Section 4.1 Percent, Decimal and Fraction Notations
Percent Notation
The notation n% means n parts per one hundred
Percent notation, n% can be expressed as:
Ratio:
n% = ratio of n to 100
Fraction notation
n%
Decimal notation
n%
Example:
Percent can be always written as a fraction:
Changing a Percent to a Fraction
Drop % symbol and write a given number over 100. Then simplify the fraction if possible.
Example:
Convert from percent to a fraction:
Changing a Percent to a Decimal
Drop % symbol and divide a given number by 100 (move decimal point 2 places to the left).
Example:
Convert from percent to a decimal:
Problem: There is ethanol in 87gasoline. Convert it to a decimal
Changing a Decimal to a Percent
Multiply the decimal by 100 (move decimal point 2 places to the right) and attach % symbol at the end.
Example:
Changing a Fraction to a Percent
1. Write a fraction as a decimal by dividing numerator by denominator.
2. Multiply the decimal by 100 and insert % symbol
Example:
Applications of
Percent
In any percent problem the relationship between the amount, the percent and the base is as follows:
Amount is a percent of the base
Amount = Percent Base
Example:
24 is 75% of 32
means or in decimal
Percent Problems:
q Each of the problems contains the word is. It can be translated as an = sign.
q Each problem contains the word of. In this context of means multiply.
q Each problem contains a phrase “What number” or “What percent”. This represents an unknown quantity which can be represented as a variable.
Example:
8.25 is 33% of 25
37 is 20% of 185
3 is 12% of 25
Solving Percent Problems Using Proportions
Example:
What is 30% of 120?
As a proportion we can write this relation as
Translating Percent Problem into a
Proportion
1. Use a percent formula to write a relation.
Amount = Percent Base
2. Convert this equation into a proportion using the fraction notation of a percent.
3. Solve a proportion.
Example:
Answer: 45% of 160 is 72
Answer: 45 is 125% of 36