Decimals

As a pharmacy technician you will encounter decimals every day. Medications are frequently prescribed in decimals, and you will find that many dosage calculations will be worked out using the decimal format.

The word "Decimal" means "based on 10" and comes from the Latin word: decima which means "a tenth part". Decimal numbers are used in situations which call for more precision than whole numbers provide. As with whole numbers, a digit in a decimal number has a value which depends on the place of the digit. The places to the left of the decimal point are ones, tens, hundreds, and so on, just as with whole numbers. The following illustration shows the decimal place value for various positions:

It should be noted that adding extra zeros to the right of the last decimal digit does not change the value of the decimal number. With this in mind, trailing zeros should be avoided.

Adding Decimals

To add decimals, line up the decimal points and then follow the rules for adding whole numbers:

When one number has more decimal places than another, you can use 0s to give it the same number of decimal places.

Subtracting Decimals

To subtract decimals, line up the decimal points and then follow the rules for subtracting whole numbers:

If one number has more decimal places than another, you can use 0s to give it the same number of decimal places.

Multiplying Decimal Numbers

Multiplying decimals is just like multiplying whole numbers. The only extra step is to decide how many digits to leave to the right of the decimal point. To do that, add the numbers of digits to the right of the decimal point in both factors.

Example: 6.123 × 5

We can multiply 6123 by 5 to get 30615. There are three decimal places in 6.123, so place the decimal three digits from the right: 6.123 × 5 = 30.615

Example: 5.67 × 6.123

We can multiply 567 by 6123 to get 3471741. Then there are 5 decimal places: two in the number 5.67 and three in the number 6.123, so place the decimal five digits from the right: 5.67 × 6.123 = 34.71741.

Rounding Decimals

To round a number to the nearest tenth (one place to the right of the decimal point), compute the number to the hundredths place (two places after the decimal) . If the number in the hundredths place is "five" or more , add "one" to the number in the tenths place and drop the number in the hundredths place. If the number in the hundredths place is under "five," leave the number in the tenths place as is and drop the number in the hundredths place.

Dividing Whole Numbers, with Decimal Portions

Example: Find 32 ÷ 6 to the nearest whole number.

32 ÷ 6 = 5 r 2. 6 is the divisor; 2 is the remainder. 2 is closer to 0 than 6, so round down. The answer is 5.

Dividing Decimals by Whole Numbers

To divide a decimal by a whole number, use long division, and just remember to line up the decimal points:

Example: 13.44 ÷ 12

When rounding an answer, divide one place further than the place you're rounding to, and round the result. Add 0's to the right of the number being divided, if necessary.

Example: 1.0 ÷ 6 (Round to the nearest thousandth.)

To round 0.16666 to the nearest thousandth, we take 4 places to the right of the decimal point and round to 3 places. Here, we round 0.1666 to 0.167, the answer.

Dividing Decimals by Decimals

To divide by a decimal, multiply that decimal by a power of 10 great enough to obtain a whole number. Multiply the dividend by that same power of 10. Then the problem becomes one involving division by a whole number instead of division by a decimal.

Example: 0.144 ÷ 0.12

Multiplying the divisor (0.12) and the dividend (0.144) by 100, then dividing, gives the same result. The answer is 1.2. Be aware that some problems are less difficult and do not require this procedure.

Example: 6 ÷ 2.00

This is the same as 6 ÷ 2! The answer is 3.