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1.06 Comparing and ordering real numbers

Worksheet
Conversions of real numbers
1

Express the following decimals as a:

i

Percentage

ii

Simplified fraction

a

0.98

b

0.43

c

0.075

d

0.185

e

0.02

f

0.036

g

1.05

h

3.802

2

Convert the following fractions into percentages:

a
\dfrac{3}{5}
b
\dfrac{13}{20}
c
\dfrac{38}{25}
d
\dfrac{1}{6}
e
\dfrac{3}{3}
f
\dfrac{1}{3}
g
\dfrac{2}{3}
h
\dfrac{7}{3}
3

Convert the following decimals into percentages:

a
0.89
b
0.63
c
0.91
d
0.31
e
8.9
f
0.67
g
0.048
h
2.45
Comparison of real numbers
4

For each of the following expressions:

i

Rewrite the expression as percentages.

ii

State the inequality sign, \lt or \gt, that would make the statement true.

a

69\%\, ⬚ \, 0.63

b

71\%\, ⬚ \, 0.31

c

51\%\, ⬚ \, 0.67

d

0.052 \, ⬚ \, 4.9\%

e

\dfrac{38}{25}\, ⬚ \, 131\%

f

\dfrac{13}{20}\, ⬚ \, 64\%

g

\dfrac{7}{8}\, ⬚ \, 0.88

h

0.095\, ⬚ \, \dfrac{1}{10}

5

State whether the following statements are true or false:

a
\dfrac{13}{20} > 64\%
b
\dfrac{38}{25} > 131\%
c
\dfrac{15}{8} < \sqrt{2}
d
2\dfrac{3}{4} < \sqrt{7}
e
4.5 < 2\sqrt{9}
f
3.25 < \sqrt{8}
g
\sqrt{15} > 3\sqrt{5}
h
\sqrt{65} > 2\sqrt{16}
6

State the larger value in each pair of numbers:

a

0.91 or 82\%

b

8.9 or 879\%

c

45\% or 0.31

d

37\% or 0.61

e

0.019 or 7.5\%

f

\dfrac{1}{4} or 76\%

g

\dfrac{5}{6} or 0.3

h

\dfrac{91}{92} or 45\%

7

State the smaller value in each pair of numbers:

a

0.15 or \dfrac{1}{10}

b

3.25 or \dfrac{19}{5}

c

4 or \sqrt{10}

d

2\dfrac{1}{2} or \sqrt{5}

e

4 \pi or 12

f

\pi^{2} or 144

g

\sqrt{4} or \sqrt{\pi}

h

\dfrac{\pi}{2} or \sqrt{\pi}

8

For each of the following sets of numbers:

i

State the largest value.

ii

State the smallest value.

iii

State the value that is closest to 0.5.

a

92\%, \dfrac{3}{4}, \dfrac{503}{1000}, 0.1, 0.36, 60.1\%

b

71\%, \dfrac{4}{6}, \dfrac{84}{1000}, 0.7, 0.99, 50.8\%

9

Arrange each of the following sets of numbers in ascending order:

a

0.89, \,\dfrac{3}{5}, \, 53\%

b

\dfrac{3}{3},\, \dfrac{1}{3},\, 66\dfrac{2}{3}\%

c
\sqrt{22},\, 4.8,\, \dfrac{15}{11},\, 3 \sqrt{42}
d
\sqrt{30},\, 3\sqrt{3},\, 4.3, \, \dfrac{11}{2}, \, \dfrac{19}{4}
10

Arrange each of the following sets of numbers in descending order:

a

\dfrac{2}{3}, \, 33\dfrac{1}{3}\%, \, 100\%

b

\dfrac{5}{8}, \, 63\dfrac{2}{5}\%, \, 0.7, \, \dfrac{13}{20}

c
2\sqrt{2}, \, 2\sqrt{3}, \, 3.6, \,\dfrac{10}{3}
d
5.2, \, 3\sqrt{5}, \, \sqrt{35}, \, \dfrac{32}{5}, \, \dfrac{23}{4}
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Outcomes

MA.8.NSO.1.1

Extend previous understanding of rational numbers to define irrational numbers within the real number system. Locate an approximate value of a numerical expression involving irrational numbers on a number line.

MA.8.NSO.1.2

Plot, order and compare rational and irrational numbers, represented in various forms.

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