CHAPTER 2 Operations with Rational Numbers and Introduction to Real Numbers
CHAPTER 2 Operations with Rational Numbers and Introduction to Real Numbers
2.3 Decimals
Learning Objectives
By the end of this section, you will be able to:
- Name and write decimals
- Round decimals
- Add and subtract decimals
- Multiply and divide decimals
- Convert decimals, fractions, and percent
Name and Write Decimals
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.
EXAMPLE 1
Name the decimal 4.3
TRY IT 1.1
Name the decimal: .
Show answer
six and seven tenths
TRY IT 1.2
Name the decimal: .
Show answer
five and eight tenths
We summarize the steps needed to name a decimal below.
HOW TO: Name a Decimal
- Name the number to the left of the decimal point.
- Write “and” for the decimal point.
- Name the “number” part to the right of the decimal point as if it were a whole number.
- Name the decimal place of the last digit.
EXAMPLE 2
Name the decimal: .
| Name the number to the left of the decimal point. | negative fifteen __________________________________ |
| Write “and” for the decimal point. | negative fifteen and ______________________________ |
| Name the number to the right of the decimal point. | negative fifteen and five hundred seventy-one __________ |
| The 1 is in the thousandths place. | negative fifteen and five hundred seventy-one thousandths |
TRY IT 2.1
Name the decimal: .
Show answer
negative thirteen and four hundred sixty-one thousandths
TRY IT 2.2
Name the decimal: .
Show answer
negative two and fifty-three thousandths
When we write a check we write both the numerals and the name of the number. Let’s see how to write the decimal from the name.
EXAMPLE 3
Write “fourteen and twenty-four thousandths” as a decimal.
TRY IT 3.1
Write as a decimal: thirteen and sixty-eight thousandths.
Show answer
13.68
TRY IT 3.2
Write as a decimal: five and ninety-four thousandths.
Show answer
5.94
We summarize the steps to writing a decimal.
HOW TO: Write a Decimal
- Look for the word “and”—it locates the decimal point.
- Place a decimal point under the word “and.” Translate the words before “and” into the whole number and place it to the left of the decimal point.
- If there is no “and,” write a “0” with a decimal point to its right.
- Mark the number of decimal places needed to the right of the decimal point by noting the place value indicated by the last word.
- Translate the words after “and” into the number to the right of the decimal point. Write the number in the spaces—putting the final digit i