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