Transcript Fraction, Decimal, & Percent Equivalencies

Fraction, Decimal, &
Percent Equivalencies
Coach Lesson 4
Also see textbook pages 108 – 110, & 202 – 205.
Jeff Rhodus
6th Grade
Elsanor Elementary
Getting the Idea!
Fractions, decimals, and percents can all be used
to show parts of a whole.
The word percent means “of 100.”
That is why percents can be written as fractions with
denominators of 100.
The symbol for percent is %.
This chart shows some common fraction-decimal-percent
equivalencies.
Fraction Decimal
1
100
1
10
1
8
1
5
Percent Fraction Decimal Percent
0.01
1%
0.1
10%
1
4
1
2
3
4
0.125 12.5%
0.2
20%
1
1
or
1
0.25
25%
0.5
50%
0.75
75%
1.0
100%
To convert a fraction or mixed number to a decimal, find an equivalent fraction or improper
fraction that has a denominator of 10 or 100, then write the decimal.
Example 1: Convert the fraction 3/5 to a decimal.
Strategy: Find the equivalent fraction with a
denominator of 10.
Step 1: Multiply the numerator and denominator by 2 to
find the equivalent fraction with a denominator of 10.
3
3x5
6
=
=
5
5 x 2 10
Step 2: Write the decimal.
6
= 0.6
10
Solution: The decimal equivalent of 3/5 is 0.6
Example 2: Convert the decimal 1.44 to a mixed number.
Strategy: Write the decimal as an improper with a denominator
of 100, then simplify.
Step 1: Since the decimal goes to the hundredths place,
remove the decimal point and write the digits as the numerator
and 100 as the denominator.
1.44 = 144
100
Step 2: Change the improper fraction to a mixed number. Then
simply the fraction part by dividing the numerator and
denominator by 4.
144
44 44 : 4 11
=1
=
100 100 100 : 4 25
144 11
=1
100 25
11
Solution: The mixed number equivalent of 1.44 is 1 25
Example 3: Write 23/100 as a percent.
Strategy: Look at the denominator of the fraction. It is
100.
Since the denominator of 23/100 is 100, the percent is
the same as the numerator.
Solution: 23/100 = 23%
Example 4: Convert the fraction 9/20 to a percent.
Strategy: Find an equivalent fraction with a denominator of
100, then write the percent.
Step 1: Multiply the numerator and denominator by 5 to find the
equivalent fraction with a denominator of 100.
9 = 9 x 5 = 45
20 20 x 5 100
Step 2: Change the fraction to a percent. Since the
denominator is 100, the percent is the same as the numerator.
45
= 45%
100
Solution: 9/20 = 45%
To convert a percent to a fraction, first convert the percent to a decimal. Then
convert the decimal to a fraction. Remember that percents over 100% will be
written as mixed numbers since they are greater than a whole.
Example 5: Convert 140% to a mixed number.
Strategy: Write the percent as an improper fraction with a
denominator of 100, then simplify.
Step 1: Remove the percent symbol and write the digits as the
numerator and 100 as the denominator.
140
140 = 100
Step 2: Change the improper fraction to a mixed number. Then
simply the fraction part by dividing the numerator and denominator
by 20.
140
=
100
40
1100
40 : 20
2
=
100 : 20 5
140 = 2
1
100
5
Solution: 140% = 1 2
5
To convert a decimal to a percent, move the decimal point two places to the right and insert a
percent symbol(%) after the number. Insert zeros as placeholders when necessary.
Example 6: Convert the decimal 0.7 to a percent.
Strategy: Move the decimal point two places to the right.
Step 1: Think of place value.
0.7 = 0.70
Move the decimal point in 0.70 two places to the right.
0.70.
Step 2: Insert a percent symbol at the end of the number.
70%
Solution: 0.7 = 70%