Question
Perform following calculations and express results in scientific notations $($exponential notations$).$
$i. \ (2.5 \times 10^{-6}) \times (1.8 \times 10^{-7})$
$ii. \ (4.5 \times 10^{-3}) \times (1.8 \times 10^3)$
$iii. \ (8.5 \times 10^7) \times (3.5 \times 10^9)$

Answer

$i. (2.5 \times 10^{-6}) \times (1.8 \times 10^{-7}) = (2.5 \times 1.8) (10^{-6+(-7)})$
$= (2.5 \times 1.8) \times (10^{-6-7})$
$= 4.5 \times 10^{-13}$
$ii. (4.5 \times 10-3) \times (1.8 \times 103) = (4.5 \times 1.8) (10^{-3+3})$
$= (4.5 \times 1.8) \times (10^0)$
$= 8.1$
$iii. (8.5 \times 10^7) \times (3.5 \times 10^9) = (8.5 \times 3.5) (10^{7+9})$
$= (8.5 \times 3.5) \times 10^{16}$
$= 29.75 \times 10^{16}$
$= 2.975 \times 10^{17}$
[Note: To express number in scientific notation, the number has to be greater than or equal to $10$ or less than $1.$ The number, $8.1$ is greater than $1,$ but less than $10$ and hence, it cannot be expressed in scientific notation.]

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