Skill Focus

Fractions,

Decimals &

Percentages Certificate I

Access to Work & Training

NSWTAFE New England

Institute

The Relationship Among

Fractions, Decimals, Percents:

All represent a part of a whole A fraction is based on the number into which the whole is

divided (the denominator). The numerator (the top) is the PART, the denominator (the bottom) is the WHOLE.

A decimal is based on the number in terms of tenths,

hundredths, thousandths, etc.

A percent is based on the number in terms of 100.

Example:

How do we get

from one form to another?

1. Fraction to Decimal

Divide the denominator (the bottom of the fraction) into the numerator (the top of the fraction).

Place a decimal point after the number inside the division

"box" and attach as many zeros as necessary to handle the

division.

If the quotient does not come out evenly,

follow any rounding instructions.

How do we get

from one form to another?

2. Decimal to Percent

Move the decimal point two places to the right (this

multiplies the number by 100).

. 5 0 = 50%

OROR 0.50 x 100 = 50.0 Attach the percent sign: 50%

How do we get

from one form to another?

3. Percent to Decimal

Move the decimal point two places to the left

(this divides the number by 100).

5 0 % = .50

How do we get

from one form to another?

4. Percent to Fraction

Place the number in the percent over 100 and

reduce.

How do we get

from one form to another?

5. Fraction to Percent

Multiply the fraction by 100, reduce, and attach a

percent sign.

How do we get

from one form to another?

6. Decimal to Fraction

You will be using place value to do this one!

Count the decimal places of the decimal starting from the

decimal point.

If there is one decimal place, place the number over 10 and reduce. If there are two decimal places, place the number

over 100 and reduce. If there are three decimal places,

place the number over 1000 and reduce. And so on ….

Percentages

Percentages refer to fractions of a whole;

that is, whatever you're looking at, the percentage is how much of the

whole thing you have.

For instance, 50% means 1/2 ; 25% means 1/4 ; 40% means 2/5

Often you will need to figure out what percentage of something another thing is.

For example: For example: if a class has 26 students, and 14 are female, what percentage of the students are female?

It is 14 out of 26, or 14/26 = 0.538461538462..., or about 54%.

Per cent

"Percent" is actually "per cent", meaning "out of a hundred".

(It comes from the Latin per centum for "thoroughly hundred".)

You can use this "out of a hundred" meaning, along with the fact that

fractions indicate division, to convert between fractions, percents, and

decimals.

What does % mean in

everyday life?

We use percentages to

describe fractions.

Percentages mean more to us

than fractions We quite freely use the

term “percent” to describe a portion but seem to stumble

with a decimal amount or fraction.

Decimal to Percent

DecimalDecimal--toto--percent conversions are simple:percent conversions are simple: just move the decimal point two places to the right.

(Remember, $0.50 is one-half, or 50%, of a dollar.)

For exampleFor example:

0.23 = 23% 0.23 = 23%

2.34 = 234% 2.34 = 234%

0.0097 = 0.97% 0.0097 = 0.97%

(Note that 0.97% is less than one percent.

It should not be confused with 97%, which is 0.97 as a decimal.)

Fraction to Percent

This conversion starts the same as the previous one, but the final answer

can come in a couple different formats sometimes.

You always start by doing the division (fractions are division,

remember!), and then (usually) you move the decimal point two places

to the right.

ExampleExample:

Table

of

Common

Fractions

and their

Percentage

Equivalents

Table of

Common

Fractions and

their Decimal

Equivalents or

Approximations

Remember:Remember:

Always show your working:

It keeps your thinking

methodical and gives you

a chance to find if and

where you made a

mistake.

http://www.tc3.edu/instruct/sbrown/stat/showwork.htm