How to find the fractional equivalent of a decimal - GRE Quantitative Reasoning

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Question

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

Answer

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

Now, this is the same thing as:

We can rewrite this:

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

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

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

This is your answer.

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Question

What is the fractional equivalent of ?

Answer

In decimal form is said 33 hundredths.

This is equal to

$\frac{33}{100}$ .

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

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Question

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

Answer

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:

$\frac{865}{1000}$

Then, you can simplify, as both and are divisible by :

$\frac{173}{200}$

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Question

Simplify the following expression:

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

Answer

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

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

$\frac{1.5* 10^{-4}(210^{-1})(710^{-3})}{3.510^{-6}(310^{-3})(4*10^{-1})}$

Now remove common divisors from the numerator and denominator:

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

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

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

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Question

Write 0.45 as a fraction.

Answer

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

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

$\frac{9}{20}$

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Question

Choose the answer below which best expresses the following decimal as a fraction (choose the answer which has been reduced/simplified the most):

Answer

To convert from a decimal to a fraction, simply put the digits over followed by a number of zeroes equal to the number of digits:

$.122 = \frac{122}{1000}$

Then, you can reduce:

$\frac{122}{1000}=\frac{2\cdot 61}{2 \cdot 500}=\frac{61}{500}$

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Question

Choose the answer below which best expresses the following decimal as a fraction (choose the answer which has been reduced/simplified the most):

Answer

To convert from a decimal to a fraction, simply put the digits over one followed by a number of zeroes equal to the number of digits:

$0.47=0.47 \cdot \frac{100}{100}=\frac{47}{100}$

is prime, so there's no way to reduce. You're done!

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Question

Choose the answer below which best expresses the following decimal as a fraction (choose the answer which has been reduced/simplified the most):

Answer

To convert from a decimal to a fraction, simply put the digits over one followed by a number of zeroes equal to the number of digits:

$0.022=0.022\cdot \frac{1000}{1000}=\frac{022}{1000}$

The zero in front of the can be removed, leaving: $\frac{22}{1000}$ , which can be reducted to:

$\frac{22}{1000}=\frac{2\cdot 11}{2\cdot 500}=\frac{11}{500}$

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Question

Choose the answer below which best expresses the following decimal as a fraction (choose the answer which has been reduced/simplified the most):

Answer

To convert from a decimal to a fraction, simply put the digits over one followed by a number of zeroes equal to the number of digits:

$0.97=0.97\cdot \frac{100}{100}=\frac{97}{100}$

You cannot reduce, as one of the numbers in the fraction is prime, so that's your final answer.

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Question

Choose the answer below which best expresses the following decimal as a fraction (choose the answer which has been reduced/simplified the most):

Answer

To convert from a decimal to a fraction, simply put the digits over one followed by a number of zeroes equal to the number of digits:

$0.82=0.82\cdot \frac{100}{100}=\frac{82}{100}$

Then, you can reduce for your final answer:

$\frac{82}{100}=\frac{2\cdot 41}{2\cdot 50}=\frac{41}{50}$

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