Let's solve the problem step by step.
---
Given:
- Speed of light = $ 3 \times 10^8 $ meters per second
- Distance from the Sun to Mars = $ 230,000,000,000 $ meters
We want to find
how many seconds it takes for sunlight to reach Mars.
---
Step 1: Use the formula for time
$$
\text{Time} = \frac{\text{Distance}}{\text{Speed}}
$$
Plug in the values:
$$
\text{Time} = \frac{230,000,000,000}{3 \times 10^8}
$$
---
Step 2: Write the distance in scientific notation
$ 230,000,000,000 = 2.3 \times 10^{11} $
So,
$$
\text{Time} = \frac{2.3 \times 10^{11}}{3 \times 10^8}
$$
---
Step 3: Divide the numbers and subtract exponents
$$
\frac{2.3}{3} = 0.7666... \approx 0.767
$$
$$
10^{11} \div 10^8 = 10^{11-8} = 10^3
$$
So,
$$
\text{Time} \approx 0.767 \times 10^3
$$
But we need
scientific notation, which requires a number between 1 and 10.
$$
0.767 \times 10^3 = 7.67 \times 10^2
$$
---
✔ Final Answer:
$$
\boxed{7.67 \times 10^2} \text{ seconds}
$$
That is,
about 767 seconds for sunlight to reach Mars.
---
Bonus: Check with approximate calculation
- $ 3 \times 10^8 $ m/s × 767 s = $ 3 \times 10^8 \times 7.67 \times 10^2 = 2.3 \times 10^{11} $ m → matches the distance!
✔ Correct.
---
Answer in boxed form:
$$
\boxed{7.67 \times 10^2} \text{ seconds}
$$
Parent Tip: Review the logic above to help your child master the concept of scientific notation word problem worksheet.
