Fractions, Decimals, Percents

Fractions, Decimals, Percents

October, 2011

Reminder… Numerator represents the…

“part” Denominator represents the…

“whole”

So,

Example: There were 15 elephants in the zoo that has 236 animals. Write a fraction representing this situation.

wholepart

Terminating Decimals Examine the decimal below. What do you

notice?6.375

Definition: Any decimal that “terminates”“Terminates” means “to end or stop”

Examples of Terminating Decimals:5.67 4.23-6.901 -3.75

A terminating decimal is part of the real number system. How is it classified?

Repeating Decimals Examine the decimals below. What do you

notice?6.33333….

Definition: Any decimal that has a constant pattern of digits that repeat.

Examples: 5.3333… “3” is the repeating digit6.3030… “30” is the repeating pattern -1.233233… “233” is the repeating

pattern

3.6

Repeating Decimals A repeating decimal is part of the

real number system. How is it classified?

The line above the repeating digits is called…Bar Notation

Fractions, Decimals & Percents

All three have the same value, they are just represented in different ways.

We can calculate with fractions AND decimals, but NOT percents!

FRACTIONS TO DECIMALS

Fractions to Decimals

Method 1 If the denominator is a power of

10 (10, 100, 1000, etc.), then use the place value to write the decimal.

7/10 .753/100 .53

Fractions to Decimals

Method 2 Any fraction can be written as a decimal –How?

Divide the numerator by the denominator.

YOU MUST BE ABLE TO SHOW THIS USING LONG DIVISION!!

5/8 = .625

2/5 = .40

FRACTIONS TO PERCENTS

Fractions to Percents

Percent means…“Per 100” or “Out of 100”

Method 1Convert fraction to equivalent

fraction with denominator of 100.

1/4 = 25/100 = 25%12/25 = 48/100 = 48%

Fractions to Percents

Method 2Make the fraction a decimal and multiply by 100 (move decimal 2 places to right)

1/4 = .25 = 25%12/25 = .48 = 48%

DECIMALS TO PERCENTS

Decimals to Percents

Multiply by 100 (move decimal 2 places to right)

.25 = 25%.48 = 48%

DECIMALS TO FRACTIONS

Decimals to Fractions

“SAY” the decimal and create the fraction using the place value as the denominator…then, simplify!

.35 = 35/100 = 7/20.217 = 217/1000

Repeating Decimals to Fractions

How do you make a repeating decimal into a fraction?There is a very complicated process that ultimately says “take the repeating part of the decimal and put it over a denominator that has the same number of 9’s.”

Example – 0.3333… = 3/9 = 1/3

PERCENTS TO FRACTIONS

Percents to Fractions

Percent = “Per 100” or “Out of 100”…So create the fraction by removing

the % sign and placing the number over 100.

23% = 23/10055% = 55/100 (simplify)

PERCENTS TO DECIMALS

Percents to Decimals

Divide the percent by 100 (move decimal 2 places to the left)

23% = 23/100 = .2364% = 64/100 = .64

Practice

Write each fraction as a decimal.1/8 5/9 7 ½

Write each decimal as a fraction..22 0.1 4.6

Practice

Write each fraction as a percent.¼ 6/10 17/20

Write each percent as a fraction.90% 75% 22%

Practice

Write each percent as a decimal.27% 70% 6%

Write each decimal as a percent..95 .08 5.8