Bonnie was asked to estimate the diameter of one species of bacteria. This is what she came up with.
0.00000025691 ≈ 3 * 10^(- 11)
We want to decide if her answer is correct. 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 0.00000025691 to its greatest place value. Note that the digit following the greatest place value is 5.
0.0000002 5691
This means we will be rounding up. Let's do it!
0.00000025691 ≈ 0.0000003
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.
.0000003
We see that there are 7 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 0.0000003 is less than 1, the exponent is negative. This means that the exponent of 10 is - 7. We now have everything we need to rewrite our number.
0.0000003 = 3 * 10^(- 7)
Let's compare this estimate with Bonnie's answer.
0.0000003 &= 3 * 10^(- 11) *
0.0000003 &= 3 * 10^(- 7) ✓
Bonnie likely counted all the digits in the number instead of only the zeros of the rounded number. This is why her answer is incorrect.
