How do you write #13,560,000# in scientific notation?

1 Answer
Feb 27, 2016

Answer:

#" "color(blue)(1.356xx10^7)#

Explanation:

#color(blue)("How it works")#

Scientific notation format is that you have a single, non zero digit to the left of a decimal point and everything else to the right of it.

The problem in doing this is that you changed the value. So you have to apply a correction that if it were to be implemented would return the number back to its original format.
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Example: Consider the value of 23

To convert this into the required format you would divide it by 10

so that #23 -: 10 = 2.3#

the problem is that #2.3!=23#

However: #2.3xx10# does
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(brown)("So what has happened?")#

We have done two thing.

#color(brown)("Step 1")#

We multiplied 23 by 1 but 1 was in the form of #10/10#

#" "color(brown)( 23xx10/10" " = " "23/10xx10)#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(brown)("Step 2")#

We applied the division but leave the other ten in place:

#" "color(brown)( 2.3 xx 10)#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Solving your question")#

Given:#" " 13560000.0#

Keeping the decimal place still we have to slide the digits to the right for 7 digits to get: 1.356

So we have
#" "13560000.0xx10^7/10^7#

#" "13560000.0/10^7xx10^7#

#" "color(blue)(1.356xx10^7)#