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PSAT Math : Decimals

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Example Questions

Example Question #11 : Fractions

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

Possible Answers:

$\frac{2}{250}$ $\displaystyle \frac{2}{250}$

$\frac{2}{25}$ $\displaystyle \frac{2}{25}$

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

$\frac{1}{250}$ $\displaystyle \frac{1}{250}$

$\frac{1}{25}$ $\displaystyle \frac{1}{25}$

Correct answer:

$\frac{1}{250}$ $\displaystyle \frac{1}{250}$

Explanation:

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

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

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Example Question #12 : Fractions

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

Possible Answers:

$10\%$ $\displaystyle 10\%$

$1\%$ $\displaystyle 1\%$

$2\%$ $\displaystyle 2\%$

$5\%$ $\displaystyle 5\%$

$7.5\%$ $\displaystyle 7.5\%$

Correct answer:

$5\%$ $\displaystyle 5\%$

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 #2041 : Psat Mathematics

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

Possible Answers:

1.6 $\displaystyle 1.6$

0.5625 $\displaystyle 0.5625$

$0.5\overline{6}$ $\displaystyle 0.5\overline{6}$

$1.\overline{7}$ $\displaystyle 1.\overline{7}$

$1.6\overline{7}$ $\displaystyle 1.6\overline{7}$

Correct answer:

$1.\overline{7}$ $\displaystyle 1.\overline{7}$

Explanation:

Divide 16 by 9:

Division

The "7" repeats forever, so

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

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Example Question #1 : Decimals

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

Possible Answers:

$0.\overline{5}$ $\displaystyle 0.\overline{5}$

$0.5\overline{6}$ $\displaystyle 0.5\overline{6}$

0.5625 $\displaystyle 0.5625$

$1.\overline{7}$ $\displaystyle 1.\overline{7}$

1.6 $\displaystyle 1.6$

Correct answer:

0.5625 $\displaystyle 0.5625$

Explanation:

Divide 9 by 16:

Division

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

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Example Question #2043 : Psat Mathematics

Convert the fraction to a decimal.

$\frac{13}{25}$ $\displaystyle \frac{13}{25}$

Possible Answers:

0.78 $\displaystyle 0.78$

0.26 $\displaystyle 0.26$

0.42 $\displaystyle 0.42$

0.53 $\displaystyle 0.53$

0.52 $\displaystyle 0.52$

Correct answer:

0.52 $\displaystyle 0.52$

Explanation:

We can multiply our numerator and denominator by $\displaystyle 4$ , which leads to $\frac{52}{100}$ $\displaystyle \frac{52}{100}$ . From here we divide by our denominator, moving the decimal two places to the left.

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Example Question #15 : Fractions

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

Possible Answers:

0.01

0.07

0.10

0.05

0.04

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 #1 : How To Find The Fractional Equivalent Of A Decimal

Write 0.45 as a fraction.

Possible Answers:

$\frac{5}{9}$ $\displaystyle \frac{5}{9}$

$\frac{3}{4}$ $\displaystyle \frac{3}{4}$

$\frac{11}{20}$ $\displaystyle \frac{11}{20}$

$\frac{9}{20}$ $\displaystyle \frac{9}{20}$

$\frac{2}{5}$ $\displaystyle \frac{2}{5}$

Correct answer:

$\frac{9}{20}$ $\displaystyle \frac{9}{20}$

Explanation:

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

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

$\frac{9}{20}$ $\displaystyle \frac{9}{20}$

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Example Question #2 : Decimals

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

Possible Answers:

$\frac{34}{101}$ $\displaystyle \frac{34}{101}$

$\frac{34}{90}$ $\displaystyle \frac{34}{90}$

$\frac{31}{90}$ $\displaystyle \frac{31}{90}$

$\frac{34}{99}$ $\displaystyle \frac{34}{99}$

$\frac{31}{99}$ $\displaystyle \frac{31}{99}$

Correct answer:

$\frac{31}{90}$ $\displaystyle \frac{31}{90}$

Explanation:

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

Then

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

and

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

Subtract:

$\displaystyle 100 x = 34.44...$

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

$\displaystyle 90x = 31$

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

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Example Question #1 : How To Multiply Decimals

45.728 x 3.2 = ?

Possible Answers:

146.3296

14632.96

146329.6

14.63296

1463.296

Correct answer:

146.3296

Explanation:

Multiply the numbers out in long format, then move the decimal point over the total number of decimal points in the two numbers (3 in the first, 1 in the second, so 4 total):

45.728 * 3.2 = 91456

91456 + 1371840 = 1,463,296 → 146.3296

Or just count the decimal points in the answer and make sure it's 4.

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Example Question #1 : Decimal Operations

At the farmer's market, oranges are $0.30 each, apples are $0.25 each, bananas are $0.40 each, and tomatoes are $0.60 each. If Scott buys 3 oranges, 7 apples, 4 bananas, and 8 tomatoes, how much does he spend?

Possible Answers:

$7.75

$11.40

$6.80

$9.05

$10.40

Correct answer:

$9.05

Explanation:

To find out how much Scott spends, we need to multiply the quantity of each fruit by its price and add them all up.

3 * $0.30 + 7 * $0.25 + 4 * $0.40 + 8 * $0.60 = $9.05

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PSAT Math : Decimals

Study concepts, example questions & explanations for PSAT Math

All PSAT Math Resources

Example Questions

Example Question #11 : Fractions

Example Question #12 : Fractions

Example Question #2041 : Psat Mathematics

Example Question #1 : Decimals

Example Question #2043 : Psat Mathematics

Example Question #15 : Fractions

Example Question #1 : How To Find The Fractional Equivalent Of A Decimal

Example Question #2 : Decimals

Example Question #1 : How To Multiply Decimals

Example Question #1 : Decimal Operations

All PSAT Math Resources

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