# Pharmacy Math  -  Decimals

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

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: To add decimals, line up the decimal points, then follow rules for adding whole numbers. If a number has more decimal places, use 0s to give it the same number of places. Subtracting Decimals:

To subtract, line up the decimal points and follow rules for subtracting whole numbers. If a number has more decimal places, use 0s to give it the same number of 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 1 6.123×     5

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 2 6.123×5.67

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), look to the hundredths place (two places after the decimal).

If the number in the hundredths place is 5 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 5, leave the number in the tenths place as is and drop the number in the hundredths place.

Where would you like to go now?

Prescription Abbreviations