Negative exponents
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Negative exponents. What do we know? . Which number is in exponential form: -10, , 10 Identify the Base of that number What is the exponent in that number ?. - the number being multiplied by itself ie . 10. +2. What does the exponent represent? 10.

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What do we know
What do we know?

  • Which number is in exponential form:

    -10, , 10

  • Identify the Base of that number

  • What is the exponent in that number?

- the number being multiplied by itself ie. 10

+2


What does the exponent represent 10
What does the exponent represent? 10

  • 10 x 10

Or the number of times the base is used as a factor.

Also called the “power”


Finish this pattern
Finish this pattern:

1

10

100

1000

  • 100 =

  • 101=

  • 102=

  • 103=

    What are we doing each time to get the next number in standard form?

= 1 x 10

= 10 x 10

= 100 x 10

Multiplying by 10


Reverse
Reverse!!!!

  • 103 = 1000

  • 102= 100

  • 101= 10

  • 100 = 1

  • Do you see a pattern?

  •  10 =

  •  10 =

  •  10 =


Negative exponents

What if we keep going down and use our negative integers as exponents?

Based on our patterns we have just seen, what will happen?


Writing negative exponents in multiple forms
Writing negative exponentsin multiple forms

  • If 10-1 = 1/10 how could you write that in decimal form?

  • How about 10-2 = 1/100, write it in decimal form.

  • How about 10-3 ? Write it in decimal form.

Answer: 0.1

Answer: 0.01

Answer: 0.001



What do we know now
What do we know now?

  • What type of numbers will be represented by powers of 10 with negative exponents?

Answer: decimals and fractions, small numbers between 0 and 1

.01

or

10-2

1

0


Write a rule to show the fraction form of a negative exponent
Write a rule to show the fraction form of a negative exponent

10-x =

1

10x

  • Ex. 10-2 = 1 = 1 = .01

  • 102 100