Example: Convert -72 5/11 to a decimal to the

nearest hundredth.

Solution: In this case, you would divide 5 by 11 to

one place past the desired place value of hundredths and

then round.

Example: Convert -200.4 to a fraction and reduce

to lowest terms.

Solution:

So, -72 5/11 = -72.45 to the nearest hundredth.

Converting a repeating decimal to a fraction is a

little more confusing than the conversions we have

To convert a terminating decimal to a fraction,

previously performed. A repeating decimal can be

count the number of digits to the right of the decimal

converted to a fraction by the following steps:

point. Move the decimal point that many places to the

1. Form an equation letting n equal the repeating

right, and write the answer you get over a denominator

decimal.

beginning with 1 followed by as many zeros as places

moved to the right. Reduce to lowest terms, if possible.

2. Multiply both sides of the equation by a multiple

of 10 in order to shift a set of the repeating

Example: Convert 0.77 to a fraction.

pattern.

Solution: The number of digits to the right of the

3. Subtract the original equation from the new

decimal point is 2. Therefore, we will move the decimal

equation (in step 2).

point 2 places to the right and place 77 over 100. So

4. Solve for *n *and reduce to lowest terms.

Example: Convert 0.2 to a fraction.

Example: Convert -0.045 to a fraction and reduce

Solution: First, let n equal the repeating decimal, or

to lowest terms.

Solution:

Second, multiply both sides of the equation by 10 since

there is only one digit in the repeating pattern. Hence,

10*n *= 2.222...

Third, subtract the original equation from the new

equation. That is,

When converting mixed decimals to fractions, you

will usually find it is easier to keep the integer portion

as an integer and change the decimal fraction to a

common fraction.

Fourth, solve for *n.*

Example: Convert 12.625 to a fraction and reduce

to lowest terms.

9*n *= 2

Solution:

14-5

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