Exponents and Fractions

Negative exponents with fraction review

Fractions Review!

 $\frac{1}{10}$  can be shown as a fraction:

All 10 pieces add up to 1 whole shape

We can also represent  $\frac{1}{10}$  as 0.1

Why?

Hundredths are smaller than tenths

Breaking into 100 pieces gives smaller pieces than breaking into 10 pieces

Negative exponents are used to represent fractions

 $10^{-1}=\frac{1}{10^1}=\frac{1}{10}$  

(negative exponents are positive fractions!)

Negative exponents are positive fractions

•  $10^{-4}=\frac{1}{10^4}$  

•  $5^{-3}=\frac{1}{5^3}$  

•  $10^{-16}=\frac{1}{10^{16}}$  

• What's the pattern?

Multiple Choice

What is

$$10^{-2}\$$  as a fraction?

• $$\frac{1}{10^2}$$  

• $$\frac{1}{10^{-2}}$$  

• $$\frac{10^2}{1}$$  

Multiple Choice

What is

$$10^{-5}\$$  as a fraction?

• $$\frac{1}{10^{-5}}$$  

• $$\frac{1}{10^5}$$  

• $$-10^5$$  

Multiple Choice

What is

$$5^{-7}$$  as a fraction?

• $$\frac{1}{5^{-7}}$$  

• $$\frac{1}{5^7}$$  

• $$\frac{5^7}{1}$$  

Writing negative exponents as decimals

Open Ended

How do we write

$$\frac{1}{100}$$  as a decimal?