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Adding Scientific Notation

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 103 - 5.63 x 102 into 6300 - 563. Then subtract normally to get 5.737 x 103. 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 1011 + 4.8 x 1010, now we change the larger number to the same power as the small number or vise versa.

Change 4.8 x 1010 into 0.48 x 1011, the problem becomes 5.75 x 1011 + 0.48 x 1011 = 6.23 x 1011, which is already in scientific notation.

Just before Adding Numbers with Scientific Notation, they are required to have same or matching exponent.
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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How to Add Scientific Notation

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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 103) + (2.0 x 103) = 8.9 x 103

Adding Scientific Notation Problems

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Below are the examples for Adding Numbers with Scientific Notation:

Solved Examples

Question 1: 3.557 × 105 + 8.0039 × 108 = ?
Solution:
 

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 × 105 = 0.003557 × 108

iii . 0.003557 × 108 + 8.0039 × 108 = 8.007457 × 108

iv . 8.007457 × 108 is in scientific notation.

Thus, 3.557 × 105 + 8.0039 × 108 = 8.007457 × 108


 

Question 2: 5.80808 × 103 - 6.9 × 10-2 = ?
Solution:
 

i . First we have to convert the common exponent .3 - (-2) = 5
The smaller exponent (-2) must be increased by
5.

ii . 6.9 × 10-2 = 0.000069 × 103
iii . 5.80808 × 103 - 0.000069 × 103 = 5.808011 × 103
iv . 5.808011 ×103 is in scientific notation.

Thus, 5.80808 × 103 - 6.9 × 10-2 = 5.808011 × 103


 

Question 3: 3.5 ×1018 + 5.3 × 1012 =?
Solution:
 

i . First we have to convert the common exponent .18 - 12 = 6.
The lesser exponent (12) have to be increased by
6.

ii . 5.8 × 1012 = 0.0000058 × 1018

iii . 8.5 × 1018 + 0.0000085 × 1018 =8.5000085 × 1018
iv . 8.5000085 × 1018 is in scientific notation.

Thus, 8.5 × 1018 + 5.8 × 1012 = 8.5000085 × 1018


 

Question 4: 9.5 × 103 + 5.8 × 101 = ?
Solution:
 

i . First we have to convert the common exponent .
3 - 1 = 2

The lesser exponent (1) have to be increase by
2.

ii 5.8 × 101 = 0.058 × 103
iii 0.058 × 103 + 9.5 × 103 = 9.558 × 103
iv 9.558 × 103 is in scientific notation.

Thus, 9.5 × 103 + 5.8 × 101 = 9.558058 × 103


 

Adding Scientific Notation Practice Problems

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Practice Problems

Question 1: Add scientific notation: 6.801 × 103 - 2.2 × 107 = ?
Question 2: Add scientific notation: 5 × 103 + 2.6 × 104
Question 3: Subtract scientific notation: 8 × 105 – 9.2 × 104
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