Adding numbers in scientific notation can be done in two different methods.

First method is to change the numbers out of scientific notation and work the problem normally.

**Example:** change 6.3 x 10^{3} - 5.63 x 10^{2} into 6300 - 563. Then subtract normally to get 5.737 x 10^{3}. Its an simplest way of working when the numbers are not very large or not very small.

Second method to add numbers in a scientific notation is best when working with very large or very small numbers.

**Example:** add 5.75 x 10^{11} + 4.8 x 10^{10}, now we change the larger number to the same power as the small number or vise versa.

Change 4.8 x 10^{10} into 0.48 x 10^{11}, the problem becomes 5.75 x 10^{11} + 0.48 x 10^{11} = 6.23 x 10^{11}, which is already in scientific notation.

So we have to rework one of the numerals to cover the same exponent and match it with the other. We need to regulate the exponents of 10 in the 2 numerals so that they have the similar index.

It is very simpler to alter the minor exponent to equal the larger exponent.

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Addition problems are handled the way as follows:

- Write the numbers to be added in scientific notation.
- Addition operation is done in the initial part of the numerals, except the exponent portion if it is unchanged.
- If the values of the exponent are not similar then we have to expand it to similar exponent and then perform the next step.
- The concluding solution is written in scientific notation.

Addition in scientific notation for example:** (6.9 x 10 ^{3}) + (2.0 x 10^{3}) = 8.9 x 10^{3}**

Below are the examples for Adding Numbers with Scientific Notation:

i .** First we have to convert the common exponent **8 - 5 = 3.

The lesser exponent (5) have to be increased by **3**.

ii . 3.557 × 10^{5} = 0.003557 × 10^{8}

iii . 0.003557 × 10^{8} + 8.0039 × 10^{8} = 8.007457 × 10^{8}

iv . 8.007457 × 10^{8} is in scientific notation.

Thus, 3.557 × 10^{5} + 8.0039 × 10^{8} = 8.007457 × 10^{8}

i . ** First we have to convert the common exponent .**3 - (-2) = 5

The smaller exponent (-2) must be increased by

ii . 6.9 × 10^{-2} = 0.000069 × 10^{3}

iii . 5.80808 × 10^{3} - 0.000069 × 10^{3} = 5.808011 × 10^{3}

iv . 5.808011 ×10^{3}** **is in scientific notation.

Thus, 5.80808 × 10^{3} - 6.9 × 10^{-2} = 5.808011 × 10^{3}

i . ** First we have to convert the common exponent .**18 - 12 = 6.

The lesser exponent (12) have to be increased by

ii . 5.8 × 10^{12} = 0.0000058 × 10^{18}

iii . 8.5 × 10^{18} + 0.0000085 × 10^{18} =8.5000085 × 10^{1}^{8}

iv . 8.5000085 × 10^{18} is in scientific notation.

Thus, 8.5 × 10^{18} + 5.8 × 10^{12} = 8.5000085 × 10^{18}

i . ** First we have to convert the common exponent .**

3 - 1 = 2

The lesser exponent (1) have to be increase by

ii 5.8 × 10^{1} = 0.058 × 10^{3}

iii 0.058 × 10^{3} + 9.5 × 10^{3} = 9.558 × 10^{3}

iv 9.558 × 10^{3} is in scientific notation.

Thus, 9.5 × 10^{3} + 5.8 × 10^{1} = 9.558058 × 10^{3}

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