Multiply numbers written in scientific notation :
Here we are going to see some example problems to understand how to multiply numbers written in scientific notation.
Example 1 :
Find the value of (8.18 × 10⁻⁶)(1.15 × 10⁻⁵)
Solution :
The given two terms are in scientific notation already, so we have to multiply 8.18 by 1.15 and combine the number which are having the same base 10.
= 8.18 x 1.15 × 10⁻⁶ × 10⁻⁵
= 8.18 x 1.15 × 10⁻⁶ × 10⁻⁵
= 9.407 x 10^(-6 - 5)
= 9.407 x 10^(-11)
Example 2 :
Find the value of (5000)⁴ x (200)³
Solution :
Since the given numbers are not in scientific notation, first we have to convert the given numbers in scientific notation.
5000 = 5.0 x 10³ (5000)⁴ = (5 x 10³)⁴ |
(200) = 2.0 x 10² (200)⁶ = (2 x 10²)³ |
By distributing the power, we get
= (5.0)⁴ x (10³)⁴ = 5⁴ x 10^12 = 625 x 10^12 |
= (2 x 10²)³ = 2³ x (10²)³ = 8 x 10^6 |
By combining the above two terms, we get
= 625 x 10^12 x 8 x 10^6
= 5000 x 10 ^(12 + 6)
= 5000 x 10 ^(18)
= 5.0 x 10³ x 10 ^(18)
= 5.0 x 10^(3+18)
= 5 x 10^21
Example 3 :
Find the value of (2000)⁴ x (0.0001)⁻³
Solution :
Since the given numbers are not in scientific notation, first we have to convert the given numbers in scientific notation.
2000 = 2.0 x 10³ (2000)⁴ = (2 x 10³)⁴ = 2⁴ x (10³)⁴ = 16 x 10^12 |
0.0001 = 1.0 x 10⁴ (0.0001)⁻³ = (1 x 10⁴)⁻³ = 1⁻³ x (10⁴)⁻³ = 1 x 10^-12 |
By combining the above two terms, we get
= 16 x 10^12 x 1 x 10^-12
= 16 x 10^(12 - 12)
= 16 x 10⁰
= 16
After having gone through the stuff given above, we hope that the students would have understood "Multiply numbers written in scientific notation".
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