Magnitude!

Magnitude!

Powers of Ten

 $10^{-2}=\frac{1}{10^2}=\frac{1}{100}=.01$  one one-hundredth

 $10^{-1}=\frac{1}{10^1}=\frac{1}{10}=0.1$  one tenth

Remember:

• With negative exponents, the bigger the negative exponent, the smaller the number

• With positive exponents, the bigger the exponent, the bigger the number

Which is smaller?

 $10^{-4}\ or\ 10^{-10}$  ?

Which is bigger?

 $10^{30}\ or\ 10^5$  ?

Multiple Choice

Pick the biggest number:

• $10^4$

• $10^{25}$

• $10^{13}$

Multiple Choice

Pick the biggest number:

•  $89^{300}$ 

•  $89^6$ 

•  $89^{45,000}$ 

Multiple Choice

Pick the smallest number:

• $3^{-56}$

• $3^{-10}$

• $3^{-4}$

Multiple Choice

Pick the smallest number:

•  $10^{-65}$ 

•  $10^{-200}$ 

•  $10^{-34}$ 

Time to watch a video!

How do digits relate to exponents?

•  $10^0=1$  (1 digit)

•  $10^1\ =\ 10$  (2 digits)

•  $10^2\ =\ 100$  (3 digits)

•  $10^3\ =\ 1000$  (4 digits)

• Predict: how many digits is $10^4$  ?

• How many digits is  $10^5$  ?

• How many digits is $10^{13}$  ?

The world population:

7,815,574,754 people

• How many digits does this number have?

• What power of ten has the same number of digits?

The US national debt:

$26,823,745,743,842

• How many digits does this number have?

• What power of ten has the same number of digits?