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

##### 1 Answer

Aug 20, 2016

#### 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

- 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

#1.13 xx 10^5#