Concepts
1 BasicFunctions
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Unit 1C
Review of Operations with
Decimal Fractions and Percent
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1.13
Percent
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Percent
Percent is the comparison of any number of parts to 100
parts. The word percent means “per hundred.” The symbol
for percent is %.
You wish to put milk in a pitcher so that it is 25% “full”
(Figure 1.34a).
(a) This pitcher is 25% full.
(b) This pitcher is 83% full.
(c) This pitcher is 100% full.
How full is each pitcher?
Figure 1.34
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Percent
First, imagine a line drawn down the side of the pitcher.
Then imagine the line divided into 100 equal parts.
Each mark shows 1%: that is, each mark shows one out of
100 parts.
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Percent
Finally, count 25 marks from the bottom. The amount of
milk below the line is 25% of what the pitcher will hold.
Note that 100% is a full, or one whole, pitcher of milk.
One dollar equals 100 cents or
100 pennies. Then, 36% of one dollar
equals 36 of 100 parts, or 36 cents
or 36 pennies. (See Figure 1.35.)
Figure 1.35
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Percent
To save 10% of your salary, you would have to save $10
out of each $100 earned.
When the U.S. government spends 15% of its budget on its
debt, interest payments are taking $15 out of every $100
the government collects.
A salesperson who earns a commission of 8% receives $8
out of each $100 of goods he or she sells.
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Percent
A car’s radiator holds a mixture that is 25% antifreeze. That
is, in each hundred parts of mixture, there are 25 parts of
pure antifreeze.
A state charges a 5% sales tax. That is, for each $100 of
goods that you buy, a tax of $5 is added to your bill. The
$5, a 5% tax, is then paid to the state.
Just remember: percent means “per hundred.”
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Changing a Percent to a Decimal
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Changing a Percent to a Decimal
Percent means the number of parts per 100 parts. Any
percent can be written as a fraction with 100 as the
denominator.
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Example 1
Change each percent to a fraction and then to a decimal.
a.
75 hundredths
b.
45 hundredths
c.
16 hundredths
d.
7 hundredths
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Changing a Percent to a Decimal
Changing a Percent to a Decimal
To change a percent to a decimal, move the decimal point
two places to the left (divide by 100). Then remove the
percent sign (%).
If the percent contains a fraction, write the fraction as a
decimal.
For problems involving percents, we must use the decimal
form of the percent, or its equivalent fractional form.
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Changing a Decimal to a Percent
13
Changing a Decimal to a Percent
Changing a decimal to a percent is the reverse of what we
did in Example 1.
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Example 4
Write 0.75 as a percent.
0.75 =
= 75%
75 hundredths
hundredeths means percent
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Changing a Decimal to a Percent
Changing a Decimal to a Percent
To change a decimal to a percent, move the decimal point
two places to the right (multiply by 100). Write the percent
sign (%) after the number.
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Changing a Fraction to a Percent
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Changing a Fraction to a Percent
In some problems, we need to change a fraction to a
percent.
Changing a Fraction to a Percent
1. First, change the fraction to a decimal.
2. Then change this decimal to a percent.
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Example 6
Change
to a percent.
First, change to a decimal by dividing the
numerator by the denominator.
0.6 = 60%
So
Then change 0.6 to a percent by moving the
decimal point two places to the right. Write
the percent sign (%) after the number.
= 0.6
= 60%.
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Changing a Percent to a Fraction
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Changing a Percent to a Fraction
Changing a Percent to a Fraction
1. Change the percent to a decimal.
2. Then change the decimal to a fraction in lowest terms.
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Example 10
Change 25% to a fraction in lowest terms.
First, change 25% to a decimal by moving
the decimal point two places to the left.
Remove the percent sign (%).
25% = 0.25
Then change 0.25 to a fraction. Reduce
it to lowest terms.
0.25 =
=
So 25% = 0.25 =
.
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Changing a Percent to a Fraction
Changing a Percent That Contains a Mixed Number to a
Fraction
1. Change the mixed number to an improper fraction.
2. Then multiply this result by
sign (%).
and remove the percent
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Example 12
Change
to a fraction.
First, change the mixed number to an
improper fraction.
Then multiply this result by
remove the percent sign (%).
and
So
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