# ADDING AND SUBTRACTING WITH SCIENTIFIC NOTATION

## How to add and subtract numbers in scientific notation with same exponent ?

Let us consider the addition of two numbers in scientific notation.

(9.35 x 103) + (8.34 x 103)

Factor 103 out.

Then,

=  (8.35 + 9.34) x 103

=  17.69 x 103

Write the above number in scientific notation.

=  1.769 x 104

Therefore,

(9.35 x 103) + (8.34 x 103)  =  17.69 x 103

Note :

The same process has to be followed for subtracting numbers in scientific notation.

## How to add and subtract numbers in scientific notation with different exponents ?

Step 1 :

Adjust the exponents of 10 in the given numbers such that they have the same exponent.

(Tip : Always it is easier to adjust the smaller exponent to equal the larger exponent).

Step 2 :

In step 2, you will have the same exponent for 10 in all the numbers. For example, 10n

So, factor 10out from all the numbers.

Step 3 :

Now, add or subtract the numbers and write the final answer in scientific notation.

## Solved Examples

Example 1 :

Evaluate :

(1.328 x 107) + (2.034 x 105)

Solution :

(1.328 x 107) + (2.034 x 105)

In the given numbers, we don't have the same exponent for 10.

Adjust the exponents of 10 in the given numbers such that they have the same exponent.

It is easier to adjust the smaller exponent to equal the larger exponent.

Then,

=  (1.328 x 107) + (0.02034 x 107)

In the above numbers, we have the same exponent for 10.

So, factor 107 out from the given numbers.

=  (1.328 + 0.02034) x 107

=  1.34834 x 107

The above number is in scientific notation.

Therefore,

(1.328 x 107) + (2.034 x 105)  =  1.34834 x 107

Example 2 :

Evaluate :

(3.2 x 10-3) - (8.02 x 10-5)

Solution :

(3.2 x 10-3) - (8.02 x 10-5)

In the given numbers, we don't have the same exponent for 10.

Adjust the exponents of 10 in the given numbers such that they have the same exponent.

Then,

=  (3.2 x 10-3) - (0.0802 x 102 x 10-5)

=  (3.2 x 10-3) - (0.0802 x 102-5)

=  (3.2 x 10-3) - (0.0802 x 10-3)

In the above numbers, we have the same exponent for 10.

So, factor 10-3 out from the given numbers.

=  (3.2 - 0.0802) x 10-3

=  3.1198 x 10-3

Write the above number in scientific notation.

=  3.1198 x 10-3

Therefore,

(3.2 x 10-3) - (8.02 x 10-5)  =  3.1198 x 10-3

Example 3 :

Simplify the expression given below.

(0.723 x 108) + (338.2 x 105) - (6.1 x 107)

Solution :

Method 1 :

Step 1 :

In the given numbers, the highest power of 10 is 8.

So, write each number with 10 power 8.

0.723 x 108  =  0.723 x 108

338.2 x 105  =  0.3382 x 108

6.1 x 107  =  0.61 x 108

Step 2 :

Simplify the multipliers.

0.723 + 0.3382 - 0.61  =  0.4512

Step 3 :

Write the final answer in scientific notation :

0.4512 x 108  =  4.512 x 107

Method 2 :

Step 1 :

First, write each number in standard notation.

0.723 x 108  =  72,300,000

338.2 x 105  =  33,820,000

6.1 x 10⁷  =  61,000,000

Step 2 :

Simplify the numbers in standard notation.

72,300,000 + 33,820,000 - 61,000,000  =  45,120,000

Step 3 :

Write the final answer in scientific notation :

45,120,000  =  4.512 x 107 Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here.

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