1. Introduction to Decimals
Section
3.1
Introduction to Decimals

2. Decimal Notation and Writing Decimals in Words
Like fractional notation, decimal notation is used to denote a part of a whole. Numbers written in decimal notation are called decimal numbers, or simply decimals. Place names and place values for the decimal parts are also shown.
Objective A

3. Writing and Reading Decimals in Words
Step 1: Write the whole number part in words. Step 2: Write “and” for the decimal point. Step 3: Write the decimal part in words as though it were a whole number, followed by the place value of the last digit.
Objective A 3

4. Example Write the decimal 143.056 in words. 143.056 whole number part
decimal part
one hundred forty-three
and
fifty-six thousandths

5. Examples Write each decimal in words. 0.06 six hundredths –124. 52
0.0829
six hundredths
negative one hundred twenty-four and fifty- two hundredths
Objective A
eight hundred twenty-nine ten thousandths 5

6. Examples Write the decimals in words. a. 87.31 b. 52.1085
eighty-seven and thirty-one hundredths
fifty-two and one thousand eighty-five ten-thousandths

7. Writing Decimals in Standard Form
A decimal written in words can be written in standard form by reversing the procedure.
Write one hundred six and five hundredths in standard form.
one hundred six and five hundredths
whole-number part
decimal
decimal part
5 must be in the
hundredths place
106 . 05

8. Examples Write each decimal in standard form.
Twelve and six hundredths
12.06
Fifty-four and seventy-two thousandths
54.072
Objective A

9. Writing Decimals as Fractions
In Words
Fraction
0.5
five tenths
0.36
thirty-six hundredths
0.002
two thousandths
0.07
seven hundredths
Objective A 9

10. Examples Write the decimals as a fraction or mixed number. 0.9 21.094
1 decimal place
1 zero
Objective A
3 decimal places
3 zeros 10

11. Examples
Write each decimal as a fraction or a mixed number. Write your answer in simplest form.
0.12
64.8 –
Objective A 11

12. Comparing Two Positive Decimals37
100 . =
029 29
1000 . =
2 decimal places
2 zeros
3 decimal places
3 zeros
Notice that the number of decimal places in a decimal number is the same as the number of zeros in the denominator of the equivalent fraction. We can use this fact to write decimals as fractions.

13. Comparing Two Positive Decimals
Chapter 1 / Whole Numbers and Introduction to Algebra
Comparing Two Positive Decimals
Compare digits in the same places from left to right. When two digits are not equal, the number with the larger digit is the larger decimal. If necessary, insert 0s after the last digit to the right of the decimal point to continue comparing.
Compare hundredths place digits
5 <
so <

14. Chapter 1 / Whole Numbers and Introduction to Algebra
Helpful Hint
For any decimal, writing 0s after the last digit to the right of the decimal point does not change the value of the number.
8.5 = 8.50 = 8.500, and so on
When a whole number is written as a decimal, the decimal point is placed to the right of the ones digit.
15 = = 15.00, and so on

15. Example
Insert <, >, or = to form a true statement Add a zero < < 26.28

16. Example
Insert <, >, or = to form a true statement Add a zero > > 0.026

17. Chapter 1 / Whole Numbers and Introduction to Algebra
Rounding Decimals
We round the decimal part of a decimal number in nearly the same way as we round whole numbers. The only difference is that we drop digits to the right of the rounding place, instead of replacing these digits by 0s. For example,
rounded to the nearest hundredth is
63.78

18. Chapter 1 / Whole Numbers and Introduction to Algebra
Rounding Decimals
Chapter 1 / Whole Numbers and Introduction to Algebra
Step 1: Locate the digit to the right of the given place value. Step 2: If this digit is 5 or greater, add 1 to the digit in the given place value and drop all digits to the right. If this digit is less than 5, drop all digits to the right of the given place.

19. Example Round 326.4386 to the nearest tenth.
Locate the digit to the right of the tenths place.
tenths place
digit to the right
Since the digit to the right is less than 5, drop it and all digits to its right.
rounded to the nearest tenth is 326.4

20. Example Round 0.5942 to the nearest thousandth.
Step 1: Locate the digit to the right of the given place value.
0.5942
2 is to the right of the thousandth place value.
Step 2: Since the digit to the right is less than 5, we delete it and all digits to its right.
Thus rounded to the nearest thousandth is 0.594
Objective A 20

21. Example Round $0.067 to the nearest cent.
Step 1: Locate the digit to the right of the given place value.
$0.067
7 is to the right of the hundredths place value
Step 2: Since the digit to the right is more than 5, we round up.
Thus $0.067 rounds to $0.07.
Objective A 21

22. Example
An aquarium costs $ Round the price to the nearest dollar.
The nearest dollar means the ones place. Locate the digit to the right of the ones place.
$245.69
6 is to the right of the ones place value
Thus $ rounds to $
Objective A 22

23. Example
Water bills in Mexia are always rounded to the nearest dollar. Round a water bill of $24.62 to the nearest dollar. Rounding to the nearest whole dollar means rounding to the ones place is greater than 5 A water bill of $24.62 is rounded to $25.00.