Coverting between decimals and fractions
Topic Notes
In this lesson, we will learn:
- What are equivalent decimal fractions (denominators that are powers of 10)
- How to convert between decimals and decimal fractions
- How to convert between decimals and non-decimal fractions
- How to represent decimal fractions with base ten (block) models
Notes:
- Decimals are also the short form of a fraction! We talked about decimals as the place values smaller than the ones place, but they are also another way to write fractions.
- Decimal fractions are fractions with a denominator that is a power of 10 (Ex. )
- How do we convert between decimals and decimal fractions?
- To convert a decimal into a decimal fraction:
- Take all the digits of the decimal and put them in the fraction’s numerator as a whole number (and remove any leading zeroes)
- Ex. 0.073=
- Look at the number of decimal place values in your decimal, that’s how many zeroes you will put in your fraction’s denominator
- Ex. 0.07 3 =
- To convert a decimal fraction into a decimal:
- Look at the number zeroes in the denominator, that’s how many decimal place values you will have in your decimal
- Ex. = 0. _ _ _
- Take all the numbers in your numerator; start from the smallest place values on the right and fill in the number backwards (back-fill them); any empty place values will be filled in with leading zeroes.
- Ex. = 0. _ _ _ → 0. _ _ 3 → 0. _ 7 3 → 0. 0 7 3
- Trailing zeroes are not important in the value of a decimal number.
- Ex. 0.5 and 0.50 are the same! This is because =
- Tenths and hundredths are easily converted into equivalent fractions (factor of 10). This is also true for hundredths and thousandths
- Ex. 0.50 = 0.500 because =
- What are NOT decimal fractions?
- Other fractions with denominators that are NOT powers of ten are non-decimal fractions (Ex. , , , , )
- Some non-decimal fractions have denominators that are factors or multiples of powers of 10
- They can be converted into equivalent decimal fractions
- The common fractions that you should know the decimal values for are:
![Decimals: Dividing decimals by power of 10](
https://dmn92m25mtw4z.cloudfront.net/img_set/math5-10-4-x-1/v1/math5-10-4-x-1-834w.jpg)
- To represent decimal fractions with base ten (block) models:
- (1) figure out what pieces represents what place value
- (2) tally the number of each tenth, hundredth, thousandth
- (3) and finally, write in standard form and/or fraction form
- We can represent more than one whole for base ten models and decimals.
- Fractions that represent greater than one whole are mixed fractions
- Follow the same three steps as before
- The number of complete wholes is written as a big number on the left side
- The decimal fraction is written on the right side