4.1 Powers of
10
QUESTION: What does it mean for 10 to be raised to zero or to a negative power?
STEP 1 Complete the table
Copy the table and complete the next two rows by evaluating 102 and
101.
Power
Standard form
103
102
101
100
10–1
1000
10–2
10–3
STEP 2
 Look
Find a pattern
at the rows you have completed.
How does the standard form change
each time the exponent decreases by 1?
STEP 3
 Use
Finish the table
the pattern you identified in Step 2 to
complete the remaining rows in the table.
DRAW CONCLUSIONS: Use your
observations to complete these
exercises
1.
2.
3.
4.
5.
104
109
10–4
10–6
Reasoning Let n be a positive integer.
How many zeros are there in the
standard form of 10n? in the standard
form of 10–n?
Reverse Practice
Write the number as a power of 10
6. 1,000,000
7. 1,000,000,000
8. .001
9. .0001
10. .00000001
Negative Exponents to make
fractions



A negative power of 10 can mean a number
like .01, or you can use it to make a fraction
EXAMPLE: 10-2 means the decimal .01 and if
we say the name it is one hundredth. So
instead of making 10-2 the decimal .01 we
can make it
1
100
Try making 10-3 into a fraction WITHOUT turning
it to a decimal first.
Extra Practice
Write the negative power of 10 as a fraction
11. 10-4
12. 10-5
13. 10-1
Order from least to greatest
14. 10, 0.0001, 102, .001
15. 10-4, 102, 1, 10-3, 1
10