a × 10^{n} where 1≤ a <10 and n ∈ { ... -3, -2, -1, 0, 1, 2, 3 ... )

Rules of exponents: 10^{x} × 10^{y} = 10^{(x + y)} 10^{x} ÷ 10^{y} = 10^{(x - y)} 10^{-n} = 1 ÷ 10^{n}

628 nm = ? meters628 nm = 628 × 10^{-9} meters [definition of the metrix prefix nano]628 nm = 6.28 × 10^{2} × 10^{-9} meters628 nm = 6.28 × 10^{2+(-9)} meters 628 nm = 6.28 × 10^{-7} meters

628 nm = ? μm using the answer to Example #1 we can replace 628 nm with 6.28 × 10^{-7} meters 6.28 × 10^{-7} meters = ? μm since 1 μm equals 10^{-6} meters, we rewrite -7 as -1+(-6) 6.28 × 10^{-1+(-6)} meters = ? μm remember that adding exponents means multiplying powers of 10 6.28 × (10^{-1} × 10^{-6} ) meters = ? μm (6.28 × 10^{ -1}) × (10^{-6} meters) = 6.28 × 10^{-1} μm = 0.628 μm

If a liter equals 1000 cm^{3}, then a cube that is 100 cm on each edge would hold how many liters? V = l w h = (100 cm)^{3} = (10^{2} cm)^{3} = 10^{6} cm^{3} our question has now become how many liters are in 10^{6} cm^{3} 10^{6} cm^{3} = ? L since 1 L = 10^{3} cm^{3}, we rewite 6 as 3+3 10^{(3+3)} cm^{3} = ? Lremember that adding exponents means multiplying powers of 10 (10^{3}× 10^{3}) cm^{3} = ? L 10^{3}× (10^{3} cm^{3}) = 10^{3} L

How many m^{3} does a cube 100 cm on an edge occupy? V = l w h = (100 cm)^{3} = (10^{2} cm)^{3} = 10^{6} cm^{3}V = l w h = (100 cm)^{3} = (1 m)^{3} = 1 m^{3} Therefore, 10^{6} cm^{3} = 1 m^{3}

How many m^{3} are present in a cube having a volume of 1000 cm^{3}? 1000 cm^{3} = 10^{3} cm^{3} = ? m^{3} using the answer to Example #4 we know that 10^{6} m^{3} = 1 m^{3} 10^{3} cm^{3} = 10^{(-3+6)} cm^{3} = ? m^{3} remember that adding exponents means multiplying powers of 10 (10^{-3} × 10^{6}) cm^{3} = ? m^{3} 10^{-3} × (10^{6} cm^{3} ) = 10^{-3} m^{3}