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3.03 Converting between fractions and decimals

Worksheet
Convert fractions to decimals
1

Write the number "fifty three hundredths" as a decimal.

2

Consider the following diagram:

a

What fraction of the row of blocks is shaded?

b

Write this fraction as a decimal.

c

What fraction of the row of blocks is not shaded?

d

Write this fraction as a decimal.

3

Consider the following diagram:

a

What fraction of the grid is shaded?

b

Write this fraction as a decimal.

c

What fraction of the grid is not shaded?

d

Write this fraction as a decimal.

4

Write the following fractions as decimals:

a

\dfrac{1}{10}

b

\dfrac{2}{10}

c

\dfrac{7}{10}

d

\dfrac{1}{100}

e

\dfrac{47}{100}

f

\dfrac{93}{100}

g

\dfrac{1}{1000}

h

\dfrac{6}{1000}

i

\dfrac{68}{1000}

j

\dfrac{111}{1000}

k

\dfrac{747}{1000}

l

\dfrac{954}{1000}

m

\dfrac{13}{10}

n

\dfrac{94}{10}

o

\dfrac{698}{100}

p

\dfrac{5527}{1000}

5

Write the following mixed numbers as decimals:

a

1\dfrac{1}{10}

b

9\dfrac{3}{10}

c

9\dfrac{65}{100}

d

7\dfrac{3}{25}

6

Complete the following conversion tables:

a
Fraction\dfrac{1}{10}\dfrac{1}{100}\dfrac{1}{1000}
Decimal0.1
b
Fraction\dfrac{1}{2}\dfrac{1}{4}\dfrac{3}{4}
Decimal0.5
c
Fraction\dfrac{1}{5}\dfrac{1}{20}\dfrac{1}{50}
Decimal
d
Fraction\dfrac{2}{5}\dfrac{3}{10}\dfrac{7}{50}
Decimal
7

Write the following fractions as decimals:

a

\dfrac{6}{12}

b

\dfrac{2}{5}

c

\dfrac{23}{50}

d

\dfrac{17}{25}

e

\dfrac{7}{20}

f

\dfrac{146}{200}

g

\dfrac{358}{500}

h

\dfrac{9}{4}

i

\dfrac{3}{2}

j

\dfrac{25}{20}

k

\dfrac{62}{50}

l

\dfrac{217}{25}

Convert decimals to fractions
8

For each of the following, fill in the boxes with the missing numbers:

a
0.8 = \dfrac{ ⬚ }{10}=\dfrac{⬚}{5}
b
0.75 = \dfrac{ ⬚ }{100}=\dfrac{⬚}{4}
c
0.68 = \dfrac{ ⬚ }{100}=\dfrac{⬚}{25}
d
2.2 = 2\dfrac{ ⬚ }{10}=2\dfrac{⬚}{5}
e
0.225 = \dfrac{ ⬚ }{1000}=\dfrac{⬚}{40}
f
3.035 = 3\dfrac{ ⬚ }{1000}=3\dfrac{⬚}{200}
9

Write the following decimals as a simplified fraction. Express your answer in mixed form when necessary.

a

0.9

b

0.4

c

0.29

d

0.92

e

0.09

f

0.907

g

0.535

h

1.9

i

5.8

j

7.19

k

5.62

l

4.09

m

9.007

n

3.065

o

76.25

p

223.205

10
a

If 0.2 of a row of blocks is shaded, find the decimal number that represents the unshaded part of the row.

b

Write the fraction that is unshaded in simplest form.

11
a

If 0.72 of a grid is shaded, find the decimal number that represents the unshaded part of the grid.

b

Write the fraction that is unshaded in simplest form.

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Multiply and divide fractions and decimals using efficient written strategies and digital technologies.

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