GRE Arithmetic - Decimals

Decimal is the term most-often used to indicate that a number is not a whole number. For example, in the decimal number 3.12, the decimal component is ".12", while the whole number component is "3". Keep in mind, however, that all numbers can be written as decimals, but for convenience, the decimal part is dropped if a number is a whole number. The number 3 is actually 3.0, and can also be written as 3.0, 3.00, 3.000000, etc.

If you want to add or subtract decimals, line up the decimal points that you want to add or subtract and then simply perform the required operation. You may need to write in zeros in the places where such a 0 is implied and not really written. For example, 2.01+3.140=5.150 or 5.15.

2 . 010
+ 3 . 140

5 . 150

You probably won't be given a question on the GRE that simply asks you to add or subtract two decimal numbers that have the same number of whole digits as well as the same number of decimal digits, like the example above. That's a bit too simple. But, you might see a question on the GRE where you are presented with several decimal numbers, each with different decimal values and lengths. For example, the following sample GRE question, albeit it still measures your ability to grapple with the addition and subtraction of decimals, is a bit more difficult than the above example, only for the reason that the numbers are not so neatly presented, nor do they have the same number of decimal digits:


What is the sum of 1,324, 3.765, -4.986 and 68.


Not as straight-forward as the first example, is it? And, did you notice that one of the numbers is a large number, where a comma is used to designate that the number is larger than one thousand? Having said all this, don't expect the math questions on the GRE to simply ask you to compute a sum or addition. However, you'll want to be familiar with the concept of decimal addition and subtraction for the reason that you'll often have to employ these concepts "en route" to answering some of the harder GRE math questions.

To multiply decimals, multiply the two numbers as usual and then write the decimal point in the answer based on the total number of decimal places in the original decimal numbers. For example, if you want to multiply 2.3 and 4.2, first do the multiplication of 23 times 42, which gives you 966, and the total number of decimal places is two, one from 2.3 and one from 4.2, so add two decimal places to the answer to get 9.66.

To divide two decimals, set up a division problem as usual, count the number of decimal places in the divisor, and remove the decimal point in the divisor. Move the decimal point of both numbers to the right the number of decimal places that there were in the divisor. Perform the division as usual and give the answer the same number of decimal points as are in the dividend.

For example, consider the following:


7.701 ÷ 2.55


The divisor (2.55) has two decimal places. Move the decimal point of both numbers two places to the right:


7.701 ÷ 2.55
770.1 ÷ 255
3.02