1. Powers of Ten – Negative Exponents

2. Exponent
An exponent is the number that indicates how many times the base is used as a factor

3. Positive Exponents
𝟏𝟎 𝟑 𝟏𝟎×𝟏𝟎×𝟏𝟎 = 1,000
𝟏𝟎 𝟒
𝟏𝟎×𝟏𝟎×𝟏𝟎×𝟏𝟎
= 10,000

4. Negative Exponents 𝟏𝟎 −𝟑 𝟎.𝟎𝟎𝟏 What’s does that say?
Since the exponents is negative, put this into your calculator.
It gives you a decimal:
𝟎.𝟎𝟎𝟏
What’s does that say?
One thousandths, which is
𝟏 𝟏,𝟎𝟎𝟎 = this is the same as 𝟏 𝟏𝟎 × 𝟏 𝟏𝟎 × 𝟏 𝟏𝟎 .

5. Which of the following is equivalent to 10 −4 ?
10,000
0.001
0.0001
1 10,000
When you put the problem in the calculator it gives you the decimal form.
10 −4= = 1 10, Write the fraction the way you say it. “One ten thousandth”.
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6. What is the fraction and decimal equivalent for 10 −2 ?
0.01
-0.01
1 100
Common mistakes – many think because the exponent is negative, the equivalent solutions are negative. That is wrong. Because the exponent is negative, the equivalent forms are a fraction and a decimal!
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7. Which is not an equivalent form for 0.001?
10 −3
1 1,000
1 10 × 1 10 × 1 10
10 3
The first three all equal They are equivalent forms. The only one that is not is item # 4. Item # 4 has a positive exponent so it’s solutions are not a fraction nor a decimal. It is equivalent to 10 X 10 X 10 and 1,000.
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