Converting Simple Decimals to Fractions and Vice Versa

Today’s Learning Goals We will continue to link our understanding of

fractions with decimals. We will continue to develop our understanding

of place value when determining the fraction equivalence of decimals.

Representing Decimals Recently, we have seen how to represent a

decimal number to the hundredths using a rectangle cut up into 100 parts.

For example, how would we represent the number 2.34 if we let the large rectangle below represent 1 whole?Good…we need 2 wholes and 34 hundredths.

Decimals to Fractions The number 2.34 and the representation above show

different ways to write the number as a fraction.

2 3 4

ones

tenth

shundre

dth

s First, you could write the decimal out in

expanded form. Expanded form shows the value of each place.

How would we write 2.34 in expanded form?

Nice…1004

103

2

Decimals to Fractions Another way to write a decimal is as a mixed

fraction. When writing a decimal as a mixed fraction,

we must state how many wholes there are and then what part of another whole by combining everything to the right of the decimal place.

2 3 4

ones

tenth

shundre

dth

s

How would we write 2.34 as a mixed fraction?

Good…

10034

2

1004

10030

2

Decimals to Fractions A third way to write a decimal is just as a

single fraction. When writing a decimal as a single fraction, we

must combine all place values together. How would we write 2.34

as a single fraction?

Good…

100

234100

4

100

30

100

200

2 3 4

ones

tenth

shundre

dth

s

Fractions to Decimals As we have discussed, all decimal numbers

are fractions with a denominator that is a power of 10 (e.g. tenths, hundredths).

Consider the following fractions. How would you write the following as decimals?

a)10

3= 0.3 b)

100

6= 0.06 c)

100

52= 0.52

d)10

62 = 2.6 e)

100

2435 =

35.24f)

100

71 = 1.07

Fractions to Decimals Suppose the fraction was . This fraction is

not in tenths or hundredths. What could we do to write this fraction as a decimal?

52

Excellent…we could get an equivalent fraction for 2/5.

Now that we have 2/5 written with a base-10 denominator, how could we write 2/5 as a decimal?

5

2

10

4

Awesome… = 0.45

2

10

4

Fractions to Decimals Consider the following fractions. How would

you write the following as decimals?

a)5

48.0

10

8 5.2

10

52 75.3

100

753 b)

2

12 c)

4

33

Partner Work You have 20 minutes to work on the following

problems with your partner.

For those that finish early

What number does each letter represent?

0 0.05 0.1 0.15 0.2 0.25

A B C D E

Big Idea from Today’s Lesson We can represent the same decimal number in

many different ways. In expanded form, mixed fraction form, or as a single

fraction.

One way to go from a fraction to a decimal is to get the fraction to have a denominator that is a power of 10.

Homework Complete Homework Worksheet. Pg. 155 (2, 3, 15, 17, 18)