Question

Looking into the sky one night, Tori wondered how far into outer space she would get if she drove a car for 3.21 × 103 hours at a rate of 70mph. She calculated and determined that a car travelling at 70 mph covers approximately 1.13 × 105 meters per hour.

Tori wrote this expression to determine the distance she would travel into outer space.

(3.21 × 103)(1.13 × 105)

Estimate the distance travelled.
Almost-equals30 × 1015 meters
Almost-equals3 × 108 meters
Almost-equals30 × 108 meters
Almost-equals3 × 1015 meters

Answer 1

To estimate the distance Tori would travel into outer space, we need to calculate the expression:

\[
(3.21 \times 10^3)(1.13 \times 10^5)
\]

We can break it down as follows:

1. **Multiply the coefficients**:
\[
3.21 \times 1.13 \approx 3.6263 \quad (\text{we can round to } 3.63)
\]

2. **Add the exponents**:
\[
10^3 \times 10^5 = 10^{3+5} = 10^8
\]

Combining these, we get:
\[
(3.21 \times 10^3)(1.13 \times 10^5) \approx 3.63 \times 10^8
\]

Now we round \(3.63\) to \(3\) for estimation purposes:
\[
\approx 3 \times 10^8 \text{ meters}
\]

Thus, the estimated distance travelled is:

**Almost-equals \(3 \times 10^8\) meters**.