How do you evaluate #\frac { 5\times 10^ { 7} } { 25\times 10^ { 4} }#? What is the answer in scientific notation?

1 Answer
Shwetank Mauria
Mar 21, 2017

#(5xx10^7)/(25xx10^4)=2xx10^2#

Explanation:

In scientific notation, we write a number so that it has single digit to the left of decimal sign and is multiplied by an integer power of #10#.

For example here we have #5xx10^7# in numerator and #25xx10^4# in denominator.

While dividing first by second, we can use the identity #a^m/a^n=a^((m-n))# and doing this we get

#(5xx10^7)/(25xx10^4)#

= #5/25xx10^((7-4))#

= #1/5xx10^3#

= #0.2xx10^((7-4))#

Now here we have first digit #2# in one-tenth place and not in unit's place as desired for scientific notation. Hence, we put #0.2# as #2/10# and this gives us

#(5xx10^7)/(25xx10^4)=2/10xx10^3=2xx10^2#

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