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]
Answers
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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