How do you add #2.113 xx 10^4 + 9.2 xx 10^4# in scientific format?

1 Answer
Aug 20, 2016

Answer:

#(2.113 xx 10^4) + (9.2 xx 10^4) = 1.1313 xx 10^5 ~~ 1.13 xx 10^5#

Explanation:

To add two expressions in scientific format:

  • First ensure that they both have the same exponent, by rescaling one of them if necessary.

In our example both of the numbers are expressed with exponent #4#, so we do not need to do anything.

  • Add the mantissas.

#2.113 + 9.2 = 11.313#

So:

#(2.113 xx 10^4) + (9.2 xx 10^4) = 11.313 xx 10^4#

  • Rescale into scientific format by adjusting the mantissa and exponent to bring the mantissa into the range #[1, 10)# if required.

So in our example:

#11.313 xx 10^4 = 1.1313 xx 10^5#

  • Round to an appropriate number of significant digits as appropriate.

If the original numbers were approximations - only expressed to a limited precision - then it is appropriate to give the result to a similar precision.

In our example, the least precise figure is #9.2 xx 10^4#, which is quoted with a precision of #0.1 xx 10^4 = 0.01 xx 10^5#. So we should only quote the answer with two decimal places in the mantissa:

#1.13 xx 10^5#