Question

The speed of an electric train is 4.5 * 10^7 mm/s and that of a bus is 2.5 * 10^4 mm/s. What is the difference between the speeds? Express your answer in index form.

Answer 1

4.4975 × 10⁷ mm/s

Explanation:

If we write each of these in standard form:

`4.5*10^7=45,000,000` mm/s

`2.5*10^4=25,000` mms/s

Now, subtracting the two, we find the difference is

45,000,000 - 25,000 = 44,975,000 mm/s

To express this in index form, we first need to move the decimal on 44,975,000 until it's a number between 1 and 10. Moving it 7 decimals to the left works for this, giving us the number 4.4975. The last piece is adding the index: to get back to 44,975,000, we need to move the decimal on 4.4975 seven places to the right, which is the same as multiplying it by 10⁷. So in index form, our difference is 4.4975 × 10⁷ mm/s