Question

Question #3519b

Answer 1

`1.32 xx 10^5`

Explanation:

You know that a sack of cocoa beans has a mass of `"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, `color(blue)(m)`, that is

`1 <= color(blue)(m) < 10 ->` 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

`color(blue)(132000)" " " "` and `" " " " 10^0`

Divide by `10` once

`color(blue)(13200)" " " "` and `" " " " 10^1`

Divide by `10` again

`color(blue)(1320)" " " "` and `" " " "10^2`

Divide by `10` again

`color(blue)(132)" " " "` and `" " " "10^3`

Divide by `10` again

`color(blue)(13.2)" " " "` and `" " " "10^4`

Divide by `10` again

`color(blue)(1.32)" " " "` and `" " " "10^5`

At this point, you have

`1 <= color(blue)(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 xx 10^5`