**Section 4.1 Percent, Decimal and Fraction Notations**

**Percent Notation**

** **The notation

**Percent notation**,** n%**

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 *“*W*hat
number”* or *“What percent”. *This
represents an unknown quantity which can be represented as a variable.

*Example:*

- What number is 33% of 25?

8.25 is 33% of 25

- 37 is what percent of 185?

37 is 20% of 185

- 3 is 12% of what number?

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:*

- 45% of what number is 72?

*Answer:*
45% of 160 is 72

- What number is 125% of 36?

*Answer:*
45 is 125% of 36