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1.07 Converting fractions to 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}{10}

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}

8

Convert the following fractions into decimals using long division:

a
\dfrac{1}{8}
b
\dfrac{9}{11}
c
\dfrac{5}{6}
d
\dfrac{9}{15}
e
\dfrac{9}{15}
f
\dfrac{13}{25}
g
\dfrac{1}{18}
h
\dfrac{2}{11}
9

Evaluate the following, writing your answer as a decimal:

a
11+\dfrac{4}{10}+\dfrac{6}{100}
b
5+\dfrac{1}{10}+\dfrac{9}{100}
c
32+\dfrac{8}{10}+\dfrac{5}{1000}
d
27+\dfrac{7}{10}+\dfrac{1}{1000}
e
14+\dfrac{3}{100}+\dfrac{1}{1000}
f
7+\dfrac{2}{100}+\dfrac{3}{1000}
g
5+\dfrac{1}{5}+\dfrac{1}{100}
h
6+\dfrac{2}{5}+\dfrac{9}{1000}
i
12+\dfrac{6}{10}+\dfrac{4}{50}
j
18+\dfrac{4}{10}+\dfrac{3}{50}
Convert decimals to fractions
10

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}
11

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

12

Explain your process to convert a decimal into a fraction.

13
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.

14
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.

15

Arrange the following numbers in ascending order:

\dfrac{7}{10},\, 0.74, \, 0.0069, \, 0.007, \, 0.071
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Outcomes

MA.7.NSO.1.2

Rewrite rational numbers in different but equivalent forms including fractions, mixed numbers, repeating decimals and percentages to solve mathematical and real-world problems.

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