Question 1: Convert the following decimals into like decimals:

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

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 $88.08765$

 i) $0.1$$0.1$ and $0.01$$0.01$ $0.1 > 0.01$$0.1 > 0.01$ ii) $4.001$$4.001$ and $3.987$$3.987$ $4.001 > 3.987$$4.001 > 3.987$ iii) $0.1$$0.1$ and $0.0999$$0.0999$ $0.1 > 0.0999$$0.1 > 0.0999$ iv) $88.123$$88.123$ and $88.08765$$88.08765$ $88.123 > 88.08765$$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) $153.607 4$

i) $3.57$

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

ii) $0.864$

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

iii) $1.002$

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

iv) $153.607 4$

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

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

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

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

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

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

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

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

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

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

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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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) $2.38 + 23.8 + 238.28 + 28.383 + 0.382$

 i) $0.351 + 2.96 + 19.6 + 0.005 + 137.09 + 0.0809$$0.351 + 2.96 + 19.6 + 0.005 + 137.09 + 0.0809$ $\rightline{ 0.3510} \\ \rightline{2.9600} \\ \rightline{19.6000} \\ \rightline{0.0050} \\ \rightline{137.0900} \\ \rightline{+ \underline{\ \ \ \ 0.0809}} \\ \rightline{\underline{160.0869}}$$\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$$9.89 + 0.989 + 98.09 + 989.098 + 98.0989$ $\rightline{ 9.8900} \\ \rightline{0.9890} \\ \rightline{98.0900} \\ \rightline{989.0980} \\ \rightline{+ \underline{\ \ \ \ 98.0989}} \\ \rightline{\underline{1196.1659}}$$\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$$66.666 + 6.6 + 6.066 + 666.006$ $\rightline{ 66.666} \\ \rightline{6.600} \\ \rightline{6.066} \\ \rightline{+ \underline{\ \ 666.006}} \\ \rightline{\underline{745.338}}$$\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$$2.38 + 23.8 + 238.28 + 28.383 + 0.382$ $\rightline{ 2.380} \\ \rightline{23.800} \\ \rightline{238.280} \\ \rightline{28.383} \\ \rightline{+ \underline{\ \ \ \ 0.382}} \\ \rightline{\underline{293.225}}$$\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 $0.198$

 i) Increase $37.984$$37.984$ by $7.089$$7.089$ $\rightline{ 37.984} \\ \rightline{+ \underline{\ \ 7.089}} \\ \rightline{\underline{45.073}}$$\rightline{ 37.984} \\ \rightline{+ \underline{\ \ 7.089}} \\ \rightline{\underline{45.073}}$ ii) Increase $99.9809$$99.9809$ by $0.198$$0.198$ $\rightline{ 99.9809} \\ \rightline{+ \underline{\ \ 0.1980}} \\ \rightline{\underline{100.1789}}$$\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 $0.1$

 i) $16.48$$16.48$ from $20.3$$20.3$ $\rightline{ 20.30} \\ \rightline{- \underline{\ \ 16.48}} \\ \rightline{\underline{3.82}}$$\rightline{ 20.30} \\ \rightline{- \underline{\ \ 16.48}} \\ \rightline{\underline{3.82}}$ ii) $0.0051$$0.0051$ from $0.01$$0.01$ $\rightline{ 0.0100} \\ \rightline{- \underline{\ \ 0.0051}} \\ \rightline{\underline{0.0049}}$$\rightline{ 0.0100} \\ \rightline{- \underline{\ \ 0.0051}} \\ \rightline{\underline{0.0049}}$ iii) $9.841$$9.841$ from $11.001$$11.001$  $\rightline{ 11.001} \\ \rightline{- \underline{\ \ 9.841}} \\ \rightline{\underline{1.160}}$$\rightline{ 11.001} \\ \rightline{- \underline{\ \ 9.841}} \\ \rightline{\underline{1.160}}$ iv) $0.0838$$0.0838$ from $0.1$$0.1$ $\rightline{ 0.1000} \\ \rightline{- \underline{\ \ 0.0838}} \\ \rightline{\underline{0.0162}}$$\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 $0.0001$

 i) Decrease $10$$10$ by $0.854$$0.854$ $\rightline{ 10.000} \\ \rightline{- \underline{\ \ 0.854}} \\ \rightline{\underline{9.146}}$$\rightline{ 10.000} \\ \rightline{- \underline{\ \ 0.854}} \\ \rightline{\underline{9.146}}$ ii) Decrease $11$$11$ by $10.9091$$10.9091$ $\rightline{ 11.0000} \\ \rightline{- \underline{\ \ 10.9091}} \\ \rightline{\underline{0.0909}}$$\rightline{ 11.0000} \\ \rightline{- \underline{\ \ 10.9091}} \\ \rightline{\underline{0.0909}}$ iii) Take $2.53$$2.53$ from $25.3$$25.3$ $\rightline{ 25.30} \\ \rightline{- \underline{\ \ 2.53}} \\ \rightline{\underline{22.77}}$$\rightline{ 25.30} \\ \rightline{- \underline{\ \ 2.53}} \\ \rightline{\underline{22.77}}$ iv) Find the difference between $0.1$$0.1$ and $0.0001$$0.0001$ $\rightline{ 0.1000} \\ \rightline{- \underline{\ \ 0.0001}} \\ \rightline{\underline{0.0999}}$$\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) $1.11 \times 0.11 \times 1.1 \times 1.01 \times 1000$

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) $1.21663 \div 0.89$

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

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)  $\displaystyle \frac{ 4.8 \times 8-3.8 \times 3.8 }{ 4.8+3.8 }$

ii)  $\displaystyle \frac{ 6.3 \times 3-3.7 \times 3.7 }{ 6.3 \times 6.3 + 2 \times 6.3 \times 3.7 + 3.7 \times 3.7 }$

iii)  $\displaystyle \frac{ 3.2 \times 3.2 - 2 \times 3.2 \times 2.7 + 2.7 \times 2.7 }{ 3.2 \times 3.2+ 1.8 \times 1.8 + 2 \times 3.2 \times 1.8 }$

iv)  $\displaystyle \frac{ 4.1 \times 1-2 \times 4.1 \times 3.7 + 3.7 \times 3.7 }{ 3.7 \times 3.7-2 \times 3.7 \times 3.5 +3.5 \times 3.5 }$

v)  $\displaystyle \frac{ 1.7 \times 7 \times l.7 - 0.9 \times 0.9 \times 0.9 }{ 1.7 \times 1.7 + 1.7 \times 0.9 +0.9 \times 0.9 }$

vi)  $\displaystyle \frac{ 2.3 \times 3 \times 2.3 + 1.8 \times 1.8 \times 1.8 }{ 2.3 \times 2.3- 2.3 \times 1.8 + 1.8 \times 1.8 }$

i)  $\displaystyle \frac{ 4.8 \times 8-3.8 \times 3.8 }{ 4.8+3.8 } = 1$
ii)  $\displaystyle \frac{ 6.3 \times 3-3.7 \times 3.7 }{ 6.3 \times 6.3 + 2 \times 6.3 \times 3.7 + 3.7 \times 3.7 } = \frac{26}{100} =0.26$
iii)  $\displaystyle \frac{ 3.2 \times 3.2 - 2 \times 3.2 \times 2.7 + 2.7 \times 2.7 }{ 3.2 \times 3.2+ 1.8 \times 1.8 + 2 \times 3.2 \times 1.8 } = \frac{0.25}{25} =0.01$
iv)  $\displaystyle \frac{ 4.1 \times 1-2 \times 4.1 \times 3.7 + 3.7 \times 3.7 }{ 3.7 \times 3.7-2 \times 3.7 \times 3.5 +3.5 \times 3.5 } = \frac{0.16}{0.04} =4$
v)  $\displaystyle \frac{ 1.7 \times 7 \times l.7 - 0.9 \times 0.9 \times 0.9 }{ 1.7 \times 1.7 + 1.7 \times 0.9 +0.9 \times 0.9 } = \frac{4.184}{5.642} =0.74158$
vi)  $\displaystyle \frac{ 2.3 \times 3 \times 2.3 + 1.8 \times 1.8 \times 1.8 }{ 2.3 \times 2.3- 2.3 \times 1.8 + 1.8 \times 1.8 } = \frac{17.999}{4.39} =4.1$