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.
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 10n out from all the numbers.
Step 3 :
Now, add or subtract the numbers and write the final answer in scientific notation.
Example 1 :
Evaluate :
(9.32 x 107) + (9.78 x 107)
Give your answer in scientific notation.
Solution :
(9.32 x 107) + (9.78 x 107)
In the given numbers, we have the same exponent for 10.
So, factor 107 out from the given numbers.
= (9.32 + 9.78) x 107
= 19.1 x 107
Write the above number in scientific notation.
= 1.91 x 108
Therefore,
(9.32 x 107) + (9.78 x 107) = 1.91 x 108
Example 2 :
Evaluate :
(9.598 x 1017) – (4.58 x 1017)
Give your answer in scientific notation.
Solution :
(9.598 x 1017) – (4.58 x 1017)
In the given numbers, we have the same exponent for 10.
So, factor 1017 out from the given numbers.
= (9.598 - 4.58) x 1017
= 5.018 x 1017
The above number is in scientific notation.
Therefore,
(9.598 x 1017) – (4.58 x 1017) = 5.018 x 1017
Example 3 :
Evaluate :
(1.328 x 107) + (2.034 x 105)
Give your answer in scientific notation.
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 4 :
Evaluate :
(5.76 x 102) + (6.61 x 10-3)
Give your answer in scientific notation.
Solution :
(5.76 x 102) + (6.61 x 10-3)
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,
= (5.76 x 102) + (0.0000661 x 105 x 10-3)
= (5.76 x 102) + (0.0000661 x 105-3)
= (5.76 x 102) + (0.0000661 x 102)
In the above numbers, we have the same exponent for 10.
So, factor 102 out from the given numbers.
= (5.76 + 0.0000661) x 102
= 5.7600661 x 102
The above number is in scientific notation.
Therefore,
(5.76 x 102) + (6.61 x 10-3) = 5.7600661 x 102
Example 5 :
Evaluate :
(3.2 x 10-3) - (8.02 x 10-5)
Give your answer in scientific notation.
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
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