How to find the fractional equivalent of a decimal

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SSAT Upper Level Quantitative › How to find the fractional equivalent of a decimal

Questions 1 - 10

1

Convert into a fraction in simplest form.

$\frac{19}{50}$

$\frac{19}{25}$

$\frac{38}{50}$

$\frac{5}{19}$

Explanation

Think of the decimal as the fraction $\frac{0.38}{1}$ .

Now, multiply the numerator and denominator by for every digit after the decimal. In this case, because there are digits after the decimal, we will be multiplying by twice, or by .

$\frac{0.38}{1}\times 100=\frac{38}{100}$

Now, simplify this fraction.

$\frac{38}{100}=\frac{19}{50}$

2

Convert into a fraction.

$\frac{9}{25}$

$\frac{18}{25}$

$\frac{36}{7}$

$\frac{25}{9}$

Explanation

Write the decimal divided by .

$0.36=\frac{0.36}{1}$

Multiply the numerator and denominator by to get rid of the decimal, then simplify.

$\frac{0.36\times100}{1\times100}=\frac{36}{100}=\frac{9}{25}$

3

Convert to a fraction.

$\frac{14}{25}$

$\frac{25}{14}$

$\frac{7}{50}$

$\frac{7}{100}$

Explanation

Write the decimal divided by .

$0.56=\frac{0.56}{1}$

Multiply the numerator and denominator by to get rid of the decimal, then simplify.

$\frac{0.56\times100}{1\times100}=\frac{56}{100}=\frac{14}{25}$

4

Convert into a fraction.

$\frac{7}{8}$

$\frac{8}{9}$

$\frac{3}{4}$

$\frac{4}{5}$

Explanation

Write the decimal divided by .

$0.875=\frac{0.875}{1}$

Multiply the numerator and denominator by to get rid of the decimal, then simplify.

$\frac{0.875\times1000}{1\times1000}=\frac{875}{1000}=\frac{7}{8}$

5

What is the fractional equivalent of

$\frac{1}{4}$

$\frac{25}{101}$

$\frac{1}{3}$

$\frac{1}{5}$

Explanation

To find the fractional equivalent, we convert the number given into a whole number and divide by the corresponding tenth power needed to move the decimal into a whole number.

So for

we need to multiply by to turn the decimal into the whole number

We divide by to get our fraction

$\frac{25}{100}$

this can be reduced to

$\frac{1}{4}$

6

Convert into a fraction.

$\frac{163}{250}$

$\frac{81}{125}$

$\frac{13}{100}$

$\frac{7}{25}$

Explanation

Write the decimal divided by .

$0.652=\frac{0.652}{1}$

Multiply the numerator and denominator by to get rid of the decimal, then simplify.

$\frac{0.652\times1000}{1\times1000}=\frac{652}{1000}=\frac{163}{250}$

7

Express as a fraction.

$\frac{247}{250}$

$\frac{49}{50}$

$\frac{47}{50}$

$\frac{250}{257}$

Explanation

Write the decimal divided by .

$0.988=\frac{0.988}{1}$

Multiply the numerator and denominator by to get rid of the decimal, then simplify.

$\frac{0.988\times1000}{1\times1000}=\frac{988}{1000}=\frac{247}{250}$

8

Find the fractional equivalent of .

$\frac{15}{16}$

$\frac{13}{16}$

$\frac{9}{16}$

$\frac{12}{13}$

Explanation

Write the decimal divided by .

$0.9375=\frac{0.9375}{1}$

Multiply the numerator and denominator by to get rid of the decimal, then simplify.

$\frac{0.9375\times10000}{1\times10000}=\frac{9375}{10000}=\frac{15}{16}$

9

Find the fractional equivalent of .

$\frac{49}{400}$

$\frac{49}{100}$

$\frac{49}{500}$

$\frac{49}{250}$

Explanation

Write the decimal divided by .

$0.1225=\frac{0.1225}{1}$

Multiply the numerator and denominator by to get rid of the decimal, then simplify.

$\frac{0.1225\times10000}{1\times10000}=\frac{1225}{10000}=\frac{49}{400}$

10

Find the fractional equivalent of .

$\frac{1}{20}$

$\frac{1}{50}$

$\frac{1}{30}$

$\frac{1}{10}$

Explanation

Write the decimal divided by .

$0.05=\frac{0.05}{1}$

Multiply the numerator and denominator by to get rid of the decimal, then simplify.

$\frac{0.05\times100}{1\times100}=\frac{5}{100}=\frac{1}{20}$

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