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# Representing Percents

## Introduction:

### Percent greater than 100 or less than 1:

100% is equal to 100 out of 100, or 1. Percents greater than 100% are fractions (or decimals). Generally, percent greater than 100% is an improper fraction in types of fractions, while percents less than 100% are proper fractions (or decimals) less than 1.

### Expressing Percents as Decimals:

To convert a percent into a decimal, move the decimal point 2 places to the left and drop the percent sign.

155% becomes 1.55.

If the number in front of the percent has fewer than two places in front of the decimal, add zeros to the left of the number, and then move the decimal place.

1.98% = 01.98% = 0.0198.

### Expressing Decimals as Percents:

To convert a decimal into a percent, move the decimal point two places to the right and add the % sign.

If there are fewer than two places to the right of the decimal, add zeros at the end of the number after the decimal point.

For example,

1. 0.986 = 98.6%
1. 1.8 = 1.80 = 180%.

## Represent Percent Greater than 100 or Less than 1

Example1: The Length of the ribbon is 120% compare to the old ribbon. Write 120% as a fraction.

Example: You want to see a movie. The cost of admission to a movie is 1 7/8 times of renting a video. Write the fraction into a decimal.

Solution:  We have,

Steps1: Use the definition of percent

Step 2: Move the decimal point two places to the right.

Example: Classify the decimal 0.065 as

(A) Less than 1 %

(B) Greater than 100%

(C) Between 1% and 100%

Solution:

The value of the given decimal is less than 1.

It may be either between 1% and 100% or less than 1%.

To make sure of the category, let us convert the given decimal into percent as given below.

= 0.065

=(0.065× 100)%

=6.5%

In the above calculation, the decimal is 6.5% which is between 1% to 100%.

Convert each percent as a decimal.

1. 380%
1. 300%
1. 150%
1. 440%
1. 355%
1. 452%

### Concept Map:

• All mixed numbers/fractions are greater than 100%.
• In the fraction 13/8 the numerator is greater than denominator.
• So the fraction 13/8 is greater than 100%.
• When the value of given decimal is greater than 1, then the conversion of decimal number to percent is always greater than 100%.
• A proper fraction represents a percent less than 100%.

### What have we learned:

• Percent greater than 100 or less than 1.

• Use a model to represent a part that is greater than 100 or less than 1.

• Represent percent more than 100 as a fraction.

• Represent percent more than 100 as a decimal.

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