# Common fractions and decimals

### Common fractions and decimals

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

#### Lessons

• Introduction
Introduction to Common Fractions and Decimals:
a)
How are decimals related to fractions?

b)
How to convert decimal tenths into decimal fractions ($\large \frac{1}{10}$)

c)
How to convert decimal hundredths into decimal fractions ($\large \frac{1}{100}$)

d)
How to convert between decimals and common fraction halves ($\large \frac{1}{2}$)

e)
How to convert between decimals and common fraction quarters ($\large \frac{1}{4}$)

• 1.
Writing common fractions as decimals
Write the following fractions as decimals
a)
Unit fractions:

b)
Decimal fractions:

c)
Common fractions related to $\large \frac{1}{2}$ or $\large \frac{1}{4}$:

• 2.
Fraction and figure equivalents for decimals
Complete the table for the equivalent decimal, fraction, and shaded in figure:
a) b) c) d) • 3.
Fraction and figure equivalents for decimals
Complete the table for the equivalent decimal, fraction, and shaded in figure:
a)
0.28 = $\large \frac{}{100}$ = $\large \frac{20}{100}$ + $\large \frac{}{100}$ = $\large \frac{}{10}$ + $\large \frac{}{100}$

b)
0.51 = $\large \frac{}{100}$ = $\large \frac{50}{100}$ + $\large \frac{}{100}$ = $\large \frac{}{10}$ + $\large \frac{}{100}$

c)
0.73 = $\large \frac{?}{?}$ = $\large \frac{}{100}$ + $\large \frac{}{100}$ = $\large \frac{}{10}$ + $\large \frac{}{100}$

d)
0.49 = $\large \frac{?}{?}$ = $\large \frac{?}{?}$ + $\large \frac{?}{?}$ = $\large \frac{?}{?}$ + $\large \frac{?}{?}$

• 4.
Common fractions and decimal number lines
Using common fractions and decimals:

A:$\large \frac{25}{100} \qquad \;$ B:$\large \frac{7}{10} \qquad \;$ C:$\large \frac{90}{100} \qquad \;$ D:$\large \frac{5}{10} \qquad \;$ A:$\large \frac{75}{100} \qquad$
a)
Draw each fraction as a point on the number line. Label each point with its corresponding letter b)
Which fractions can be rewritten in lowest forms as common fraction halves and quarters?