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

Aug 20, 2016

$\left(2.113 \times {10}^{4}\right) + \left(9.2 \times {10}^{4}\right) = 1.1313 \times {10}^{5} \approx 1.13 \times {10}^{5}$

#### 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.

$2.113 + 9.2 = 11.313$

So:

$\left(2.113 \times {10}^{4}\right) + \left(9.2 \times {10}^{4}\right) = 11.313 \times {10}^{4}$

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

So in our example:

$11.313 \times {10}^{4} = 1.1313 \times {10}^{5}$

• 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 $9.2 \times {10}^{4}$, which is quoted with a precision of $0.1 \times {10}^{4} = 0.01 \times {10}^{5}$. So we should only quote the answer with two decimal places in the mantissa:

$1.13 \times {10}^{5}$