# Common fractions and decimals

##### Topic Notes

In this lesson, we will learn:

• How to convert between decimals and decimal fractions (tenths and hundredths)
• How to convert between decimals and unit fractions
• How to convert between decimals and fraction halves and quarters

Notes:

• Decimals can be converted into fractions and vice versa
• Recall that place values are related to their neighbors by a factor of 10

• Decimals can be easily converted into decimal fractions
• Decimal fractions have denominators that are powers of 10
• Decimal tenths are fractions out of 10
• Ex. 0.3 = $\large \frac{3}{10}$; 3 tenths = 3 out of 10
• Decimal hundredths are fractions out of 100
• Ex. 0.22 = $\large \frac{22}{100}$; 22 hundredths = 22 out of 100
• Decimal hundredths can also be expressed as a sum of fractions, because of equivalent decimals (i.e. 0.2 = 0.20)
• 0.22 = $\large \frac{22}{100}$ = $\large \frac{20}{100}$ + $\large \frac{2}{100}$ = $\large \frac{2}{10}$ + $\large \frac{2}{100}$

• Two type of common fractions have a denominator of 2 or 4

 Type Fraction Decimal Value "half" $\frac{1}{2}$ = $\frac{50}{100}$ = $\frac{5}{10}$ 0.5 "quarter" $\frac{1}{4}$ = $\frac{25}{100}$ 0.25