Converting between decimals and fractions

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. $\frac{5}{10}, \frac{73}{100}, \frac{426}{1000}$)


• 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= $\frac{73}{?}$
• 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 =$\frac{73}{1000}$
• 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. $\frac{73}{1000}$ = 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. $\frac{73}{1000}$ = 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 $\frac{5}{10}$ = $\frac{50}{100}$
• 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 $\frac{50}{100}$ = $\frac{500}{1000}$


• What are NOT decimal fractions?
• Other fractions with denominators that are NOT powers of ten are non-decimal fractions (Ex. $\frac{1}{2}$, $\frac{2}{5}$, $\frac{5}{18}$, $\frac{7}{25}$, $\frac{547}{900}$)
• 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:

• 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