Question

An expression is shown.
(11 × 108)
(7 × 106) + (9 × 106)


Which expression is equivalent?
Responses
A 6.875 × 1016.875 × 10 1
B 1.74 × 10-51.74 × 10 -5
C 6.875 × 1056.875 × 10 5
D 1.74 × 105

Answer 1

To simplify the given expression:

\[
\frac{(11 \times 10^8)}{(7 \times 10^6) + (9 \times 10^6)}
\]

First, we simplify the denominator:

\[
(7 \times 10^6) + (9 \times 10^6) = (7 + 9) \times 10^6 = 16 \times 10^6
\]

Now, we rewrite the expression:

\[
\frac{(11 \times 10^8)}{(16 \times 10^6)}
\]

To divide, we divide the coefficients and subtract the exponents of 10:

\[
\frac{11}{16} \times 10^{8-6} = \frac{11}{16} \times 10^2
\]

Now we calculate \(\frac{11}{16}\):

\[
\frac{11}{16} = 0.6875
\]

Thus, we can rewrite the expression as:

\[
0.6875 \times 10^2
\]

To express \(0.6875\) in scientific notation, we write it as:

\[
6.875 \times 10^{-1}
\]

Therefore:

\[
0.6875 \times 10^2 = (6.875 \times 10^{-1}) \times 10^2 = 6.875 \times 10^{1}
\]

So the final result is:

\[
6.875 \times 10^{1}
\]

Thus, the equivalent expression from the provided options is:

**A: \(6.875 \times 10^{1}\)**.