Foundations
Decimals
Learning Objectives
By the end of this section, you will be able to:
-
- Round decimals
- Add and subtract decimals
- Multiply and divide decimals
- Convert decimals, fractions, and percents
- Simplify expressions with square roots
- Identify integers, rational numbers, irrational numbers, and real numbers
- Locate fractions and decimals on the number line
A more thorough introduction to the topics covered in this section can be found in the Elementary Algebra chapter, Foundations.
Round Decimals
Decimals are another way of writing fractions whose denominators are powers of ten.
Just as in whole numbers, each digit of a decimal corresponds to the place value based on the powers of ten. (Figure) shows the names of the place values to the left and right of the decimal point.
When we work with decimals, it is often necessary to round the number to the nearest required place value. We summarize the steps for rounding a decimal here.
- Locate the given place value and mark it with an arrow.
- Underline the digit to the right of the place value.
- Is the underlined 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.
Round 18.379 to the nearest ⓐ hundredth ⓑ tenth ⓒ whole number.
Round
ⓐ to the nearest hundredth
| Locate the hundredths place with an arrow. | |
| Underline the digit to the right of the given
place value. |
|
| Because 9 is greater than or equal to 5, add 1 to
the 7. |
|
| Rewrite the number, deleting all digits to the
right of the rounding digit. |
|
| Notice that the deleted digits were NOT
replaced with zeros. |
ⓑ 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. |
ⓒ 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. |
|
Round to the nearest ⓐ hundredth ⓑ tenth ⓒ whole number.
ⓐⓑⓒ 7
Round to the nearest ⓐ thousandth ⓑ hundredth ⓒ tenth.
ⓐⓑ
ⓒ
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.
- Determine the sign of the sum or difference.
- Write the numbers so the decimal points line up vertically.
- Use zeros as placeholders, as needed.
- Add or subtract the numbers as if they were whole numbers. T