Examples:
4-3 = 1 4 × 1 4 × 1 47-5 = 1 7 × 1 7 × 1 7 × 1 7 × 1 7
Positive exponents tell us how many times we multiply by a number. Negative exponents tell us how many times we divide by a number — or how many times we multiply by 1number.
Examples:
4-3 = 1 4 × 1 4 × 1 4
Based on the two examples given above, fill in the following table.
10-1 |
10-2 |
10-3 |
10-4 |
10-5 |
10-6 |
|
1
10
|
1
10
×
1
10
|
||||
0.1 |
0.01 |
10-1 |
10-2 |
10-3 |
10-4 |
10-5 |
10-6 |
1
10
|
1
10
×
1
10
|
1
10
×
1
10
×
1
10
|
1
10
×
1
10
×
1
10
×
1
10
|
1
10
×
1
10
×
1
10
×
1
10
×
1
10
|
1
10
×
1
10
×
1
10
×
1
10
×
1
10
×
1
10
|
0.1 |
0.01 |
0.001 |
0.0001 |
0.00001 |
0.000001 |
Based on the information in the table, answer the following questions in your notes.
What happens to the number in the bottom row as you move from left to right?
Interactive popup. Assistance may be required. The number gets smaller. There is another zero between the decimal and the one.
How does the number of zeros after the decimal compare to the number of times you use 1 10 as a factor?
Interactive popup. Assistance may be required. The number of zeros after the decimal is one less than the number of times that you use 1 10 as a factor.
How does the decimal place where you write the 1 compare to the number of times you use 1 10 as a factor?
Interactive popup. Assistance may be required. The decimal place where I write the 1 is the same as the number of times that you use 1 10 as a factor. If I use 1 10 as a factor 3 times, the 1 goes in the third decimal place: 0.001.
What general rule can you use to tell where to write the 1 in the decimal based on the exponent?
Interactive popup. Assistance may be required. The 1 goes in the same decimal place as the number of the exponent. 10-3 means write the 1 in the third decimal place: 0.001.
Based on your rule, how do you write 0.00000001 as 10 raised to an exponent?
Interactive popup. Assistance may be required. 0.00000001 = 10-8.
Interactive popup. Assistance may be required.
| 10-6 | 1 10 x 1 10 x 1 10 x 1 10 x 1 10 x 1 10 | 0.000001 |  |
| 10-5 | 1 10 x 1 10 x 1 10 x 1 10 x 1 10 | 0.00001 | |
| 10-4 | 1 10 x 1 10 x 1 10 x 1 10 | 0.0001 | |
| 10-3 | 1 10 x 1 10 x 1 10 | 0.001 |  |
| 10-2 | 1 10 x 1 10 | 0.01 | |
| 10-1 | 1 10 | 0.1 | |
| 100 | 1 | 1 | |
| 101 | 10 | 10 |  |
| 102 | 10 x 10 | 100 | |
| 103 | 10 x 10 x 10 | 1,000 | |
| 104 | 10 x 10 x 10 x 10 | 10,000 |  |
| 105 | 10 x 10 x 10 x 10 x 10 | 100,000 | |
| 106 | 10 x 10 x 10 x 10 x 10 x 10 | 1,000,000 |