# GRE Math : Decimals

## Example Questions

### Example Question #11 : Decimals

Solve for :

Explanation:

To solve for , subtract  from both sides of the equation.  , therefore, .

If you have trouble subtracting the decimals, you can multiply both of them by  to get whole numbers, then subtract as normal, then divide your result by

### Example Question #12 : Decimals

Explanation:

Make sure to follow the order of operations. Begin by combining all terms inside the parentheses:

Convert the fraction to a decimal and once again complete the operations inside the parentheses:

### Example Question #1 : Decimal Operations

find 0.72

0.0049

0.49

4.9

0.049

49

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

### Example Question #14 : 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?

30 more

50 fewer

20 fewer

30 fewer

15 more

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.

### Example Question #361 : Arithmetic

Given that , which best describes the relationship between , and ?

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 and (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).

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

Finally,  is largest, since dividing a larger number by a smaller one gives a result greater than 1.

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

### Example Question #5 : How To Multiply Decimals

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

Explanation:

Set the equation up as

Solve for , which equals

or

Therefore the percent sales tax is:

### Example Question #16 : Decimals

Solve for :

Explanation:

To solve, first divide both sides of the equation by , leaving you with:

.

If you have trouble dividing the decimals, you can multiply both of the numbers by one followed by a number of zeroes equal to the number of digits beyond the decimal point (one hundred, in this case), then divide, then divide your result by the same number (one hundred again).

### Example Question #17 : Decimals

Solve for  (round to the nearest hundredth if necessary)

Explanation:

To solve, first divide both sides of the equation by :

To do this division, you can divide as normal, or if you are having trouble, you can multiply both numbers by 10 to eliminate the decimal:

### Example Question #18 : Decimals

Solve for :

Explanation:

To solve, first divide both sides of the equation by  so you isolate the variable:

Then, divide the decimal--if you have trouble doing so, remember that you can multiply both numbers by  to eliminate the decimal, and then divide as normal:

Solve for :