2 Mark Question

Question 12 Marks

Find the value of:
$\Big(\frac{1}{2}\Big)^{-2}+\Big(\frac{1}{3}\Big)^{-2}+\Big(\frac{1}{4}\Big)^{-2}$

Answer

$\Big(\frac{1}{2}\Big)^{-2}+\Big(\frac{1}{3}\Big)^{-2}+\Big(\frac{1}{4}\Big)^{-2}$
$=(2)^2+(3)^2+(4)^2$
$=4+9+16$
$=29$

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Question 22 Marks

1 micron $=\frac{1}{1000000}\text{m}$. Express it in standard form.

Answer

$1\ \text{micron}=\frac{1}{1000000}$
$=\frac{1}{10^6}$
$=(1\times10^{-6})$

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Question 32 Marks

Evaluate:
$\Bigg\{\Big(\frac{1}{3}\Big)^{-3}-\Big(\frac{1}{2}\Big)^{-3}\Bigg\}\div\Big(\frac{1}{4}\Big)^{-3}$

Answer

$\Bigg\{\Big(\frac{1}{3}\Big)^{-3}-\Big(\frac{1}{2}\Big)^{-3}\Bigg\}\div\Big(\frac{1}{4}\Big)^{-3}$
$=\Big\{(3)^3-(2)^3\Big\}\div(4)^3$
$=(27-8)\div64$
$=\frac{19}{64}$

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Question 42 Marks

Write the following numbers in usual form:
$6.82 \times 10^{-6}$

Answer

$6.82\times10^{-6}$
$=\frac{682}{100}\times\frac{1}{10^6}$
$=\frac{682}{10^2\times10^6}$
$=\frac{682}{10^{(2+6)}}$
$=\frac{682}{10^8}$
$=\frac{682}{100000000}$
$=0.00000682$

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Question 52 Marks

Evaluate:
$\Big(\frac{-2}{3}\Big)^{-3}\times\Big(\frac{-2}{3}\Big)^{-2}$

Answer

$\Big(\frac{-2}{3}\Big)^{-3}\times\Big(\frac{-2}{3}\Big)^{-2}$$=\Big(\frac{3}{-2}\Big)^{3}\times\Big(\frac{3}{-2}\Big)^{2}$
$=\frac{3^3}{-2^3}\times\frac{3^3}{-2^3}$
$=\frac{3^{(3+2)}}{-2^{(3+2)}}$
$=\frac{3^5}{-2^5}$
$=\frac{-243}{32}$

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Question 62 Marks

Write the following numbers in standard form:
0.00000165

Answer

$0.00000165$
$=\frac{165}{100000000}$
$=\frac{165}{10^8}$
$=165\times10^{-8}$
$=1.65\times100\times10^{-8}$
$=1.65\times10^2\times10^{-8}$
$=1.65\times10^{-6}$

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Question 72 Marks

Evaluate $\Big[\big(5^{-1}\times3^{-1}\big)\div6^{-1}\Big]$

Answer

$\Big[\big(5^{-1}\times3^{-1}\big)\div6^{-1}\Big]$$=\Big(\frac{1}{5}\times\frac{1}{3}\Big)^{-1}\div\frac{1}{6}$
$=\Big(\frac{1}{15}\Big)^{-1}\div\frac{1}{6}$
$=(15)^1\div\frac{1}{6}$ $=15\times\frac{6}{1}$ $=90$

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Question 82 Marks

Find the value of:
$\big(2^{0}+3^{-1}\big)\times3^2$

Answer

$(2^{0}+3^{-1})\times3^2$
$=\Big(1+\frac{1}{3}\Big)\times9$
$=\frac{3+1}{3}\times9$
$=\frac{4}{3}\times9$
$=12$

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Question 92 Marks

Size of a bacteria = 0.0000004m. Express it in standard form.

Answer

Size of bacteria = 0.0000004m
$=\frac{4}{10000000}\text{m}$
$=\frac{4}{10^7}\text{m}$
$=(4\times10^{-7})\text{m}$

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Question 102 Marks

Write the following numbers in usual form:
$5.673\times10^{-4}$

Answer

$5.673\times10^{-4}$
$=\frac{5673}{10000}\times{10^{-4}}$
$=\frac{5673}{10^3\times10^4}$
$=\frac{5673}{10^{7}}$
$=0.0005673$

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Question 112 Marks

Evaluate:
$\bigg\{\Big(\frac{-2}{3}\Big)^3\bigg\}^{-2}$

Answer

$\bigg\{\Big(\frac{-2}{3}\Big)^3\bigg\}^{-2}$$=\Big(\frac{-2}{3}\Big)^{-6}$
$=\Big(\frac{3}{-2}\Big)^{6}$
$=\frac{3^6}{-2^6}$
$=\frac{729}{64}$

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Question 122 Marks

Write the following numbers in usual form:
$4.1253 \times 10^7$

Answer

$4.1253\times10^7$
$=\frac{41253}{10000}\times10^7$
$=\frac{41253}{10^4}\times10^7$
$=41253\times10^3$
$=41253000$

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Question 132 Marks

Write the following numbers in standard form:
0.0006

Answer

$0.0006$
$=\frac{6}{10000}$
$=\frac{6}{10^4}$
$=6.10^{-4}$

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Question 142 Marks

Write the following numbers in usual form:
$1.679\times10^9$

Answer

$1.679\times10^9$
$=\frac{1679}{1000}\times10^9$
$=\frac{1679}{10^3}\times10^9$
$=1679\times10^6$
$=1679000000$

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Question 152 Marks

Evaluate:
$\bigg\{\Big(\frac{3}{2}\Big)^{-2}\bigg\}^{2}$

Answer

$\bigg\{\Big(\frac{3}{2}\Big)^{-2}\bigg\}^{2}$$=\Big(\frac{3}{2}\Big)^{-2\times2}=\Big(\frac{3}{2}\Big)^{-4}$
$=\Big(\frac{2}{3}\Big)^{4}$
$=\frac{2}{3}\times\frac{2}{3}\times\frac{2}{3}\times\frac{2}{3}$
$=\frac{16}{81}$

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Question 162 Marks

Write the following numbers in usual form:
$5.17 \times 10^6$

Answer

$5.17\times10^6$
$=\frac{517}{100}\times10^6$
$=\frac{517}{10^2}\times10^6$
$=517\times10^4$
$=5170000$

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Question 172 Marks

Write the following numbers in standard form:
0.0027

Answer

$ 0.0027$
$=\frac{27}{10000}$
$=\frac{27}{10^4}$
$=27\times10^{-4}$
$=2.7\times10^1\times10^{-4}$
$=2.7\times10^{-3}$

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Question 182 Marks

Write the following numbers in standard form:
0.00000083

Answer

$0.00000083$
$=\frac{83}{100000000}$
$=\frac{83}{10^8}$
$=83\times10^{-8}$
$=8.3\times10^{1}\times10^{-8}$
$=8.3\times10^{-7}$

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Question 192 Marks

Evaluate:
$\Bigg\{\Big(\frac{4}{3}\Big)^{-1}-\Big(\frac{1}{4}\Big)^{-1}\Bigg\}^{-1}$

Answer

$\Bigg\{\Big(\frac{4}{3}\Big)^{-1}-\Big(\frac{1}{4}\Big)^{-1}\Bigg\}^{-1}$$=\Bigg\{\Big(\frac{3}{4}\Big)^{1}-\Big(\frac{4}{1}\Big)^{1}\Bigg\}^{-1}$
$=\Big(\frac{3}{4}-\frac{4}{1}\Big)^{-1}$
$=\Big(\frac{3-16}{4}\Big)^{-1}$
$=\Big(\frac{-13}{4}\Big)^{-1}$
$=\frac{-4}{13}$

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Question 202 Marks

Evaluate:
$\Bigg[\bigg\{\Big(\frac{-1}{3}\Big)^{2}\bigg\}^{-2}\Bigg]^{-1}$

Answer

$\Bigg[\bigg\{\Big(\frac{-1}{3}\Big)^{2}\bigg\}^{-2}\Bigg]^{-1}$$=\Big(\frac{-1}{3}\Big)^{2\times(-2)(-1)}$
$=\Big(\frac{-1}{3}\Big)^{4}$
$=\Big(\frac{-1}{3}\Big)\times\Big(\frac{-1}{3}\Big)\times\Big(\frac{-1}{3}\Big)\times\Big(\frac{-1}{3}\Big)$
$=\frac{1}{81}$

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Question 212 Marks

Evaluate:
$\Big(\frac{-3}{5}\Big)^{-4}\times\Big(\frac{-2}{5}\Big)^{2}$

Answer

$\Big(\frac{-3}{5}\Big)^{-4}\times\Big(\frac{-2}{5}\Big)^{2}$$=\Big(\frac{5}{-3}\Big)^{4}\times\Big(\frac{-2}{5}\Big)^{2}$
$=\frac{5^4}{-3^4}\times\frac{-2^2}{5^2}$
$=5^{(4-2)}\times\frac{-2^2}{-3^4}$
$=5^2\times\frac{-2^2}{-3^4}$
$=25\times\frac{4}{81}$
$=\frac{100}{81}$

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Question 222 Marks

Evaluate:
$\bigg\{\Big(\frac{-2}{3}\Big)^2\bigg\}^{-2}$

Answer

$\bigg\{\Big(\frac{-2}{3}\Big)^2\bigg\}^{-2}$$=\Big(\frac{-2}{3}\Big)^{2\times(-2)}$
$=\Big(\frac{-2}{3}\Big)^{-4}$
$=\Big(\frac{-3}{2}\Big)^{4}$ $=\frac{(-3)\times(-3)\times(-3)\times(-3)}{2\times2\times2\times2}$ $=\frac{81}{16}$

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Question 232 Marks

Write the following numbers in usual form:
$2.5 \times 10^4$

Answer

$2.5\times10^4$
$=\frac{25}{10}\times10^4$
$=25\times10^3$
$=25000$

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Question 242 Marks

Write the following numbers in standard form:
0.00000000689

Answer

$=0.00000000689$
$=\frac{689}{100000000000}$
$=\frac{689}{10^{11}}$
$=689\times10^{-11}$
$=6.89\times100\times10^{-11}$
$=6.89\times10^2\times10^{-11}$
$=6.89\times10^{-9}$

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Question 252 Marks

Write the following numbers in standard form:
0.0000000534

Answer

$0.0000000534$
$=\frac{534}{10000000000}$
$=\frac{534}{10^{10}}$
$=534\times10^{-10}$
$=5.34\times100\times10^{-10}$
$=5.34\times10^2\times10^{-10}$
$=5.34\times10^{-8}$

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Question 262 Marks

Write the following numbers in usual form:
$5 \times 10^{-7}$

Answer

$5\times10^{-7}$
$=\frac{5}{10^7}$
$=\frac{5}{10000000}$
$=0.0000005$

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Question 272 Marks

Write the following numbers in usual form:
$4.129 \times 10^{-3}$

Answer

$4.129\times10^{-3}$
$=\frac{4129}{1000}\times\frac{1}{10^{3}}$
$=\frac{4129}{10^3\times10^3}$
$=\frac{4129}{10^{(3+3)}}$
$=\frac{4129}{10^6}$
$=\frac{4129}{1000000}$
$=0.004129$

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Question 282 Marks

Write the following numbers in usual form:
$2.06 \times 10^{-5}$

Answer

$2.06\times10^{-5}$
$=\frac{2.06}{10^5}$
$=\frac{2.06}{100000}$
$=\frac{206}{100000\times100}$
$=\frac{206}{10000000}$
$=0.0000206$

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Question 292 Marks

Thickness of a paper = 0.03mm. Express it in standard form.

Answer

Thickness of a paper = 0.03mm
$=\frac{3}{100}\text{mm}$
$=\frac{3}{10^2}\text{mm}$
$=(3\times10^{-2})\text{mm}$

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Question 302 Marks

Write the following numbers in usual form:
$1.8 \times 10^{-2}$

Answer

$1.8\times10^{-2}$
$=\frac{18}{10}\times\frac{1}{10^{2}}$
$=\frac{18}{10\times10^2}$
$=\frac{18}{10^{(1+2)}}$
$=\frac{18}{10^3}$
$=\frac{18}{1000}=0.018$

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Question 312 Marks

Express the following in standard form:0.000027

Answer

$0.000027$$=\frac{27}{100000}$
$=\frac{27}{10^6}$
$=\frac{2.7\times10}{10^6}$
$=2.7\times10^{(1-6)}$
$=2.7\times10^{-5}$

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Question 322 Marks

Express the following in standard form:
$180000$

Answer

$180000$
$=18 \times 10000$
$=18 \times 10^4$
$=18 \times 10 \times 10^4$
$=18 \times 10^{(1+4)}$
$=18 \times 10^5$

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Question 332 Marks

Find the value of:
$\big(2^{-1}\times3^{-1}\big)\div2^{-3}$

Answer

$\big(2^{-1}\times3^{-1}\big)\div2^{-3}$$=\Big(\frac{1}{2}\times\frac{1}{3}\Big)\div\frac{1}{2^3}$
$=\frac{1}{6}\div\frac{1}{8}$
$=\frac{1}{6}\times\frac{8}{1}$
$=\frac{4}{3}$

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Question 342 Marks

Write the following numbers in usual form:
$6.912 \times 10^8$

Answer

$6.912\times 10^8$
$=\frac{6.912}{1000}\times10^8$
$=\frac{6912}{10^3}\times10^8$
$=6912\times10^5$
$=691200000$

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