Transcript I can convert between decimals and fractions.

4-4 Decimals and Fractions
Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes
4-4 Decimals and Fractions
Warm Up
Find the GCF of each set of numbers.
1. 15, 24
3
2. 30, 60
30
3. 54, 102
6
4. 12, 16, 24
4
4-4 Decimals and Fractions
Problem of the Day
Write the day of the month as the product of
two factors.
Possible answer: 12th of the month, 6  2
4-4 Decimals and Fractions
I can convert between decimals and
fractions.
4-4 Decimals and Fractions
Vocabulary
mixed number
terminating decimal
repeating decimal
4-4 Decimals and Fractions
A number that contains both a whole
number greater than 0 and a fraction,
3
__
such as 1 4 , is called a mixed number.
1
4
0
0.25
1
2
Mixed numbers
1
1
3
1
1
__
__
1__ 1 __ 1 __
2
2
4
2
4
4
2
3
4
0.5 0.75
1
1.25
1.5
1.75
2
2.25
2.5
4-4 Decimals and Fractions
Additional Example 1A: Writing Decimals as
Fractions or Mixed Numbers
Write each decimal as a fraction or mixed
number.
0.67
0.67 Identify the place value of the digit farthest to the right.
Remember!
Thousandths
Hundredths
Place Value
Tenths
100
The 7 is in the hundredths place,
so use 100 as the denominator.
Ones
67
____
4-4 Decimals and Fractions
Additional Example 1B: Writing Decimals as
Fractions or Mixed Numbers
Write each decimal as a fraction or mixed
number.
5.9
5.9
Identify the place value of the digit farthest to the
right.
9
5 ___ Write the whole number, 5. The 9 is in the tenths
10 place, so use 10 as the denominator.
4-4 Decimals and Fractions
Check It Out: Example 1A
Write each decimal as a fraction or mixed
number.
0.73
0.73 Identify the place value of the digit farthest to the right.
73
____
100
The 3 is in the hundredths place,
so use 100 as the denominator.
4-4 Decimals and Fractions
Check It Out: Example 1B
Write each decimal as a fraction or mixed
number.
4.8
4.8
Identify the place value of the digit farthest to the
right.
8
4 ___ Write the whole number, 4. The 8 is in the tenths
10 place, so use 10 as the denominator.
4-4 Decimals and Fractions
Additional Example 2A: Writing Fractions as
Decimals
Write each fraction or mixed number as a
decimal.
3
____
20
0.15
20 3 .00
- 20
100
- 100
0
Divide 3 by 20.
Add zeros after the decimal point.
The remainder is 0.
3
____
= 0.15
20
4-4 Decimals and Fractions
Writing Math
To write a repeating decimal, you can show
three dots or draw a bar over the repeating
part: 0.666… = 0.6
4-4 Decimals and Fractions
Additional Example 2B: Writing Fractions as
Decimals
Write each fraction or mixed number as a
decimal.
6
1
__
3
0.333
3 1 .000
-9
10
-9
10
-9
1
Divide 1 by 3.
Add zeros after the decimal point.
The 3 repeats in the
quotient.
6
1
__
3
_
= 6.333… = 6.3
4-4 Decimals and Fractions
Check It Out: Example 2A
Write each fraction or mixed number as a
decimal.
5
____
20
0.25
20 5 .00
- 40
100
- 100
0
Divide 5 by 20.
Add zeros after the decimal point.
The remainder is 0.
5
____
= 0.25
20
4-4 Decimals and Fractions
Check It Out: Example 2B
Write each fraction or mixed number as a
decimal.
7
2
__
3
0.666
3 2 .000
- 18
20
- 18
20
- 18
2
Divide 2 by 3.
Add zeros after the decimal point.
The 6 repeats in the
quotient.
7
2
__
3
_
= 7.666… = 7.6
4-4 Decimals and Fractions
A terminating decimal, such as 0.75, has a
finite number of decimal places. A repeating
decimal, such as 0.666…, has a block of one or
more digits that repeat continuously
Common Fractions and Equivalent Decimals
1
__
1
__
1
__
1
__
5
2
__
3
__
4
3
5
2
0.4
0.5
0.2 0.25 0.3
2
__
3
__
5
3
4
__
4
5
0.6
0.6
0.75
0.8
4-4 Decimals and Fractions
Additional Example 3: Comparing and Ordering
Fractions and Decimals
Order the fractions and decimals from least
to greatest.
3
7
__
, 0.8, __
10
4
3
7
First rewrite the fractions as decimals. __ = 0.75 __ = 0.7
10
4
Order the three decimals.
7
__
10
0
3
__
4
0.7 0.75 0.8
The numbers in order from least to greatest are 7 , 3 , and 0.8.
10 4
4-4 Decimals and Fractions
Check It Out: Example 3
Order the fractions and decimals from least
to greatest.
1
1 , 0.35, __
__
4
2
1
1
First rewrite the fractions as decimals. __ = 0.5 __ = 0.25
2
4
Order the three decimals.
1
1
__
__
4
2
0
0.25
0.35
0.5
1
1
The numbers in order from least to greatest are __ , 0.35, and __ .
2
4