Module 3: Decimals

Example:

1.65

1. Determine how many digits follow the decimal point (or the place value of the final digit).

   Example: There are two digits that follow the decimal (6 is in the hundredths).

   The denominator of the fraction will be a power of 10 based on how many digits follow the decimal (refer to chart below).

   # of Decimal Digits	Example	Final Place Value	Resulting Denominator
   1	0.1	Tenths	10
   2	0.12	Hundredths	100
   3	0.0123	Thousandths	1000

2. Build the fraction by placing the decimal portion as the numerator.

   Example: 56 is the decimal portion: ${"version":"1.1","math":"\dfrac{56}{100}"}$

3. All numbers before the decimal point are whole values, which can be added to the side of the fraction to form a mixed fraction (reduce if possible).

   Example: 1.56: ${"version":"1.1","math":"1\dfrac{56}{100} \rightarrow 1\dfrac{14}{25}"}$

4. Alternatively, consider the whole as part of the numerator and create an improper fraction.

   Example: 1.56: ${"version":"1.1","math":"\dfrac{156}{100}"}$

Example:

2.33333…

1. Determine the repeating portion of the decimal.

   Example: 3 repeats constantly: 2.33333…

   The denominator of the fraction will be 9, 99, 999… (etc.) based on how many digits repeat (refer to chart).

   # of Repeating Digits	Example	Resulting Denominator
   1	0.1	9
   2	0.12	99
   3	0.0123	999

2. Build the fraction by placing the decimal portion as the numerator.

   Example: 3 is the decimal portion: $${"version":"1.1","math":"\dfrac{3}{9}"}$$

3. Apply the whole portion of the decimal in the same way as for finite fractions and reduce if possible.

   Example: 2.3: $${"version":"1.1","math":"2\dfrac{3}{9} \rightarrow 2\dfrac{1}{3} or \dfrac{7}{3}"}$$