Kim was asked to write an estimate for the number

0.00436 .

This is what she came up with.

0.00436 \approx 4 \times 1 0^{3} \times

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.

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 \approx 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.

\underline{0} . \underline{0} \underline{0} 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 \times 1 0^{- 3}

Let's compare this estimate with Kim's answer. We can see that the exponent in Kim's estimate is positive.

0.00436 \approx 4 \times 1 0^{3} \times 0.00436 \approx 4 \times 1 0^{- 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.

Exercise