Question

3. Express each of the following in the form k * 10 ^ n; (1 <= k < 10) (i) (1.25 * 10 ^ 7) / (5 * 10 ^ 3) (iii) (1.6 * 10 ^ 9)(5.0 * 10 ^ - 3) (ii) (2.5 * 10 ^ 10)(31.25 * 10 ^ - 5) (iv) [(3.4 * 10 ^ 4)(5.0 * 10 ^ - 3)] / [2.0 * 10 ^ 5]

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Answer 1

Answer:

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Step-by-step explanation:

Given :  \frac{1.25 \times 10^7}{5 \times 10^3}5×1031.25×107   (1.25 × 10raise to the power 7) ÷ (5× 10 raise to the power 3)

To find :  Express in k × 10 raise to the power n    ( 1 < k  < 10)

Solution:

\frac{1.25 \times 10^7}{5 \times 10^3}5×1031.25×107

=  \frac{1.25 \times 10^{(4+3)}}{5 \times 10^3}5×1031.25×10(4+3)

using nᵃ⁺ᵇ = nᵃ  × nᵇ

= \frac{1.25 \times 10^4 \times 10^3}{5 \times 10^3}5×1031.25×104×103

= \frac{1.25 \times 10^4 }{5 }51.25×104

= \frac{1.25 \times 10^3 \times 10 }{5 }51.25×103×10

= 1.25 x 10³  * 2

= 5 * 10³

\frac{1.25 \times 10^7}{5 \times 10^3}5×1031.25×107  = 5 * 10³

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