The microcurrent through the electrode in a delicate circuit is usually held constant at \(3.6 * 10^{-8}\) amps. Because of a defect in another part of the circuit, the current was 1,000 times smaller. What was the current, in amps, caused by this defect?

A. \(3.6*10^{-8000}\)

B. \(3.6*10^{-24}\)

C. \(3.6*10^{-11}\)

D. \(3.6*10^{-5}\)

E. \(3.6*10^{\frac{-8}{3}}\)

1,000 times smaller means we divide it by 1,000 which is basically 10^3

So (3.6 * 10^-8)/(10^3) = 3.6 * 10^(-8 -3) = 3.6 * 10^-11

Answer choice C

thanks

Key concept #1: If X is 1000 times smaller than Y, we can write: X = Y/1000

Key concept #2: \(\frac{ab}{c}=(a)(\frac{b}{c})\)


So, the measure of the resulting current = \(\frac{3.6*10^{(-8)}}{1000}\)

Rewrite as: \(\frac{3.6*10^{(-8)}}{10^3}\)

Use Concept #2 to rewrite as: \((3.6)\frac{10^{(-8)}}{10^3}\)

Apply Quotient Law for exponents to get: \((3.6)(10^{(-8-3)})\)

Simplify: \((3.6)(10^{(-11)})\)

Answer: C

Cheers,
Brent

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