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SAT Math : How to find the fractional equivalent of a decimal

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Example Questions

Example Question #1 : Decimals

Write 0.45 as a fraction.

Possible Answers:

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

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

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

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

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

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 #3 : Decimals With Fractions

A tub of food contains 0.5 $\displaystyle 0.5$ pounds of vegetables, 1.75 $\displaystyle 1.75$ pounds of lard, and $\displaystyle 15$ pounds of sausage. What is its total weight as an improper fraction?

Possible Answers:

$\frac{17}{4}$ $\displaystyle \frac{17}{4}$

$\frac{83}{4}$ $\displaystyle \frac{83}{4}$

$\frac{91}{8}$ $\displaystyle \frac{91}{8}$

$\frac{69}{4}$ $\displaystyle \frac{69}{4}$

$\frac{18}{4}$ $\displaystyle \frac{18}{4}$

Correct answer:

$\frac{69}{4}$ $\displaystyle \frac{69}{4}$

Explanation:

To begin with, it is easiest just to add these decimals together using your calculator:

$\displaystyle 0.5+1.75+15=17.25$

Now, this is the same thing as:

$\displaystyle 17 + 0.25$

We can rewrite this:

$17 + \frac{1}{4}$ $\displaystyle 17 + \frac{1}{4}$

To find this, you need to give the two numbers a common denominator:

$17 + \frac{1}{4} = \frac{68}{4}+\frac{1}{4}=\frac{69}{4}$ $\displaystyle 17 + \frac{1}{4} = \frac{68}{4}+\frac{1}{4}=\frac{69}{4}$

This is your answer.

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Example Question #2 : Decimals With Fractions

What is the fractional equivalent of 0.33 $\displaystyle 0.33$ ?

Possible Answers:

$\frac{3}{10}$ $\displaystyle \frac{3}{10}$

$\frac{333}{1000}$ $\displaystyle \frac{333}{1000}$

$\frac{33}{100}$ $\displaystyle \frac{33}{100}$

$\frac{1}{3}$ $\displaystyle \frac{1}{3}$

Correct answer:

$\frac{33}{100}$ $\displaystyle \frac{33}{100}$

Explanation:

In decimal form 0.33 $\displaystyle 0.33$ is said 33 hundredths.

This is equal to

$\frac{33}{100}$ $\displaystyle \frac{33}{100}$ .

This fraction cannot be reduced any further therefore it is in its final answer form.

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

Convert the decimal to fraction form and reduce it to its simplest form.

0.825 $\displaystyle 0.825$

Possible Answers:

$\frac{165}{200}$ $\displaystyle \frac{165}{200}$

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

$\frac{21}{55}$ $\displaystyle \frac{21}{55}$

$\frac{825}{1000}$ $\displaystyle \frac{825}{1000}$

$\frac{33}{40}$ $\displaystyle \frac{33}{40}$

Correct answer:

$\frac{33}{40}$ $\displaystyle \frac{33}{40}$

Explanation:

In order to convert 0.825 $\displaystyle 0.825$ to a fraction, you would first begin with $\frac{825}{1000}$ $\displaystyle \frac{825}{1000}$ , because the decimal literally reads 825 $\displaystyle 825$ thousandths. You can reduce by $\displaystyle 5$ a few times or just begin by dividing both numbers by $\displaystyle 25$ to get $\frac{33}{40}$ $\displaystyle \frac{33}{40}$ .

$\frac{825}{1000}=\frac{165}{200}=\frac{33}{40}$ $\displaystyle \frac{825}{1000}=\frac{165}{200}=\frac{33}{40}$

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SAT Math : How to find the fractional equivalent of a decimal

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #1 : Decimals

Example Question #3 : Decimals With Fractions

Example Question #2 : Decimals With Fractions

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

All SAT Math Resources

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