Advanced Math

Converting Repeating Decimals into Fractions

Name: Period:

Guiding Questions:

1. Are there decimals you cannot turn into fractions?2. How can you convert a terminating decimal into a fraction?3. How can you convert a repeating decimal into a fraction?

1. What are the three types of decimals we have discussed?

Type of Decimal Definition ExamplesTerminating Decimal A decimal where the digits

behind the decimal STOP!0.89512.2

Repeating Decimal A decimal where one or more digits behind the

decimal infinitely reoccur.

0.27272727…8 .536

Non-terminating and Non-repeating decimal

A decimal where the digits behind the decimal do not stop AND do not reoccur.

π3.616616661…

12.8695326488…

2. Which types of decimals can be converted into fractions?

ONLY TERMINATING OR REPEATING DECIMALS CAN BE REWRITTEN AS FRACTIONS!

Practice: Identify each of the following as terminating, repeating, or neither. Next, determine if you can write each decimal as a fraction.

A. 1.646644666444… B. π C. 6.43434343….

D. 8.45667811247… E. 11.2 F. 2.9568

3. How do you convert a terminating decimal into a fraction?

Converting a terminating decimal into a fraction1. If there is a whole number, just re-write it.2. Determine the place value of the last digit behind your decimal point. Remember, all

numbers to the right of the decimal point are fractions with denominators 10, 100, 1,000, 10,000, 100,000, etc.

3. Write the place value of the last digit to the right of the decimal as the denominator of your fraction.

4. Write all the digits to the right of the decimal point as the numerator of your fraction.5. Simplify if necessary.

Practice: Convert each of the following decimals to fractions in simplest form.

A. 4.375 B. 9.8 C. 3.64

4. What are some common repeating decimals that can be written as fractions?Practice: Convert each of the following decimals to fractions in simplest form.

A. 4 .6 B. 10 .27 C. 11.2

5. How do you convert any repeating decimal into a fraction?

Converting a repeating decimal into a fraction1. Set the repeating decimal equal to x.2. Examine the repeating decimal to determine how many digits are repeating in the

repeating decimal.3. Place the repeating digit(s) to the left of the decimal point, by multiplying each side of

your new equation by a power of 10 that has that many zeroes. For example: if you need to move your decimal two spaces to get the repeating decimal , multiply each side by 100 because 100 has two zeroes and there are two digits repeating

4. Place the repeating digit(s) to the right of the decimal point using the same method.5. Subtract the two equations. 6. Solve for x.

Examples: Convert 0 .87and 0 . 42 into a fraction

Example 1: 0 .87 Steps Example 2: 0 .42x=0 .87 Set the repeating decimal

equal to x.x=0 .42

Get the repeating

decimal on the left of

the decimal100 x=87 .7

Get the repeating

decimal on the right of the decimal10 x=8 .7

Get the repeating decimal to the left and right of the

decimal point.

Get the repeating

decimal on the left of the

decimal100 x=42 . 42

Repeating decimal is already on the right of the decimalx=0 .42

100 x=87 .7−10 x=−8 .790 x=79

Subtract the two new equations. Be sure to line up

your decimals!!!!!!!!!!!!!!!!

100 x=42 .42−1 x=−0 .4299 x=42

90 x=7990 x90

=7990

x=7990

Solve for x 99 x=4299 x99

=4299

x=4299

Practice: Convert each of the following decimals to fractions in simplest form.

A. 0 .5 B. 10 .45 C. 0 .46