How do you write #0.00083# in scientific notation?

1 Answer
Feb 27, 2016

Answer:

With practice you will probably be able do it all in your head!
#8.3xx10^(-4)#

Explanation:

#color(blue)("Explaining the principle behind this")#

Explained by example:

Consider #2.5#

If we multiply this value by 1 we have: #2.5xx1=2.5#

The really cool thing is that you can use this principle to change the way some value looks without changing its inherent value at all:

#color(brown)("If you have "10/10" this this is the equivalent of 1")#

So, if I multiply #2.5# by 1 but the 1 is in the form of #10/10# then we have:

#" "2.5xx10/10#

This is the same as#" "(2.5xx10)/10 = 25/10 = 25xx10^(-1)#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#color(blue)("Solving your question")#

Given:#" "0.00083#

Multiply by #10/10# giving #" "(0.00083xx10)/10 =color(red)((0.0083)/10)#

#color(brown)("Process repeat number 1")#

#" "color(red)((0.0083)/10)xx10/10= (0.0083xx10)/(10xx10) =color(green)(0.083/(10^2))#

#color(brown)("Process repeat number 2")#

#" "color(green)(0.083/(10^2))xx 10/10=(0.083xx10)/(10^2xx10)=color(magenta)(0.83/(10^3))#

#color(brown)("Process repeat number 3")#

#" "color(magenta)(0.83/(10^3))xx 10/10 = (0.83xx10)/(10^3xx10)=8.3/(10^4)#

#color(white)(.)#

#" "color(green)("Write this as: " 8.3xx10^(-4))#

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
This is the equivalent of keeping the decimal place where it is and sliding the number to the left four places. You than apply a correction. In this case the correction is #10^(-4)# which would change 8.3 back to 0.00083 if applied.

#color(green)("You have not changed the value but you have changed the way it looks!")#