Question

For what value of will 8 × 10^3
be 40 times larger
than a*10^2?

Answer 1

We need to find the value of \( a \) such that:

\[
8 \times 10^3 = 40 \times (a \times 10^2)
\]

First, we simplify the right-hand side:

\[
40 \times (a \times 10^2) = 40a \times 10^2
\]

Now equate both sides of the equation:

\[
8 \times 10^3 = 40a \times 10^2
\]

To simplify the equation, we can divide both sides by \( 10^2 \):

\[
\frac{8 \times 10^3}{10^2} = \frac{40a \times 10^2}{10^2}
\]

This simplifies to:

\[
8 \times 10^{3-2} = 40a
\]
\[
8 \times 10^1 = 40a
\]
\[
8 \times 10 = 40a
\]
\[
80 = 40a
\]

Now, solving for \( a \):

\[
a = \frac{80}{40} = 2
\]

Thus, the value of \( a \) is \( \boxed{2} \).