How do you write #1764.9# in scientific notation?

1 Answer
Tony B
Aug 2, 2016

#1.7649xx10^3#

Explanation:

The objective is to have just one non zero digit to the left of the decimal and the rest of the numbers to the right. This changes the value so a correction has to be built, shown but not applied. In this case the correction is #(xx10^3)#

#color(brown)("With practice you will be able to do this in a lot less lines")#

Showing what is happening 1 stage at a time

#color(blue)("Stage 1")#
Multiply by 1 but in the form of #color(magenta)(1=10/10)#

#1764.9color(magenta)(xx10/10)" " =" " 1764.9/(color(magenta)(10))color(magenta)( xx 10)" " =" " 176.49xx10#
'.................................................................................................

#color(blue)("Stage 2")#
Multiply by 1 but in the form of #color(magenta)(1=10/10)#

#176.49xx10color(magenta)(xx10/10)" " =" "176.49/10xx10^2" " =" " 17.69xx10^2#
'..............................................................................................

#color(blue)("Stage 3")#
Multiply by 1 but in the form of #color(magenta)(1=10/10)#

#17.649xx10^2 color(magenta)(xx10/10)#

#=17.649/10xx10^3" "=" "color(blue)(1.7649xx10^3)#

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