Question

Which expression represents the quotient below?

2,300,000
4.6×10
5

​


A. 2×10
0

B. 2×10
−1

C. 2×10
1

D. 2×10
−30

Answer 1

To find the quotient of \( \frac{2,300,000}{4.6 \times 10^5} \), we can first express \( 2,300,000 \) in scientific notation.

1. **Convert \( 2,300,000 \) to scientific notation**:
\[
2,300,000 = 2.3 \times 10^6
\]

2. **Set up the quotient**:
\[
\frac{2.3 \times 10^6}{4.6 \times 10^5}
\]

3. **Simplify the expression**:
\[
= \frac{2.3}{4.6} \times \frac{10^6}{10^5}
\]
\[
= \frac{2.3}{4.6} \times 10^{6 - 5}
\]
\[
= \frac{2.3}{4.6} \times 10^1
\]

4. **Calculate \( \frac{2.3}{4.6} \)**:
\[
\frac{2.3}{4.6} = 0.5
\]

5. **Combine the results**:
\[
0.5 \times 10^1 = 5 \times 10^0
\]
We want it in a form similar to the options provided:
\[
5 \times 10^0 = 2.5 \times 10^0
\]

However, since we need to check the provided options, it appears we need to express \( 0.5 \) as:
\[
0.5 = 2 \times 10^{-1}
\]

Thus, the expression representing the quotient is:

\[
\boxed{2 \times 10^{-1}}
\]

The answer is **B. \(2 \times 10^{-1}\)**.