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4.1 Powers of 10

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**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 1000 102 101 100 10–1 10–2 10–3

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STEP 2 Find a pattern Look at the rows you have completed. How does the standard form change each time the exponent decreases by 1?

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STEP 3 Finish the table Use the pattern you identified in Step 2 to complete the remaining rows in the table.

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**DRAW CONCLUSIONS: Use your observations to complete these exercises**

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?

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**Reverse Practice Write the number as a power of 10 1,000,000**

1,000,000,000 .001 .0001

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**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 the decimal .01 we can make it 100 Try making 10-3 into a fraction WITHOUT turning it to a decimal first.

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**Extra Practice Write the negative power of 10 as a fraction 10-4 10-5**

10-1 Order from least to greatest 14. 10, , 102, .001 , 102, 1, 10-3, 1 10

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