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:


n% = ratio of n to 100

Fraction notation


Decimal notation





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.




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).





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.






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






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


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.



  1. What number is 33% of 25?

            8.25 is 33% of 25


  1. 37 is what percent of 185?



            37 is 20% of 185


  1. 3 is 12% of what number?


            3 is 12% of 25


Solving Percent Problems Using Proportions



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.



  1. 45% of what number is 72?

            Answer: 45% of 160 is 72


  1. What number is 125% of 36?

            Answer: 45 is 125% of 36