Raquel was estimating for the number 304 900 000 000. This is what she came up with.
304 900 000 000 ≈ 3 * 10^8 *
We know that this answer is incorrect. We want to explain why. For that, recall that when estimating a very large or very small number, we need to follow 2 steps.
Write the number as a single digit times a power of 10.First, we want to round 304 900 000 000 to its greatest place value. See that the digit following the greatest place value is 0, which is less than 5. This means we will be rounding down. Let's do it!
304 900 000 000 ≈ 300 000 000 000
For the second step, we will rewrite the number as its greatest place value times a power of 10. To find the exponent, we need to count the zeros in the number.
3
We see that there are 11 zeros in the number. Now, recall how the sign of the exponent changes for different numbers.
Numbers Greater Than 1
Numbers Less Than 1
positive (+)
negative (-)
Since the number 300 000 000 000 is greater than 1, the exponent is positive. This means that the exponent of 10 is 11. We now have everything to rewrite our number.
300 000 000 000 = 3 * 10^(11)
Let's compare this estimate with Raquel's answer. We can see that the exponents are different.
304 900 000 000 ≈ 3 * 10^8 *
304 900 000 000 ≈ 3 * 10^(11) ✓
Raquel most likely counted the number of zeros in the original number, not the rounded number. This is why her estimate is different from ours.
