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

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Example Question #1 : Decimals

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:

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

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

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

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

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

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

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

Possible Answers:

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

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

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

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

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 #52 : Decimals

Choose the answer which best converts the following decimal into a fraction, ensure that you simplify your answer:

0.865 $\displaystyle 0.865$

Possible Answers:

$\frac{173}{200}$ $\displaystyle \frac{173}{200}$

$\frac{865}{1000}$ $\displaystyle \frac{865}{1000}$

$\frac{173}{1000}$ $\displaystyle \frac{173}{1000}$

$\frac{865}{100}$ $\displaystyle \frac{865}{100}$

$\frac{173}{2000}$ $\displaystyle \frac{173}{2000}$

Correct answer:

$\frac{173}{200}$ $\displaystyle \frac{173}{200}$

Explanation:

To convert a decimal into a fraction, simply put the digits of the decimal in the numerator of a fraction, then one followed by a number of zeroes equal to the number of digits in the decimal as your denomator. In this case:

$\frac{865}{1000}$ $\displaystyle \frac{865}{1000}$

Then, you can simplify, as both 865 $\displaystyle 865$ and 1000 $\displaystyle 1000$ are divisible by $\displaystyle 5$:

$\frac{173}{200}$ $\displaystyle \frac{173}{200}$

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Example Question #3 : How To Find The Fractional Equivalent Of A Decimal

Simplify the following expression:

$\frac{.00015(.2)(.007)}{.0000035(0.003)(0.4)}$ $\displaystyle \frac{.00015(.2)(.007)}{.0000035(0.003)(0.4)}$

Possible Answers:

0.0005 $\displaystyle 0.0005$

0.005 $\displaystyle 0.005$

$\displaystyle 5$

0.5 $\displaystyle 0.5$

$\displaystyle 50$

Correct answer:

$\displaystyle 50$

Explanation:

It can help to begin by writing the expression using scientific notation:

$\frac{.00015(.2)(.007)}{.0000035(0.003)(0.4)}$ $\displaystyle \frac{.00015(.2)(.007)}{.0000035(0.003)(0.4)}$

$\frac{1.5* 10^{-4}(2*10^{-1})(7*10^{-3})}{3.5*10^{-6}(3*10^{-3})(4*10^{-1})}$ $\displaystyle \frac{1.5* 10^{-4}(2*10^{-1})(7*10^{-3})}{3.5*10^{-6}(3*10^{-3})(4*10^{-1})}$

Now remove common divisors from the numerator and denominator:

$\frac{1(1)(1)}{10^{-2}(1)(2)}$ $\displaystyle \frac{1(1)(1)}{10^{-2}(1)(2)}$

$\frac{10^2}{2}$ $\displaystyle \frac{10^2}{2}$

$\frac{100}{2}=50$ $\displaystyle \frac{100}{2}=50$

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

Study concepts, example questions & explanations for GRE Math

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Example Questions

Example Question #1 : Decimals

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

Example Question #52 : Decimals

Example Question #3 : How To Find The Fractional Equivalent Of A Decimal

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