Question

In 2005, 8.1x10^10text messages were sent in the United States. In 2010, the number of annual text messages had risen to 1,863,000,000,000. About how many times as great was the number of text messages in 2010 then 2005?

Answer 1

You must divide the number of text messages in 2010 by the number of text messages in 2005.

Convert the number of text messages in 2010 to scientific notation:

$1\underbrace{,863,000,000,000}_{\leftarrow12}=1.863\cdot10^{12}$

Divide:

$(1.863\cdot10^{12})\div(8.1\cdot10^{10})=\dfrac{1.863\cdot10^{12}}{8.1\cdot10^{10}}=\dfrac{1.863}{8.1}\cdot10^{12-10}\\\\=0.23\cdot10^2=0.23\cdot100=23$

Answer: 23 many times.

Used:

$a^n:a^m=a^{n-m}$