1. Operations with Real Numbers
1.4 Decimals
Learning Objectives
By the end of this section it is expected that you will be able to:
- Round decimals
- Add and subtract decimals
- Multiply and divide decimals
- Convert decimals, fractions, and percent
Decimals are another way of writing fractions whose denominators are powers of 10.
Notice that “ten thousand” is a number larger than one, but “one ten-thousandth” is a number smaller than one. The “th” at the end of the name tells you that the number is smaller than one.
When we name a whole number, the name corresponds to the place value based on the powers of ten. We read 10,000 as “ten thousand” and 10,000,000 as “ten million.” Likewise, the names of the decimal places correspond to their fraction values. Figure 1 shows the names of the place values to the left and right of the decimal point.
Round Decimals
Rounding decimals is very much like rounding whole numbers. We will round decimals with a method based on the one we used to round whole numbers.
EXAMPLE 1
TRY IT 1
Round to the nearest hundredth: .
Show answer
1.05
We summarize the steps for rounding a decimal here.
HOW TO: Round Decimals
- Locate the given place value and mark it with an arrow.
- Underline the digit to the right of the place value.
- Is this digit greater than or equal to 5?
- Yes—add 1 to the digit in the given place value.
- No—do not change the digit in the given place value.
- Rewrite the number, deleting all digits to the right of the rounding digit.
EXAMPLE 2
Round 18.379 to the nearest a) tenth b) whole number.
Round 18.379
a) to the nearest tenth
| Locate the tenths place with an arrow. | |
| Underline the digit to the right of the given place value. | |
| Because 7 is greater than or equal to 5, add 1 to the 3. | |
| Rewrite the number, deleting all digits to the right of the rounding digit. | |
| Notice that the deleted digits were NOT replaced with zeros. | So, 18.379 rounded to the nearest tenth is 18.4. |
b) to the nearest whole number
| Locate the ones place with an arrow. | |
| Underline the digit to the right of the given place value. | |
| Since 3 is not greater than or equal to 5, do not add 1 to the 8. | |
| Rewrite the number, deleting all digits to the right of the rounding digit. | |
| So, 18.379 rounded to the nearest whole number is 18. |
TRY IT 2
Round to the nearest a) hundredth b) tenth c) whole number.
Show answer
a) 6.58 b) 6.6 c) 7
Add and Subtract Decimals
To add or subtract decimals, we line up the decimal points. By lining up the decimal points this way, we can add or subtract the corresponding place values. We then add or subtract the numbers as if they were whole numbers and then place the decimal point in the sum.
HOW TO: Add or Subtract Decimals
- Write the numbers so the decimal points line up vertically.
- Use zeros as place holders, as needed.
- Add or subtract the numbers as if they were whole numbers. Then place the decimal point in the answer under the decimal points in the given n