1. Chapter 5
Decimals

2. Introduction to Decimals
5.1
Introduction to Decimals

3. Chapter 1 / Whole Numbers and Introduction to Algebra
Decimal Notation
Chapter 1 / Whole Numbers and Introduction to Algebra
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. The decimal has three parts.
16.743
Whole number part
Decimal part
Decimal point

4. Place Value
The position of each digit in a number determines its place value.
hundred-thousandths
hundreds
tens
tenths
hundredths
thousandths
ten-thousandths
ones 1 10 1
1000 1
100,000
Place Value
100 10 1 1
100 1
10,000
decimal point

5. Place Value 1 Notice that the value of each place is 10
of the value of the place to its left.

6. Place Value 16.734 The digit 3 is in the hundredths place, so
its value is 3 hundredths or 3
100

7. Writing a Decimal in Words
Chapter 1 / Whole Numbers and Introduction to Algebra
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.

8. Writing a Decimal in Words
Write the decimal in words.
whole number part
decimal part
one hundred forty-three
and
fifty-six thousandths

9. 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

10. Helpful Hint
When writing a decimal from words to decimal notation, make sure the last digit is in the correct place by inserting 0s after the decimal point if necessary.
For example,
three and fifty-four thousandths is 3.054
thousandths place

11. Chapter 1 / Whole Numbers and Introduction to Algebra
Writing Decimals as Fractions
Once you master writing and reading decimals correctly, then you write a decimal as a fraction using the fractions associated with the words you use when you read it.
0.9
is read “nine tenths” and written as a fraction as

12. Writing Decimals as Fractions
0.21 is read as
twenty-one hundredths
and written as a fraction as 21
100
0.011 is read as
eleven thousandths
and written as a fraction as 11
1000

13. 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.

14. Comparing Decimals
One way to compare decimals is to compare their graphs on a number line. Recall that for any two numbers on a number line, the number to the left is smaller and the number to the right is larger. To compare 0.3 and 0.7 look at their graphs.
0.3
0.7 1
0.3 < 0.7 or > 0.3 3 10 7 10

15. Comparing Two Positive Decimals
Chapter 1 / Whole Numbers and Introduction to Algebra
Comparing Two Positive Decimals
Comparing decimals by comparing their graphs on a number line can be time consuming, so we compare the size of decimals by comparing digits in corresponding places.

16. 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.
35.638
35.657
< 5 3
35.638
<
35.657

17. 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

18. 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

19. 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.

20. Rounding Decimals to a Place Value
Round 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 tenths is 326.4