Operations with numbers in scientific notation

Since numbers written in scientific notation involve powers, when these numbers are multiplied, divided or raised to a power, the index laws come into play.

Example 3

Simplify and write in scientific notation.

Question	Solution
a \((3 × 10^4) × (2 × 10^6)\)	= \(3 × 10^4 × 2 × 10^6\)   = \(3 × 2 × 10^4 × 10^6\)   = \(6 × 10^{10}\)
b \((9 × 10^7) ÷ (3 × 10^4)\)	= \(\dfrac{9 × 10^7}{3 × 10^4}\) = \(\dfrac{9}{3}×\dfrac{10^7}{10^4}\) = \(3 × 10^3\)
c \((4.1 × 10^4)^2\)	= \(4.1^2 × 10^8 = 16.81 × 10^8\) = \(1.681 × 10^1 × 10^8\) = \(1.681 × 10^9\)
d \((2 × 10^5)^{-2}\)	= \(2^{–2} × 10^{–10}\) = \(\dfrac{1}{2^2}× 10^{–10}\) = \(0.25 × 10^{–10}\) = \(2.5 × 10^{–1} × 10^{–10}\) = \(2.5 × 10^{–11}\)