GRE Math : Decimals with Fractions

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Example Questions

Example Question #28 : Fractions

Convert 3.567567 ... to a fraction.

Possible Answers:

$\frac{3567}{1000}$

$\frac{1189}{333}$

$\frac{891}{250}$

$\frac{133}{101}$

$\frac{132}{37}$

Correct answer:

$\frac{132}{37}$

Explanation:

Let 3.567567... be . Let's multiply that value by 1000 . The reason is when we subtract it, we will get us an integer instead and the repeating decimals will disappear.

3.567567..=x

3567.567567...=1000x

If we subtract, we get 3564=999x .

Divide both sides by 999 and we get $\frac{3564}{999}$ .

If you divide by on top and bottom, you should get the answer. Otherwise, just divide top and bottom by three times based on the divisibility rules for . If the sum is divisible by , then the number is divisible by .

$\frac{3564}{999}=\frac{27 \cdot 132}{27\cdot 37}=\frac{132}{37}$

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Example Question #21 : Decimals With Fractions

Quantity A: $\frac{0.0002(0.09)(0.4)}{0.000006(0.2)}$

Quantity B:

Possible Answers:

Quantity B is greater.

The two quantities are equal.

Quantity A is greater.

The relationship cannot be determined.

Correct answer:

The two quantities are equal.

Explanation:

To compare these two quantities, we'll want to simplify Quantity A.

The fraction

$\frac{0.0002(0.09)(0.4)}{0.000006(0.2)}$

may be a bit daunting; let's convert it to scientific notation:

$\frac{2\cdot10^{-4}(9\cdot10^{-2})(4\cdot 10^{-1})}{6\cdot10^{-6}(2\cdot10^{-1})}$

Now multiply the non-ten terms, and the ten terms (add the exponents together):

$\frac{72\cdot(10^{-4-2-1})}{12\cdot10^{-6-1}}$

$\frac{72\cdot10^{-7}}{12\cdot10^{-7}}$

Now cancel like factors in the numerator and denominator:

$\frac{6(12)\cdot10^{-7}}{12\cdot10^{-7}}$

The two quantities are equal.

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Example Question #22 : Decimals With Fractions

Simplify the fraction:

$\frac{300(0.00002)(70)}{0.0021(40)}$

Possible Answers:

0.005

0.5

Correct answer:

Explanation:

To begin, it can be useful to convert the values in the fraction

$\frac{300(0.00002)(70)}{0.0021(40)}$

into a modified scientific notationnotation:

$\frac{3\cdot10^2(2\cdot10^{-5})(7\cdot10^1)}{21\cdot10^{-4}(4\cdot10^1)}$

Now multiply the ten terms (adding exponents together) and the non-ten terms:

$\frac{42\cdot 10^{-2}}{84\cdot10^{-3}}$

From here, reduce the terms, subtracting the bottom tens exponent from the top tens exponent:

$\frac{1\cdot 10^{-2-(-3)}}{2}$

$\frac{1\cdot 10^{1}}{2}$

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Example Question #21 : Decimals With Fractions

A clothing store can only purchase socks in crates. Each crate has 200 socks and costs $2091.

Quantity A: The amount of socks that can be bought with $12651.

Quantity B: The amount of socks that can be bought with $14574.

Possible Answers:

The relationship cannot be determined.

Quantity A is greater.

The two quantities are equal.

Quantity B is greater.

Correct answer:

The two quantities are equal.

Explanation:

For this problem, realize that the store cannot buy part of a crate of socks. If they only have enough to pay for part of a crate, they might as well not have any money at all.

For the amount of money listed, figure out how many crates can be purchased:

Quantity A

$\frac{12651}{2091}=6.05$

So six crates can be purchased.

Quantity B:

$\frac{14574}{2091}=6.97$

Not quite enough for seven; only six crates can be purchased.

The two quantities are equal.

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Example Question #4 : Decimals

Write 0.45 as a fraction.

Possible Answers:

$\frac{3}{4}$

$\frac{2}{5}$

$\frac{5}{9}$

$\frac{9}{20}$

$\frac{11}{20}$

Correct answer:

$\frac{9}{20}$

Explanation:

.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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Example Question #32 : Fractions

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

Possible Answers:

$\frac{122}{500}$

$\frac{122}{1000}$

$\frac{61}{250}$

$\frac{61}{500}$

$\frac{61}{1000}$

Correct answer:

$\frac{61}{500}$

Explanation:

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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Example Question #33 : Fractions

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

0.47

Possible Answers:

$\frac{47}{10}$

$\frac{47}{100}$

$\frac{47}{1000}$

$\frac{23}{56}$

$\frac{94}{200}$

Correct answer:

$\frac{47}{100}$

Explanation:

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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Example Question #34 : Fractions

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

0.022

Possible Answers:

$\frac{11}{500}$

$\frac{11}{50}$

$\frac{22}{100}$

$\frac{11}{250}$

$\frac{22}{1000}$

Correct answer:

$\frac{11}{500}$

Explanation:

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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Example Question #35 : Fractions

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

0.97

Possible Answers:

$\frac{34}{50}$

$\frac{97}{10}$

$\frac{34}{10}$

$\frac{97}{100}$

$\frac{9}{10}$

Correct answer:

$\frac{97}{100}$

Explanation:

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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Example Question #23 : Decimals With Fractions

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

0.82

Possible Answers:

$\frac{82}{1000}$

$\frac{41}{50}$

$\frac{820}{1000}$

$\frac{82}{100}$

$\frac{51}{100}$

Correct answer:

$\frac{41}{50}$

Explanation:

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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GRE Math : Decimals with Fractions

Study concepts, example questions & explanations for GRE Math

All GRE Math Resources

Example Questions

Example Question #28 : Fractions

Example Question #21 : Decimals With Fractions

Example Question #22 : Decimals With Fractions

Example Question #21 : Decimals With Fractions

Example Question #4 : Decimals

Example Question #32 : Fractions

Example Question #33 : Fractions

Example Question #34 : Fractions

Example Question #35 : Fractions

Example Question #23 : Decimals With Fractions

All GRE Math Resources

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