Chapter 6: Percents
Section 1
Percents, Fractions, and Decimals
California Standards
 Number Sense 1.0: Students solve problems
involving fractions and percentages.
Language of the Discipline
 Percent: A RATIO that compares a number to 100
 Fraction:
 A part to whole numeric structure. The value on the top is known as the
NUMERATOR and the value on the bottom is known as the DENOMINATOR.
 A mathematical relationship that indicates the quotient of two quantities,
such as 1/5.
 Decimal:
 A numeric value that relies on PLACE VALUE.
 Here, decimals show smaller and smaller parts of the whole.
 Example: 0.25 is called out as Twenty-Five Hundredths.
 Rational Numbers: A number that can be written in the form a/b where b
CANNOT equal ZERO (0).
 EQUIVALENT: EQUAL in value.
 Rounding: Mathematical process where one uses place value to take a
number up or down to the nearest whole.
Writing Decimals as Percents
 Let’s begin the lesson with DECIMALS first.
 DECIMALS are friendly and easy to work with.
 DECIMALS are helpful because you have set PLACE VALUES to help you
convert easily from one form to another.
 As you move from the WHOLE Units and focus on the values behind the
DECIMAL, you have TENTHS, HUNDREDTHS, and THOUSANDTHS.
 Here, you use the DECIMAL form itself to help you convert to PERCENTS.
 Example: 0.45 is called out as FORTY-FIVE HUNDREDTHS.
 Note the word HUNDREDTHS. This tells you that you multiple by 100 to convert
from DECIMAL to PERCENT.
 Let’s convert 0.45. If we multiply the decimal by 100:

(0.45)(100) = 45%
 Quick Trick: You can also do a quick and easy shift of 2 place values to the RIGHT
to make a PERCENT.
Examples of Converting
Decimals to Percents
 Example #1: Write 0.34 as a percent
 Here, the decimal value is called out as “THIRTY-FOUR HUNDREDTHS.”
 Once you hear the word “HUNDREDTHS” that tells you to MULTIPLY by 100 OR shift
the decimal place over 2 place values to the RIGHT.
 (0.34)(100) = 34%
 (Here, we MULTIPLIED by 100 and added the percentage symbol (%))
 0.34 = 34%
 (Here, we shifted 2 place values to the RIGHT and added in the Percentage Symbol (%))
 Example #2: Write 0.07 as a percent
 Here, the value is called out as “SEVEN HUNDREDTHS.”
 Again, you hear the word “HUNDREDTHS” and that tells you to MULTIPLY by 100 OR
shift the decimal place over 2 place values to the RIGHT.
 (0.07)(100) = 7%
 (Here, we multiplied by 100 and added the percentage symbol (%))
 0.07 = 7%
 (Here, we shifted 2 place values and added in the Percentage Symbol (%))
Writing Percents as Decimals
 Let’s look at PERCENTS.
 PERCENTS are fun and easy to work with since PERCENTS are a part of
100.
 Example: 75% is the same as 75 of 100 or 75/100
 To convert from a PERCENT to a DECIMAL, all you have to do is DIVIDE
by 100. Quick and easy.
 Write 78% as a DECIMAL.
 Here, 78% can be thought of as 78/100.
 Note: When the PERCENT is written as a FRACTION or RATIO, you are
being told to DIVIDE by 100.
 78% = 78/100 = 0.78
 Quick Trick: You can also do a quick and easy shift of 2 place values to the
LEFT to make a DECIMAL. Remember that the decimal is found BEHIND the
whole number.
Examples of Converting
Percents to Decimals
 Example #1: Write 45% as a Decimal.
 Here, we have 45%. This means 45% = 45/100
 45 ÷ 100 = 0.45
 (Here, we DIVIDED by 100 and the resulting quotient is in DECIMAL form.)
 45% = 0.45
 (Here, we shifted 2 place values to the LEFT and dropped the Percentage Symbol.)
 Example #2: Write 37.5% as a Decimal.
 Here, we have 37.5%. This means we have 37.5/100
 37.5 ÷ 100 = 0.375
 (Here, we DIVIDED by 100 and the resulting quotient is in DECIMAL form)
 This example is interesting because 37.5% is Thirty-Seven and a Half Percent.
 It is still stacked over the standard percent value of 100.
 37.5% = 0.375
 (Here, we shifted 2 place values to the LEFT and dropped the Percentage Symbol (%))
Writing Fractions as Percents
 FRACTIONS are very straightforward and easy to work with.
 Remember that FRACTIONS are values that represent Part to Whole
relationship.
 To convert from a FRACTION to a PERCENT, you begin with the FRACTION
and DIVIDE the NUMERATOR by the DENOMINATOR.
 Then once a DECIMAL is found, you rewrite it as a PERCENT. Here, this
means you will shift the DECIMAL to the RIGHT 2 place values.
 Here, your FRACTIONS are set up to be solved and changed into PERCENTS.
 Example: Write 4/5 as a Percent.
 Divide the NUMERATOR 4 by the DENOMINATOR 5. 4 ÷ 5 = 0.80
 4/5 = 0.80 The DECIMAL is found. We convert to a PERCENT by shifting over 2 place
values.
 0.80 = 80%
 Quick Trick: Divide. Determine the Decimal. Shift.
Examples of Converting
Fractions to Percents
 Example #1: Write 7/8 as a Percent.
 Here, we have the FRACTION 7/8.
 7 ÷ 8 = 0.875
 (Here, the NUMERATOR gets DIVIDED by the DENOMINATOR)
 0.875 is the resulting DECIMAL.
 0.875 = 87.5%
 (Here, we shifted 2 place values to the RIGHT and added the Percentage Symbol.)
 Example #2: Write 13/20 as a Percent.
 Here, we have the FRACTION 13/20
 13 ÷ 20 = 0.65
 (Here, the NUMERATOR gets DIVIDED by the DENOMINATOR)
 0.65 is the resulting DECIMAL.
 0.65 = 65%
 (Here, we shifted 2 place values to the RIGHT and added the Percentage Symbol (%))
Writing Percents as Fractions
 PERCENTS, like FRACTIONS are very straightforward and easy to work
with.
 Remember that PERCENTS are values that represent a PART of a 100.
 To convert from a PERCENT to a FRACTION, you begin with the
PERCENT, re-write it as a FRACTION over 100. Then simplify the
FRACTION down to the LOWEST FRACTION.
 Here, your PERCENTS are set up to be solved and changed into
FRACTIONS.
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Example: Write 75% as a Fraction.
75% = 75/100
75/100 can be simplified by DIVIDING Numerator and Denominator by 25.
75 ÷ 25/100 ÷ 25 = 3/4
Therefore 75% = 3/4
Quick Trick: Convert Percent into a Fraction. Simplify to the Lowest Terms.
Examples of Converting
Percents to Fractions
 Example #1: Write 55% as a Fraction.
 Here, we have the Percent 55%.
 55% = 55/100
 55 and 100 can be divided both by 5
 55 ÷ 5/100 ÷ 5 = 11/2055% = 11/20
 (Here, we re-write the Percent as a Fraction over 100. Find the GCD and
simplify down.)
 Example #2: Write 24% as a Fraction.
 Here, we have the Percent 24%
 24% = 24/100
 24 and 100 can be divided both by 4
 24 ÷ 4/100 ÷ 4 = 6/25
 24% = 6/25
 (Here, we re-write the Percent as a Fraction over 100. Find the GCD and
simplify down)
Quick Review
 Writing Decimals as Percents
 To write a decimal as a percent, MULTIPLY by 100.
 Writing Percents as Decimals
 To write a Percent as a decimal, DIVIDE by a 100.
 Writing Fractions as Percents
 To write a Fraction as a Percent, you DIVIDE the NUMERATOR by the
DENOMINOR. Get a resulting decimal and then convert the decimal
into a Percent by shifting the decimal over 2 place values.
 Writing Percents as Fractions
 To write a Percent as a Fraction, you write your Percent as a fRaction
over 100. Find the GCD and simplify down.
Check for Understanding
Please determine the BEST answer for the
following expression.
Carry out ALL work and calculations in your
NOTES for later reference
Please write your answer on your wipe
boards and wait for the teacher’s signal.
On the count of 3, hold up your wipe boards.
C4U Question #1
Question #1:
-Write 0.32 as a Percent
 Please work out the problem within your notes
 Write the correct answer on your white board.
 Wait for Teacher’s Signal.
C4U Question #2
Question #2:
-Write 68% as a Decimal
 Please work out the problem within your notes
 Write the correct answer on your white board.
 Wait for Teacher’s Signal.
C4U Question #3
Question #3:
-Write 17/25 as a Percent
 Please work out the problem within your notes
 Write the correct answer on your white board.
 Wait for Teacher’s Signal.
C4U Question #4
Question #4:
-Write 38% as a Fraction.
 Please work out the problem within your notes
 Write the correct answer on your white board.
 Wait for Teacher’s Signal.
Guided and Independent Practice
 Complete #’s 8-10– on pg.237 in your math textbook.
 Work carefully, show your problem solving process, and double
check all calculations.
 Use scratch paper to carry out your work.
 Once you have completed the assigned problems, please raise your
pencil and wait to be stamped by Ms. Graham. If you receive and
“R” go to the back table.
 After being stamped move onto Independent Practice in your
textbook on pg.237 #’s 18-20