If a number is greater than 1, then the exponent is positive. If a number is less than 1, then the exponent is negative.
See solution.
Practice makes perfect
Kim was asked to write an estimate for the number 0.00436. This is what she came up with.
0.00436 ≈ 4 * 10^3 *
We know that this answer is incorrect. We want to explain why. 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 0.00436 to its greatest place value. See that the digit following the greatest place value is 3. Since 3 is less than 5, we will be rounding down. Let's do it!
0.00436 ≈ 0.004
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.
. 4
We see that there are 3 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 0.004 is less than 1, the exponent is negative. Putting these concepts together, the exponent of 10 is - 3. We now have everything we need to rewrite our number.
0.004 = 4 * 10^(- 3)
Let's compare this estimate with Kim's answer. We can see that the exponent in Kim's estimate is positive.
0.00436 ≈ 4 * 10^3 *
0.00436 ≈ 4 * 10^(- 3) ✓
Kim's answer cannot be correct because only large numbers can be written with a positive exponent. Since 0.00436 is a small number, its exponent needs to be negative.
