Question

How many times larger is 9×10^−8 than 3×10^−12 ?

options:

3×10^3

6×10^−4

6×10^−3

3×10^4

Answer 1

To find how many times larger \( 9 \times 10^{-8} \) is than \( 3 \times 10^{-12} \), we need to divide the two numbers:

\[
\frac{9 \times 10^{-8}}{3 \times 10^{-12}}
\]

We can simplify this expression by dividing the coefficients and using the rules of exponents:

1. Divide the coefficients: \(\frac{9}{3} = 3\)
2. For the powers of ten, subtract the exponent in the denominator from the exponent in the numerator:

\[
10^{-8} \div 10^{-12} = 10^{-8 - (-12)} = 10^{-8 + 12} = 10^{4}
\]

Now, combining both parts:

\[
3 \times 10^{4}
\]

Thus, \( 9 \times 10^{-8} \) is \( 3 \times 10^{4} \) times larger than \( 3 \times 10^{-12} \).

The correct answer is:

\[
\boxed{3 \times 10^{4}}
\]