# Question 3519b

Oct 17, 2016

#### Answer:

$1.32 \times {10}^{5}$

#### Explanation:

You know that a sack of cocoa beans has a mass of $\text{132 lb}$, so start by figuring out the mass of $1000$ sacks.

1000 color(red)(cancel(color(black)("sacks"))) * "132 lb"/(1color(red)(cancel(color(black)("sacks")))) = "132000 lb"#

Now that you have the answer in standard notation, convert this to scientific notation by dividing it by $10$ until you are left with a number, $\textcolor{b l u e}{m}$, that is

$1 \le \textcolor{b l u e}{m} < 10 \to$ the is called the mantissa

Keep in mind that for every division that you do, you add $1$ to the exponent of the base, which for scientific notation is the number $10$.

So, you start with

$\textcolor{b l u e}{132000} \text{ " " }$ and $\text{ " " } {10}^{0}$

Divide by $10$ once

$\textcolor{b l u e}{13200} \text{ " " }$ and $\text{ " " } {10}^{1}$

Divide by $10$ again

$\textcolor{b l u e}{1320} \text{ " " }$ and $\text{ " " } {10}^{2}$

Divide by $10$ again

$\textcolor{b l u e}{132} \text{ " " }$ and $\text{ " " } {10}^{3}$

Divide by $10$ again

$\textcolor{b l u e}{13.2} \text{ " " }$ and $\text{ " " } {10}^{4}$

Divide by $10$ again

$\textcolor{b l u e}{1.32} \text{ " " }$ and $\text{ " " } {10}^{5}$

At this point, you have

$1 \le \textcolor{b l u e}{1.32} < 10$

so it's time to stop dividing the number. Finally, to write this in proper scientific notation, multiply the mantissa by the base

$132000 = 1.32 \times {10}^{5}$