Question #3519b

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#