$

Correct answer:

$1.\overline{7}$

Explanation:

Divide 16 by 9:

Division

The "7" repeats forever, so

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

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Example Question #2 : Decimals With Fractions

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

Possible Answers:

$0.5\overline{6}$

1.6

$0.\overline{5}$

$1.\overline{7}$

0.5625

Correct answer:

0.5625

Explanation:

Divide 9 by 16:

Division

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

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Example Question #3 : Decimals With Fractions

Convert the fraction to a decimal.

$\frac{13}{25}$

Possible Answers:

0.42

0.26

0.52

0.53

0.78

Correct answer:

0.52

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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Example Question #1 : Decimals

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

Possible Answers:

0.07

0.04

0.01

0.05

0.10

Correct answer:

0.07

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.

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Example Question #4 : Decimals With Fractions

Write 0.45 as a fraction.

Possible Answers:

$\frac{11}{20}$

$\frac{3}{4}$

$\frac{9}{20}$

$\frac{2}{5}$

$\frac{5}{9}$

Correct answer:

$\frac{9}{20}$

Explanation:

.45 is equivalent to 45 out of 100, or $\frac{45}{100}$ .

Divide both the numerator and denominator by 5 to simplify the fraction:

$\frac{9}{20}$

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Example Question #5 : Decimals

Express as a fraction: $0.3\overline{4}$

Possible Answers:

$\frac{34}{99}$

$\frac{31}{90}$

$\frac{31}{99}$

$\frac{34}{101}$

$\frac{34}{90}$

Correct answer:

$\frac{31}{90}$

Explanation:

Let $x = 0.3\overline{4} = 0.3444...$

Then

$10 x = 10 \times 0.3444... = 3.444...$

and

$100 x = 100 \times 0.3444... = 34.44...$

Subtract:

100 x = 34.44...

$\underline{10 x = \; \; 3.444...}$

90x = 31

$x = \frac{31}{90}$

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PSAT Math : Decimals with Fractions

Study concepts, example questions & explanations for PSAT Math

All PSAT Math Resources

Example Questions

Example Question #1512 : Act Math

Example Question #1513 : Act Math

Example Question #1 : Decimals With Fractions

Example Question #2 : Decimals With Fractions

Example Question #3 : Decimals With Fractions

Example Question #1 : Decimals

Example Question #4 : Decimals With Fractions

Example Question #5 : Decimals

All PSAT Math Resources

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