Question

One way you could approach this problem is to rewrite both numbers in terms of the same power of 10. Start by rewriting 600,000 as a number times 

103.

Chocolate consumed by Town B

Chocolate consumed by Town A

 = 

600,000

1.5·103

 = 

 · 103

1.5·103

Answer 1

To compare the chocolate consumed by Town B and Town A, you can start by rewriting both numbers in terms of the same power of 10. Given the chocolate consumed by Town A is \( 1.5 \times 10^3 \) (or 1500) and Town B consumed 600,000, we can express 600,000 in terms of \( 10^3 \).

1. **Rewrite 600,000**:
\[
600,000 = 6 \times 10^5
\]

2. **Convert \( 6 \times 10^5 \) to \( 10^3 \)**:
Since \( 10^5 \) can also be expressed as \( 10^3 \times 10^2 \), we can rewrite \( 600,000 \) as follows:
\[
600,000 = 6 \times 10^5 = 6 \times (10^3 \times 10^2) = 6 \times 10^3 \times 100
\]

3. **Now express it in units of \( 10^3 \)**:
Here,
\[
600,000 = 600 \times 10^3
\]

Now we have both towns' chocolate consumption in units of \( 10^3 \):

- Chocolate consumed by Town A: \( 1.5 \times 10^3 \)
- Chocolate consumed by Town B: \( 600 \times 10^3 \)

4. **Set up the ratio**:
Now we can compare them by forming a ratio:

\[
\text{Chocolate consumed by Town B} \div \text{Chocolate consumed by Town A} = \frac{600 \times 10^3}{1.5 \times 10^3}
\]

Since \( 10^3 \) cancels out, we simplify this to:

\[
\frac{600}{1.5}
\]

5. **Calculate the ratio**:
Performing the division:
\[
\frac{600}{1.5} = 400
\]

Thus, Town B consumed **400 times** more chocolate than Town A.