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

Study concepts, example questions & explanations for SAT Math

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Example Questions

Example Question #1 : Decimals

Write 0.45 as a fraction.

Possible Answers:

\displaystyle \frac{3}{4}

\displaystyle \frac{11}{20}

\displaystyle \frac{5}{9}

\displaystyle \frac{9}{20}

\displaystyle \frac{2}{5}

Correct answer:

\displaystyle \frac{9}{20}

Explanation:

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

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

\displaystyle \frac{9}{20}

Example Question #3 : Decimals With Fractions

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

Possible Answers:

\displaystyle \frac{17}{4}

\displaystyle \frac{83}{4}

\displaystyle \frac{91}{8}

\displaystyle \frac{69}{4}

\displaystyle \frac{18}{4}

Correct answer:

\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:

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

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

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

This is your answer.

Example Question #2 : Decimals With Fractions

What is the fractional equivalent of \displaystyle 0.33?

Possible Answers:

\displaystyle \frac{3}{10}

\displaystyle \frac{333}{1000}

\displaystyle \frac{33}{100}

\displaystyle \frac{1}{3}

Correct answer:

\displaystyle \frac{33}{100}

Explanation:

In decimal form \displaystyle 0.33 is said 33 hundredths.

This is equal to

\displaystyle \frac{33}{100}.

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

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. 

\displaystyle 0.825

Possible Answers:

\displaystyle \frac{165}{200}

\displaystyle \frac{13}{25}

\displaystyle \frac{21}{55}

\displaystyle \frac{825}{1000}

\displaystyle \frac{33}{40}

Correct answer:

\displaystyle \frac{33}{40}

Explanation:

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

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

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