3.05 Powers of 10 and place value
Powers of 10 and place value
Recall that an exponent (or power) tells us the number of times to multiply a certain number by itself. We just looked at special properties of the exponent 2, now let's look at some special properties of 10.
Exploration
Move the slider in the applet and see if you notice any patterns.
What patterns do you notice in the numbers?
Why do you think 10^{0}=1?
For any power of ten, the expanded form will have the same number of tens as the power. The number that it evaluates to will have the same number of zeros as the exponent.
The following table demonstrates another way to think of some of the powers of ten.
| Power of Ten | Meaning | Value (basic numeral) | In Words |
|---|---|---|---|
| 10^{5} | 10\cdot 10\cdot 10\cdot 10\cdot 10 | 10,000 | \text{One hundred thousand} |
| 10^{4} | 10\cdot 10\cdot 10\cdot 10 | 10,000 | \text{Ten thousand} |
| 10^{3} | 10\cdot 10\cdot 10 | 1,000 | \text{One thousand} |
| 10^{2} | 10\cdot 100 | 100 | \text{One hundred} |
| 10^{1} | 10 | 10 | \text{Ten} |
| 10^{0} | 1 | 1 | \text{One} |
We can see that the exponent relates to the place value of the 1. The larger the exponent, the larger the place value.
Examples
Example 1
If you have a 1 in the hundred thousands place, what power of 10 does this represent?
Example 2
A library has exactly 1,000,000 books. Write this number of books as a power of 10.
Example 3
Find the missing exponent.
10^{⬚}=10,000,000
For a power of ten, the number of zeros after the 1 is the same as the exponent.
The power of ten changes the place value of the 1.