Powers of Ten – Negative Exponents

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

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

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 .

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 4 = 1 10,000 . Write the fraction the way you say it. “One ten thousandth”. Answer Now

What is the fraction and decimal equivalent for 10 −2 ? 0.01 -0.01 - 1 100 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! Answer Now

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 0.001. 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. Answer Now