Question

Scientific Notation Unit Test
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Question
For what value of a
will 8×103
be 40 times larger than a×102
?(1 point)

Answer 1

To find the value of \( a \) such that \( 8 \times 10^3 \) is 40 times larger than \( a \times 10^2 \), we can set up the equation:

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

Now, we'll simplify the right side:

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

Setting the two sides equal gives us:

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

Now, we can divide both sides by \( 10^2 \):

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

Now, we solve for \( a \):

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

Thus, the value of \( a \) is:

\[
\boxed{2}
\]