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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? Power Standard form –1 10 –2 10 –3 STEP 1 Complete the table Copy the table and complete the next two rows by evaluating 10 2 and 10 1.

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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 – –6 5. Reasoning Let n be a positive integer. How many zeros are there in the standard form of 10 n ? in the standard form of 10 –n ?

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Reverse Practice Write the number as a power of ,000, ,000,000,

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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: 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 Try making 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 Order from least to greatest , , 10 2, , 10 2, 1, 10 -3, 1 10

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