Chapter 5 Section 1Writing Fractions as

DecimalsPgs. 200-204

What you will learn:

Write fractions as terminating or repeating decimals

Compare fractions and decimals

Vocabulary:Terminating decimal (200): When dividing a fraction, the division

ends, or terminates, when the remainder is zero.

Mixed number (200): The sum of a whole number and a fractionEx.) 3 1 Mixed numbers can also be written as

2 decimals.

Repeating decimal (201): A decimal that repeats Ex 2 = 23 = .66666666 3

Bar notation (201): a way to show that a decimal repeats _

Ex. 0.66666666 = .6 The digit 6 repeats so the bar goesover the 6

Period (201): is the digit or digits that repeat

Write 3 as a decimal. 8

Method 1: Use paper and pencil 0.3758 3.000 - 24

60 - 56 40 - 40

0 <---- division ends when the remainder is 0

Method 2: Use a calculator

3 8 = .375

.375 is a terminating decimal.

Example 1:

Example 2:

Write 3 1 as a decimal. 2

3 1 = 3 1 Write as a sum of an integer and a fraction 2 2 = 3 + 0.5 1/2 = 0.5 = 3.5 Add

Not all fractions can be written as terminating decimals! 0.666

2 = 3 2.0003 - 1 8 20

- 18 20 - 18

2 <-----the remainder after each step is 2

So, 2 = 0.66666666 A repeating decimal= use bar notation 3

_ .6

Concept Check: __Is 0.75 a terminating or repeating decimal? Explain.

Repeating; the digits 75 repeat

The period of a repeating decimal is the digit or digits that repeat.

Decimal Bar Notation Period

0.13131313… 0.13 13

6.8555555… 6.85 5

19.1724724… 19.1724 724

Example 3:

Write - 6 11 as a decimal

11 6.0000…0.5454…

So, - 6 __11 = - 0.54

Write 2 as a decimal15

_0.13333 = 0.13

2 _15 = 0.13

Compare Fractions and Decimals

Replace with , , or

3 0.75 5

To make this easier, change the 3/5 to a decimal and then compare

3/5 = 0.6

Rewrite the problem:

0.6 0.75

0.6 < 0.75

Compare Fractions to Solve a Problem

In a survey of students, 12 boys and 15 girls own a dog. 20 24

Of those those surveyed, do a greater fraction of boys or girlsown a dog?

Write the fractions as decimals and then compare the decimals.

Boys: 12 = 0.60 20

Girls: 15 = 0.62524

Since 0.60 < 0.625, 12/20 < 15/24

So more girls own dogs!

Your Turn!

Write each fraction or mixed number as a decimal. Use barNotation to show a repeating decimal.

1. 6/10 2. 4/25 3. 5/6 4. - 3/16 5. 8 36/44

0.6 0.16 _0.83 - 0.1875

__8.81

Replace each with <, >, = to make a true sentence..

1. 7/8 5/6 2. 0.04 5/9 3. 3/5 12/20

_4. 2.1 2 1/10 5. 3 7/8 3.78

> < =

> >

Take the sheet by the door and do the evens!