Middle Years

# 1.12 Rational and irrational numbers

Worksheet
Rational and irrational numbers
1

Identify the following numbers as rational or irrational:

a

4

b

- 4

c
8^{2}
d
912
e

\dfrac{2}{3}

f
\dfrac{3}{13}
g
\dfrac{7}{6}
h

\dfrac{17}{4}

i

4.435

j
- 0.7
k
\sqrt{7}
l

\left(\sqrt{7}\right)^{2}

m

\sqrt{35}

n

\sqrt{81}

o
\sqrt{225}
p
- \sqrt{13}
q
- \sqrt{64}
r

\sqrt[3]{23}

s

\sqrt[3]{64}

t
\sqrt[3]{512}
u
\sqrt{7} + 15
v
\sqrt{25} + \sqrt{16}
w
35 - \sqrt{13}
x
\sqrt{ 2 \times \sqrt{4}}
2

For the following roots:

i

Evaluate, correct to two decimal places when applicable.

ii

State whether the solution is an exact value or an approximation.

a
\sqrt{3}
b
\sqrt{16}
c
\sqrt{60}
d
\sqrt[3]{77}
e
\sqrt{63}
f
\sqrt[3]{27}
g
\sqrt[3]{43}
h
\sqrt[3]{100}
Convert fractions to decimals
3

Write the following fractions as decimals:

a

\dfrac{1}{4}

b
\dfrac{3}{4}
c
\dfrac{1}{5}
d
\dfrac{2}{5}
e
\dfrac{4}{5}
f
\dfrac{6}{4}
g

\dfrac{7}{10}

h
\dfrac{6}{10}
i
\dfrac{9}{10}
j
\dfrac{17}{20}
k
\dfrac{13}{20}
l
\dfrac{63}{100}
m
\dfrac{72}{100}
n
\dfrac{509}{1000}
o
5\dfrac{651}{1000}
p
8\dfrac{611}{1000}
4

Write the following fractions as recurring decimals:

a
\dfrac{1}{6}
b
\dfrac{1}{3}
c
\dfrac{2}{3}
d
\dfrac{4}{3}
e

\dfrac{2}{7}

f
\dfrac{2}{9}
g
\dfrac{6}{9}
h

\dfrac{7}{9}

i
\dfrac{16}{9}
j

\dfrac{3}{11}

k

\dfrac{5}{12}

l
\dfrac{2}{13}
m
\dfrac{44}{7}
n
\dfrac{28}{36}
o
\dfrac{73}{99}
p
\dfrac{761}{999}
Convert decimals to fractions
5

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

a
0.8 = \frac{ ⬚ }{10}=\frac{⬚}{5}
b
0.75 = \frac{ ⬚ }{100}=\frac{⬚}{4}
c
0.68 = \frac{ ⬚ }{100}=\frac{⬚}{25}
d
2.2 = 2\frac{ ⬚ }{10}=2\frac{⬚}{5}
e
0.225 = \frac{ ⬚ }{1000}=\frac{⬚}{40}
f
3.035 = 3\frac{ ⬚ }{1000}=3\frac{⬚}{200}
6

Write each of the following as a fully simplified fraction:

a
0.7
b
0.9
c
0.4
d
0.29
e
0.92
f
0.09
g
0.375
h
0.907
i
0.535
j
1.9
k
5.8
l
7.19
m
5.62
n
4.09
o
1.0625
p
4.625
q
9.007
r
3.065
s
76.25
t
223.205