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

7-5 = 1 7 × 1 7 × 1 7 × 1 7 × 1 7

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

Click here to see a completed table.

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
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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?

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The number gets smaller. There is another zero between the decimal and the one. Close Pop Up

How does the number of zeros after the decimal compare to the number of times you use 1 10 as a factor?

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The number of zeros after the decimal is one less than the number of times that you use 1 10 as a factor. Close Pop Up

How does the decimal place where you write the 1 compare to the number of times you use 1 10 as a factor?

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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. Close Pop Up

What general rule can you use to tell where to write the 1 in the decimal based on the exponent?

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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. Close Pop Up

Based on your rule, how do you write 0.00000001 as 10 raised to an exponent?

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0.00000001 = 10-8. Close Pop Up

Click here to see a table of values for 10 raised to the powers of -6 to +6.


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
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