Download The Distributive Property - Mr. Beals Quest

Convert between Fractions and
Decimals
Lesson Objectives:
• Students will be able to convert a decimal
number to a fraction in simplest form
• Students will be able to convert a fraction to a
decimal number
Example 1: Convert .5 to a fraction
in simplest form
• From our understanding of decimal
numbers, we know that .5 is read as five
tenths.
• From out understanding of fractions, we
know we can rewrite this number as:
• We can then simplify this number by
factoring a five out of both the numerator
and the denominator, and the result is:
Example #2: Write 1.35 as a mixed
number in simplest form.
• The word form of 1.35 is one and thirty-five
hundredths. Or as a mixed number:
• We can then simplify the fraction part of the
mixed number since there is a factor of 5 in both
the numerator and the denominator.
▫ 35/5 = 7
▫ 100/5 = 20
Example #3: Write 4.375 as a
fraction in simplest form.
Practice: Change to a fraction in
simplest form
.9 9/10
1.4
1 2/5
.8 4/5
3.6
3 3/5
.27 27/100
6.28
6 7/25
.75 3/4
2.65
2 13/20
.34 17/50
12.05
12 1/20
.125 1/8
4.04
4 1/25
.035 7/200
7.202
7 101/500
.008 1/125
Converting Fractions to Decimals
• Example 1: Convert 3/5 to a decimal
• Since 5 can be changed to 10 by multiplying by 2,
then I can easily change this fraction by multiplying
both the numerator and denominator by 2.
• 3/5 = 6/10 = .6
• Or, I can simply look at 3/5 as a division problem,
and divide 3 by 5.
• Try it!
Practice: Change to a Decimal
3/8
3/10
1/4
5/8
6/20
2 3/4
9/25
.375
.3
.25
.625
.3
2.75
.36
1 3/8
1 7/8
3 5/16
4 9/20
9 29/40
7 29/80
4 11/32
1.375
1.875
3.3125
4.45
9.725
7.3625
4.34375
Challenge: Change a repeating decimal
to a fraction
• Repeating decimals are rational numbers,
meaning, they can be written as fractions.
• Example: Change .777777777777… to a fraction
• Let x = .7777777777…
• When we multiply by 10, all we need to do is
move our decimal place one space to the right.
• 10x = 7.7777777…
• - x = .7777777…
• 9x = 7
• Solving for x = 7/9
• So, .77777777… = 7/9
Change .2323232323… to a fraction
•
•
•
•
•
Let x = .2323232323…
100x = 23.2323232323…
- x = .2323232323…
99x = 23
Solving for x = 23/99
Change .36363636363636… to a fraction
•
•
•
•
Let x = .363636363636…
100x = 36.36363636…
99x = 36
x = 36/99 = 4/11