Question 1: Convert the following decimals into like decimals:

i). 13, 2.212, 9.0, 5.0017, 0.44       ii). 1, 1.11, 0.1, 1.111, 1.1, 11

Answer:

i) 13, 2.212, 9.0, 5.0017, 0.44

13.0000, 2.2120, 9.0000, 0.0017, 0.4400

ii) 1, 1.11, 0.1, 1.111, 1.1, 11

1.000, 1.110, 0.100, 1.111, 11.0000

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Question 2: Compare the decimals :

i) 0.1 and 0.01      ii) 4.001 and 3.987      iii) 0.1 and 0.0999      iv) 88.123 and 88.08765

Answer:

i) 0.1 and 0.01

0.1 > 0.01

ii) 4.001 and 3.987

4.001 > 3.987

iii) 0.1 and 0.0999

0.1 > 0.0999

iv) 88.123 and 88.08765

88.123 > 88.08765

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Question 3: Write each of the following decimals in an expanded form:

i) 3.57      ii) 0.864      iii) 1.002      iv) 153.607 4

Answer:

i) 3.57

3.57 = 3 \times 10^1 + 5 \times \frac{1}{10} + 7 \times \frac{1}{10^2}

ii) 0.864

0.864 = 8 \times \frac{1}{10} + 6 \times \frac{1}{10^2} + 4 \times \frac{1}{10^3}

iii) 1.002

1.002 = 1 \times 1 + 2 \times \frac{1}{10^3}

iv) 153.607 4

153.6074 = 1 \times 102 + 5 \times 101 + 3 \times 1 + 6 \times \frac{1}{10} + 7 \times \frac{1}{10^3} + 4 \times \frac{1}{10^4}

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Question 4: Express each of the following as a decimal:

i) 4 \times 10^1 + 7 \times 1 + 5 \times \frac{1}{10}  

ii) 1 \times 10^2 + 9 \times 10^1 + 4 \times 1 + 5 \times \frac{1}{10} + 6 \times \frac{1}{10^2} + 8 \times \frac{1}{10^3}

iii) 5 \times 10^1 + 9 \times 1 + 4 \times \frac{1}{10^2} + 1 \times \frac{1}{10^3} + 6 \times \frac{1}{10^4}  

Answer:

i) 4 \times 10^1 + 7 \times 1 + 5 \times \frac{1}{10} = 47.5

ii) 1 \times 10^2 + 9 \times 10^1 + 4 \times 1 + 5 \times \frac{1}{10} + 6 \times \frac{1}{10^2} + 8 \times \frac{1}{10^3} = 194.568

iii) 5 \times 10^1 + 9 \times 1 + 4 \times \frac{1}{10^2} + 1 \times \frac{1}{10^3} + 6 \times \frac{1}{10^4} = 59.0416

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Question 5: Write the following decimals in ascending order :

(i) 0.13, 1.056, 0.394, 1.13, 0.625, 2.004      (ii) 0.01, 0.007, 0.7, 7.7, 7.007, 7.07

Answer:

i) 0.13, 1.056, 0.394, 1.13, 0.625, 2.004

0.13 < 0.394 < 0.625 < 1.056 < 1.13 < 2.004

ii) 0.01, 0.007, 0.7, 7.7, 7.007, 7.07

0.007 < 0.01 < 0.7 < 7.007 < 7.07 < 7.7

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Question 6: Write the following decimals in descending order:

i) 6.1, 7.3, 3.7, 6.07, 7.37, 3.71      ii) 12.5, 9.8, 11.31, 10.734, 9.79, 10.385

Answer:

i) 6.1, 7.3, 3.7, 6.07, 7.37, 3.71

7.37 > 7.3 > 6.1 > 6.07 > 3.71 > 3.7

ii) 12.5, 9.8, 11.31, 10.734, 9.79, 10.385

12.5 > 11.31 > 10.734 > 10.385 > 9.8 > 9.79

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Question 7: Add:

i) 0.351 + 2.96 + 19.6 + 0.005 + 137.09 + 0.0809

ii) 9.89 + 0.989 + 98.09 + 989.098 + 98.0989

iii) 66.666 + 6.6 + 6.066 + 666.006

iv) 2.38 + 23.8 + 238.28 + 28.383 + 0.382

Answer:

i) 0.351 + 2.96 + 19.6 + 0.005 + 137.09 + 0.0809

\rightline{ 0.3510} \\ \rightline{2.9600} \\ \rightline{19.6000} \\ \rightline{0.0050} \\ \rightline{137.0900} \\ \rightline{+ \underline{\ \ \ \ 0.0809}} \\ \rightline{\underline{160.0869}} 

ii) 9.89 + 0.989 + 98.09 + 989.098 + 98.0989

\rightline{ 9.8900} \\ \rightline{0.9890} \\ \rightline{98.0900} \\ \rightline{989.0980} \\  \rightline{+ \underline{\ \ \ \ 98.0989}} \\ \rightline{\underline{1196.1659}} 

iii) 66.666 + 6.6 + 6.066 + 666.006

\rightline{ 66.666} \\ \rightline{6.600} \\ \rightline{6.066} \\ \rightline{+ \underline{\ \ 666.006}} \\ \rightline{\underline{745.338}} 

iv) 2.38 + 23.8 + 238.28 + 28.383 + 0.382

\rightline{ 2.380} \\ \rightline{23.800} \\ \rightline{238.280} \\ \rightline{28.383} \\  \rightline{+ \underline{\ \ \ \ 0.382}} \\ \rightline{\underline{293.225}} 

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Question 8: Evaluate:

i) Increase 37.984 by 7.089      ii) Increase 99.9809 by 0.198

Answer:

i) Increase 37.984 by 7.089

\rightline{ 37.984} \\  \rightline{+ \underline{\ \ 7.089}} \\ \rightline{\underline{45.073}} 

ii) Increase 99.9809 by 0.198

\rightline{ 99.9809} \\  \rightline{+ \underline{\ \ 0.1980}} \\ \rightline{\underline{100.1789}} 

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Question 9: Subtract:

i) 16.48 from 20.3      ii) 0.0051 from 0.01      iii) 9.841 from 11.001       iv) 0.0838 from 0.1

Answer:

i) 16.48 from 20.3

\rightline{ 20.30} \\  \rightline{- \underline{\ \ 16.48}} \\ \rightline{\underline{3.82}} 

ii) 0.0051 from 0.01

\rightline{ 0.0100} \\  \rightline{- \underline{\ \ 0.0051}} \\ \rightline{\underline{0.0049}} 

iii) 9.841 from 11.001  

\rightline{ 11.001} \\  \rightline{- \underline{\ \ 9.841}} \\ \rightline{\underline{1.160}} 

iv) 0.0838 from 0.1

\rightline{ 0.1000} \\  \rightline{- \underline{\ \ 0.0838}} \\ \rightline{\underline{0.0162}} 

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Question 10: Evaluate:

i) Decrease 10 by 0.854      ii) Decrease 11 by 10.9091
iii) Take 2.53 from 25.3       iv) Find the difference between 0.1 and 0.0001

Answer:

i) Decrease 10 by 0.854

\rightline{ 10.000} \\  \rightline{- \underline{\ \ 0.854}} \\ \rightline{\underline{9.146}} 

ii) Decrease 11 by 10.9091

\rightline{ 11.0000} \\  \rightline{- \underline{\ \ 10.9091}} \\ \rightline{\underline{0.0909}} 

iii) Take 2.53 from 25.3

\rightline{ 25.30} \\  \rightline{- \underline{\ \ 2.53}} \\ \rightline{\underline{22.77}} 

iv) Find the difference between 0.1 and 0.0001

\rightline{ 0.1000} \\  \rightline{- \underline{\ \ 0.0001}} \\ \rightline{\underline{0.0999}} 

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Question 11: Find the following products.

i) 8.019 \times 10       ii) 0.054 \times 1000       iii) 0.076  \times  0.09       iv) 0.0567 \times 13       

v) 2.57 \times 34        vi) 0.319 \times 021       vii) 1.11  \times  0.11  \times  1.1  \times  1.01  \times  1000 

Answer:

i)    8.019 \times 10 = 80.19

ii)    0.054 \times 1000 = 54

iii)    0.076  \times  0.09 = 0.00684

iv)    0.0567 \times 13 = 0.007371

v)    2.57 \times 34 = 87.38

vi)    0.319 \times 021 = 0.006699

vii)    1.11  \times  0.11  \times  1.1  \times  1.01  \times  1000 = 135.6531

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Question 12: Divide:

i) 23.5 \div 10       ii) 47.19 \div 1000       iii) 204.6  \div  20       iv) 31.49 \div 47       v) 0.8085 \div 35 

vi) 0.00216 \div 27       vii) 0.169  \div  1.3      viii) 1.21663  \div  0.89

Answer:

i)     23.5 \div 10 = 2.35

ii)     47.19 \div 1000 = 0.04719

iii)    204.6  \div  20 = 10.23

iv)   31.49 \div 47 = 0.67

v)   0.8085 \div 35 = 2.31

vi)   0.00216 \div 27 = 0.008

vii)   0.169  \div  1.3 = 0.13

viii)   1.21663  \div  0.89 = 1.367

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Question 13: Simplify:

i) 3.5 \div 5 \ of \  5 + 0.5  \times  0.3 - 0.1      ii) 3.6 \div 4 \ of \  4 + 0.5  \times  0.2 - 0.003

iii) 3.1- 2.4  \div  0.5 \ of \  3  \times  0.75 + 0.05      iv) 36.4 - 3.6 \div 2  \times  2.5 of 4.6

v) 6.5-0.5 \ of \  (9.8 - 3.7) + 4.3 \times 05      vi) 8.1- [2 + 3.51 of(7.1 - 3.4 \times 05)]

Answer:

i) 3.5 \div 5 \ of \  5 + 0.5  \times  0.3 - 0.1

= 7  \times  5 + 0.15 - 0.1 = 35 +0.05 = 35.05

ii) 3.6 \div 4 \ of \  4 + 0.5  \times  0.2 - 0.003

= 9  \times  4 + 0.1 - 0.003 = 36 + 0.097 = 36.097

iii) 3.1- 2.4  \div  0.5 \ of \  3  \times  0.75 + 0.05

= 3.1 - 4.8  \times  3  \times  0.75 + 0.05 = 3.1 - 10.8 + 0.05 = -7.65

iv) 36.4 - 3.6 \div 2  \times  2.5 of 4.6

= 36.4 - 3  \times  2.5  \times . 4.6 = 36.4 - 34.5 = 1.9

v) 6.5-0.5 \ of \  (9.8 - 3.7) + 4.3 \times 05

= 6.5 - 0.5  \times  6.1 + 26.015 = 6.5 - 3.05 + 26.015 = 29.465

vi) 8.1- [2 + 3.51 of(7.1 - 3.4 \times 05)]

=8.1 - [2 + 3.51  \times  0.13] = 5.6437

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Question 14: Simplify:

i)  \frac{ 4.8 \times 8-3.8  \times  3.8 }{ 4.8+3.8 }      ii)  \frac{ 6.3 \times 3-3.7  \times  3.7 }{ 6.3  \times  6.3 + 2  \times  6.3  \times  3.7 + 3.7  \times  3.7 }

iii)  \frac{ 3.2  \times  3.2 - 2  \times 3.2  \times  2.7 + 2.7  \times  2.7 }{ 3.2  \times  3.2+ 1.8  \times  1.8 + 2 \times  3.2  \times  1.8 }      iv)  \frac{ 4.1 \times 1-2  \times 4.1  \times  3.7 + 3.7  \times  3.7 }{ 3.7  \times  3.7-2  \times  3.7  \times  3.5 +3.5  \times  3.5 }

v)  \frac{ 1.7 \times 7  \times  l.7 - 0.9  \times  0.9  \times  0.9 }{ 1.7  \times  1.7 + 1.7  \times  0.9 +0.9  \times  0.9 }       vi)  \frac{ 2.3 \times 3  \times 2.3 + 1.8  \times 1.8  \times  1.8 }{ 2.3  \times  2.3- 2.3 \times  1.8 + 1.8  \times  1.8 }

Answer:

i)  \frac{ 4.8 \times 8-3.8  \times  3.8 }{ 4.8+3.8 } = 1

ii)  \frac{ 6.3 \times 3-3.7  \times  3.7 }{ 6.3  \times  6.3 + 2  \times  6.3  \times  3.7 + 3.7  \times  3.7 } = \frac{26}{100} =0.26

iii)  \frac{ 3.2  \times  3.2 - 2  \times 3.2  \times  2.7 + 2.7  \times  2.7 }{ 3.2  \times  3.2+ 1.8  \times  1.8 + 2 \times  3.2  \times  1.8 } = \frac{0.25}{25} =0.01

iv)  \frac{ 4.1 \times 1-2  \times 4.1  \times  3.7 + 3.7  \times  3.7 }{ 3.7  \times  3.7-2  \times  3.7  \times  3.5 +3.5  \times  3.5 } = \frac{0.16}{0.04} =4

v)  \frac{ 1.7 \times 7  \times  l.7 - 0.9  \times  0.9  \times  0.9 }{ 1.7  \times  1.7 + 1.7  \times  0.9 +0.9  \times  0.9 } = \frac{4.184}{5.642} =0.74158

vi)  \frac{ 2.3 \times 3  \times 2.3 + 1.8  \times 1.8  \times  1.8 }{ 2.3  \times  2.3- 2.3 \times  1.8 + 1.8  \times  1.8 } = \frac{17.999}{4.39} =4.1