GRE Math : How to multiply decimals

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Example Questions

Example Question #2 : Decimal Operations

find 0.7²

Possible Answers:

0.49

0.049

0.0049

4.9

Correct answer:

0.49

Explanation:

0.7 * 0.7 = 0.49

Trick: do the numbers without the decimals (7*7)

49; move the decimal of the answer the total number of spaces per each number (one for each 0.7)

0.49

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Example Question #1 : How To Multiply Decimals

There are 3,500 people in group A and 5,000 people in group B:

Car Type	% in Group A Who Own	% in Group B Who Own
Motorbike	4	9
Sedan	35	25
Minivan	22	15
Van	9	12
Coupe	3	6

The number of people in group B who own a minivan is how much greater or less than the number of people in group A who own a minivan?

Possible Answers:

15 more

30 more

20 fewer

30 fewer

50 fewer

Correct answer:

20 fewer

Explanation:

In this question, simply take the percentage of each group that owns a minivan and compare the values. For minivans we look at the middle row which we recognize as a percent that must be converted to a decimal. Acknowledge that there's a different number of people between the groups A and B:

Group B: 0.15(5000) = 750

Group A: 0.22(3500) = 770

750 – 770 = –20; thus, group B has 20 fewer people who own minivans than group A.

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Example Question #2 : How To Multiply Decimals

Given that 0< x< y< 1 , which best describes the relationship between , $\frac{y}{x}$ , and (xy)^2 ?

Possible Answers:

$\small (xy)^{2} >\frac{y}{x }>(xy)$

$\small (xy) >\frac{y}{x }>(xy)^{2}$

$\small \frac{y}{x }>(xy)>(xy)^{2}$

$\small (xy)^{2} >(xy)>\frac{y}{x }$

$\small \frac{y}{x }>(xy)^{2}>(xy)$

Correct answer:

$\small \frac{y}{x }>(xy)>(xy)^{2}$

Explanation:

We must recognize that if x and y are both between 0 and 1, then they must be fractions (decimals). To determine their relationships, we can substitute values for x and y. Let's have $x=\frac{1}{4}$ and $y=\frac{1}{2}$ (because y must be greater than x).

If x and y are both between 0 and 1, then xy is also between 0 and 1 (though smaller than either x or y individually).

$xy=\frac{1}{4}*\frac{1}{2}=\frac{1}{8}$

The value of (xy)² will be less than (xy), since squaring any number between 0 and 1 gives a smaller result.

$(xy)^2=(\frac{1}{4}*\frac{1}{2})^2=(\frac{1}{8})^2=\frac{1}{64}$

Finally, $\frac{y}{x}$ is largest, since dividing a larger number by a smaller one gives a result greater than 1.

$\frac{y}{x}=\frac{\frac{1}{2}}{\frac{1}{4}}=\frac{1}{2}*\frac{4}{1}=2$

Note that the substituted values for x and y were purely hypothetical; any values that satisfy the given inequality could be used.

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Example Question #1373 : Act Math

You bought a dozen eggs marked at $\$2.29$ and received $\$2.55$ change from $\$5.00$ . What is the percent of sales tax?

Possible Answers:

$6\%$

$7\%$

$8\%$

$5\%$

Correct answer:

$7\%$

Explanation:

Set the equation up as

(x)($2.29)= $2.45

Solve for , which equals $\frac{2.45}{2.29}$

x=1.0698

Therefore the percent sales tax is:

$(1.0698-1) \times 100=6.98\% \approx 7\%$

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GRE Math : How to multiply decimals

Study concepts, example questions & explanations for GRE Math

All GRE Math Resources

Example Questions

Example Question #2 : Decimal Operations

Example Question #1 : How To Multiply Decimals

Example Question #2 : How To Multiply Decimals

Example Question #1373 : Act Math

All GRE Math Resources

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