Question

(2.5×10−10)(7×10−6)

Express your answer in scientific notation.

A. 1.75×1016

B. 1.75×10−15

C. 1.75×10−16

D. 1.75×10−17

Answer 1

The answer is: [B]: " 1.75 * 10⁻¹⁵ " .
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Note:
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(2.5 * 10⁻¹⁰)(7 * 10⁻⁶) = (2.5)*(7) *(10⁻¹⁰) *(10⁻⁶)

Note: (10⁻¹⁰) *(10⁻⁶) = 10⁽⁻¹⁰⁾⁺⁽⁻⁶⁾ = 10⁽⁻¹⁰⁻⁶⁾ = 10⁽⁻¹⁶⁾

{Note: xᵃ * xᵇ = x⁽ᵃ⁺ᵇ⁾ } ; ===> Property of exponents;

So; (2.5)*(7) *(10⁻¹⁰) *(10⁻⁶) = (2.5)*(7) * 10⁽⁻¹⁶⁾ ;

2.5 * 7 = 17.5 ;

so; (2.5)*(7) * 10⁽⁻¹⁶⁾ = 17.5 * 10⁻¹⁶
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SInce the answer choices are given in scientific notation;
in terms of "1.75"; we rewrite this value in such format to get the equivalent value; by dividing by "10" ; to get: "1.75 * 10⁻¹⁵ " (note: this value is equivalent; since the number of "zeros" is adjusted.
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The answer is: [B]: " 1.75 * 10⁻¹⁵ " .
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