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$\Big(\frac{1}{2}\Big)^{-2}+\Big(\frac{1}{3}\Big)^{-2}+\Big(\frac{1}{4}\Big)^{-2}$ $=(2)^2+(3)^2+(4)^2$ $=4+9+16$ $=29$
View full question & answer→Question 22 Marks
$1$ micron $=\frac{1}{1000000}\text{m}$. Express it in standard form.
Answer$1\ \text{micron}=\frac{1}{1000000}$ $=\frac{1}{10^6}$ $=(1\times10^{-6})$
View full question & answer→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 $\Bigg\{\Big(\frac{1}{3}\Big)^{-3}-\Big(\frac{1}{2}\Big)^{-3}\Bigg\}\div\Big(\frac{1}{4}\Big)^{-3}$
$=\Big\{(3)^3-(2)^3\Big\}\div(4)^3$
$=(27-8)\div64$
$=\frac{19}{64}$
View full question & answer→Question 42 Marks
Write the following numbers in usual form:
$6.82 × 10^{-6}$
Answer$6.82\times10^{-6}$
$=\frac{682}{100}\times\frac{1}{10^6}$
$=\frac{682}{10^2\times10^6}$
$=\frac{682}{10^{(2+6)}}$
$=\frac{682}{10^8}$
$=\frac{682}{100000000}$
$=0.00000682$
View full question & answer→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}$$=\Big(\frac{3}{-2}\Big)^{3}\times\Big(\frac{3}{-2}\Big)^{2}$
$=\frac{3^3}{-2^3}\times\frac{3^3}{-2^3}$
$=\frac{3^{(3+2)}}{-2^{(3+2)}}$
$=\frac{3^5}{-2^5}$
$=\frac{-243}{32}$
View full question & answer→Question 62 Marks
Write the following numbers in standard form: $0.00000165$
Answer$0.00000165$
$=\frac{165}{100000000}$
$=\frac{165}{10^8}$
$=165\times10^{-8}$
$=1.65\times100\times10^{-8}$
$=1.65\times10^2\times10^{-8}$
$=1.65\times10^{-6}$
View full question & answer→Question 72 Marks
Evaluate $\Big[\big(5^{-1}\times3^{-1}\big)\div6^{-1}\Big]$
Answer$\Big[\big(5^{-1}\times3^{-1}\big)\div6^{-1}\Big]$$=\Big(\frac{1}{5}\times\frac{1}{3}\Big)^{-1}\div\frac{1}{6}$
$=\Big(\frac{1}{15}\Big)^{-1}\div\frac{1}{6}$
$=(15)^1\div\frac{1}{6}$ $=15\times\frac{6}{1}$ $=90$
View full question & answer→Question 82 Marks
Find the value of:
$\big(2^{0}+3^{-1}\big)\times3^2$
Answer $(2^{0}+3^{-1})\times3^2$
$=\Big(1+\frac{1}{3}\Big)\times9$
$=\frac{3+1}{3}\times9$
$=\frac{4}{3}\times9$
$=12$
View full question & answer→Question 92 Marks
Size of a bacteria $= 0.0000004\ m.$ Express it in standard form.
AnswerSize of bacteria $= 0.0000004\ m$
$=\frac{4}{10000000}\text{m}$
$=\frac{4}{10^7}\text{m}$
$=(4\times10^{-7})\text{m}$
View full question & answer→Question 102 Marks
Write the following numbers in usual form:
$5.673 × 10^{-4}$
Answer$5.673\times10^{-4}$
$=\frac{5673}{10000}\times{10^{-4}}$
$=\frac{5673}{10^3\times10^4}$
$=\frac{5673}{10^{7}}$
$=0.0005673$
View full question & answer→Question 112 Marks
Evaluate: $\bigg\{\Big(\frac{-2}{3}\Big)^3\bigg\}^{-2}$
Answer$\bigg\{\Big(\frac{-2}{3}\Big)^3\bigg\}^{-2}$$=\Big(\frac{-2}{3}\Big)^{-6}$
$=\Big(\frac{3}{-2}\Big)^{6}$
$=\frac{3^6}{-2^6}$
$=\frac{729}{64}$
View full question & answer→Question 122 Marks
Write the following numbers in usual form:
$4.1253 × 10^7$
Answer$4.1253\times10^7$
$=\frac{41253}{10000}\times10^7$
$=\frac{41253}{10^4}\times10^7$
$=41253\times10^3$
$=41253000$
View full question & answer→Question 132 Marks
Write the following numbers in standard form:
$0.0006$
Answer$0.0006$
$=\frac{6}{10000}$
$=\frac{6}{10^4}$
$=6.10^{-4}$
View full question & answer→Question 142 Marks
Write the following numbers in usual form:
$1.679 × 10^9$
Answer$1.679\times10^9$
$=\frac{1679}{1000}\times10^9$
$=\frac{1679}{10^3}\times10^9$
$=1679\times10^6$
$=1679000000$
View full question & answer→Question 152 Marks
Evaluate: $\bigg\{\Big(\frac{3}{2}\Big)^{-2}\bigg\}^{2}$
Answer$\bigg\{\Big(\frac{3}{2}\Big)^{-2}\bigg\}^{2}$$=\Big(\frac{3}{2}\Big)^{-2\times2}=\Big(\frac{3}{2}\Big)^{-4}$
$=\Big(\frac{2}{3}\Big)^{4}$
$=\frac{2}{3}\times\frac{2}{3}\times\frac{2}{3}\times\frac{2}{3}$
$=\frac{16}{81}$
View full question & answer→Question 162 Marks
Write the following numbers in usual form:
$5.17 × 10^6$
Answer$5.17\times10^6$
$=\frac{517}{100}\times10^6$
$=\frac{517}{10^2}\times10^6$
$=517\times10^4$
$=5170000$
View full question & answer→Question 172 Marks
Write the following numbers in standard form: $0.0027$
Answer$ 0.0027$
$=\frac{27}{10000}$
$=\frac{27}{10^4}$
$=27\times10^{-4}$
$=2.7\times10^1\times10^{-4}$
$=2.7\times10^{-3}$
View full question & answer→Question 182 Marks
Write the following numbers in standard form: $0.00000083$
Answer$0.00000083$
$=\frac{83}{100000000}$
$=\frac{83}{10^8}$
$=83\times10^{-8}$
$=8.3\times10^{1}\times10^{-8}$
$=8.3\times10^{-7}$
View full question & answer→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}$$=\Bigg\{\Big(\frac{3}{4}\Big)^{1}-\Big(\frac{4}{1}\Big)^{1}\Bigg\}^{-1}$
$=\Big(\frac{3}{4}-\frac{4}{1}\Big)^{-1}$
$=\Big(\frac{3-16}{4}\Big)^{-1}$
$=\Big(\frac{-13}{4}\Big)^{-1}$
$=\frac{-4}{13}$
View full question & answer→Question 202 Marks
Evaluate: $\Bigg[\bigg\{\Big(\frac{-1}{3}\Big)^{2}\bigg\}^{-2}\Bigg]^{-1}$
Answer$\Bigg[\bigg\{\Big(\frac{-1}{3}\Big)^{2}\bigg\}^{-2}\Bigg]^{-1}$$=\Big(\frac{-1}{3}\Big)^{2\times(-2)(-1)}$
$=\Big(\frac{-1}{3}\Big)^{4}$
$=\Big(\frac{-1}{3}\Big)\times\Big(\frac{-1}{3}\Big)\times\Big(\frac{-1}{3}\Big)\times\Big(\frac{-1}{3}\Big)$
$=\frac{1}{81}$
View full question & answer→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}$$=\Big(\frac{5}{-3}\Big)^{4}\times\Big(\frac{-2}{5}\Big)^{2}$
$=\frac{5^4}{-3^4}\times\frac{-2^2}{5^2}$
$=5^{(4-2)}\times\frac{-2^2}{-3^4}$
$=5^2\times\frac{-2^2}{-3^4}$
$=25\times\frac{4}{81}$
$=\frac{100}{81}$
View full question & answer→Question 222 Marks
Evaluate: $\bigg\{\Big(\frac{-2}{3}\Big)^2\bigg\}^{-2}$
Answer$\bigg\{\Big(\frac{-2}{3}\Big)^2\bigg\}^{-2}$$=\Big(\frac{-2}{3}\Big)^{2\times(-2)}$
$=\Big(\frac{-2}{3}\Big)^{-4}$
$=\Big(\frac{-3}{2}\Big)^{4}$ $=\frac{(-3)\times(-3)\times(-3)\times(-3)}{2\times2\times2\times2}$ $=\frac{81}{16}$
View full question & answer→Question 232 Marks
Write the following numbers in usual form:
$2.5 × 10^4$
Answer$2.5\times10^4$
$=\frac{25}{10}\times10^4$
$=25\times10^3$
$=25000$
View full question & answer→Question 242 Marks
Write the following numbers in standard form: $0.00000000689$
Answer$=0.00000000689$
$=\frac{689}{100000000000}$
$=\frac{689}{10^{11}}$
$=689\times10^{-11}$
$=6.89\times100\times10^{-11}$
$=6.89\times10^2\times10^{-11}$
$=6.89\times10^{-9}$
View full question & answer→Question 252 Marks
Write the following numbers in standard form: $0.0000000534$
Answer$0.0000000534$
$=\frac{534}{10000000000}$
$=\frac{534}{10^{10}}$
$=534\times10^{-10}$
$=5.34\times100\times10^{-10}$
$=5.34\times10^2\times10^{-10}$
$=5.34\times10^{-8}$
View full question & answer→Question 262 Marks
Write the following numbers in usual form:
$5 × 10^{-7}$
Answer$5\times10^{-7}$
$=\frac{5}{10^7}$
$=\frac{5}{10000000}$
$=0.0000005$
View full question & answer→Question 272 Marks
Write the following numbers in usual form:
$4.129 × 10^{-3}$
Answer$4.129\times10^{-3}$
$=\frac{4129}{1000}\times\frac{1}{10^{3}}$
$=\frac{4129}{10^3\times10^3}$
$=\frac{4129}{10^{(3+3)}}$
$=\frac{4129}{10^6}$
$=\frac{4129}{1000000}$
$=0.004129$
View full question & answer→Question 282 Marks
Write the following numbers in usual form:
$2.06 × 10^{-5}$
Answer$2.06\times10^{-5}$
$=\frac{2.06}{10^5}$
$=\frac{2.06}{100000}$
$=\frac{206}{100000\times100}$
$=\frac{206}{10000000}$
$=0.0000206$
View full question & answer→Question 292 Marks
Thickness of a paper $= 0.03\ mm.$ Express it in standard form.
AnswerThickness of a paper $= 0.03\ mm$
$=\frac{3}{100}\text{mm}$
$=\frac{3}{10^2}\text{mm}$
$=(3\times10^{-2})\text{mm}$
View full question & answer→Question 302 Marks
Write the following numbers in usual form:
$1.8 × 10^{-2}$
Answer$1.8\times10^{-2}$
$=\frac{18}{10}\times\frac{1}{10^{2}}$
$=\frac{18}{10\times10^2}$
$=\frac{18}{10^{(1+2)}}$
$=\frac{18}{10^3}$
$=\frac{18}{1000}=0.018$
View full question & answer→Question 312 Marks
Express the following in standard form: $0.000027$
Answer$0.000027$$=\frac{27}{100000}$
$=\frac{27}{10^6}$
$=\frac{2.7\times10}{10^6}$
$=2.7\times10^{(1-6)}$
$=2.7\times10^{-5}$
View full question & answer→Question 322 Marks
Express the following in standard form:
$180000$
Answer$180000$
$= 18 × 10000$
$ =18 \times 10^4 $
$ =18 \times 10 \times 10^4 $
$ =18 \times 10^{(1+4)} $
$ =18 \times 10^5 $
View full question & answer→Question 332 Marks
Find the value of: $\big(2^{-1}\times3^{-1}\big)\div2^{-3}$
Answer$\big(2^{-1}\times3^{-1}\big)\div2^{-3}$$=\Big(\frac{1}{2}\times\frac{1}{3}\Big)\div\frac{1}{2^3}$
$=\frac{1}{6}\div\frac{1}{8}$
$=\frac{1}{6}\times\frac{8}{1}$
$=\frac{4}{3}$
View full question & answer→Question 342 Marks
Write the following numbers in usual form:
$6.912 × 10^8$
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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