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4.1 Powers of 10

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 10 2 and 10 1 . STEP 2   Find a pattern.

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4.1 Powers of 10

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  1. 4.1 Powers of 10

  2. 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.

  3. 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?

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

  5. 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?

  6. Reverse Practice Write the number as a power of 10 • 1,000,000 • 1,000,000,000 • .001 • .0001 • .00000001

  7. 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.

  8. Extra Practice Write the negative power of 10 as a fraction • 10-4 • 10-5 • 10-1 Order from least to greatest 14. 10, 0.0001, 102, .001 15. 10-4, 102, 1, 10-3, 1 10

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