Write the following in scientific notation: $(200)^{3}$

4 \times 10^{4}

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8 \times 10^{6}

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6 \times 10^{6}

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8 \times 10^{8}

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Solution

The correct option is B $(8 \times 10^{6})$
Given $(200)^{3} = (2 \times 100)^{3}$
Using the rule of $(a \times b)^{m} = a^{m} \times b^{m}$
$\Rightarrow (200)^{3} = (2)^{3} \times (100)^{3}$
$= 2^{3} \times (10^{2})^{3}$ [Since, $100 = 10^{2}$ ]
$= 2^{3} \times 10^{2 \times 3}$ [Since, $(a^{m})^{n} = a^{(m \times n)}$ ]
$= 8 \times 10^{6}$
$∴ (200)^{3} = 8 \times 10^{6}$

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Q. Write the number :

4 \times 10^{6} + 8 \times 10^{5} + 6 \times 10^{4} + 4 \times 10^{3} + 4 \times 10^{2} + 6 \times 10 + 9 \times 10^{0}

Write the numeral whose expanded form is given below:
(i) $6 \times 10^{4} + 3 \times 10^{3} + 0 \times 10^{2} + 7 \times 10^{1} + 8 \times 10^{0}$
(ii) $9 \times 10^{6} + 7 \times 10^{5} + 0 \times 10^{4} + 3 \times 10^{3} + 4 \times 10^{2} + 6 \times 10^{1} + 2 \times 10^{0}$
(iii) $8 \times 10^{5} + 6 \times 10^{4} + 4 \times 10^{3} + 2 \times 10^{2} + 9 \times 10^{1} + 6 \times 10^{0}$