### Addition and Subtraction of Decimals

To add or subtract decimals, simply line them up so their decimal points are in the same place, and then add or subtract as usual. Sometimes one of the numbers will have more decimal places than the other. Because adding zeros to the end of a decimal does not change its value, we can just add zeros to the end of the shorter number until the two numbers have the same number of decimal places. For example, to subtract 65.23 from 987.462:

 987 . 462 -65 . 230 922 . 232

 193 . 100 +56 . 999 250 . 099

### Multiplication of Decimals

To multiply two decimals, first count the total number of digits to the right of the decimal place in each number, and add these two totals together. Then remove the decimal points and multiply the two new whole numbers together. Take this result, and count from the right the total number of places calculated in the first step. Then insert a decimal point to the left of this number.

For example, to multiply 3.4 and 2.01:

• Step 1. There is 1 digit to the right of the decimal point in 3.4, and 2 digits to the right of the decimal point in 2.01. This is a total of 3.
• Step 2. Eliminate the decimal points and multiply 34 by 201. This equals 6834
• Step 3. Count 3 places from the right and insert a decimal point. This yields 6.834.
Thus, 3.4×2.01 = 6.834.

### Division of Decimals

To understand how to divide two numbers when one contains a decimal, we must first remember that adding zeros to the end of a decimal does not change the number. Therefore, we can add as many zeros as we want to either of our decimals. Second, we note that if we move the decimal one place to the right (or to the left) in both numbers, it does not change the answer.

To divide two numbers, then, we first add zeros to the end of either number--these must be added to the right of the decimal point--until both numbers have the same number of digits to the right of the decimal point. For example, to divide 31.8 by 2.65, we add a zero to 31.8 so we are dividing 31.80 by 2.65. Next, we move the decimal point to the right until both numbers are whole numbers; moving the decimal point changes the value of the numbers, but it doesn't change the ratio between the two numbers, which is what division measures. Be very careful to move the decimals the same distance for each number. In this case, we move the decimal point to the right 2 places so we are dividing 3,180 by 265. Finally, we carry out the long division. 3, 180/265 = 12.