a × 10n where 1≤ a <10 and n ∈ { ... -3, -2, -1, 0, 1, 2, 3 ... )
Rules of exponents: 10x × 10y = 10(x + y) 10x ÷ 10y = 10(x - y) 10-n = 1 ÷ 10n
628 nm = ? meters628 nm = 628 × 10-9 meters [definition of the metrix prefix nano]628 nm = 6.28 × 102 × 10-9 meters628 nm = 6.28 × 102+(-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 cm3, then a cube that is 100 cm on each edge would hold how many liters? V = l w h = (100 cm)3 = (102 cm)3 = 106 cm3 our question has now become how many liters are in 106 cm3 106 cm3 = ? L since 1 L = 103 cm3, we rewite 6 as 3+3 10(3+3) cm3 = ? Lremember that adding exponents means multiplying powers of 10 (103× 103) cm3 = ? L 103× (103 cm3) = 103 L
How many m3 does a cube 100 cm on an edge occupy? V = l w h = (100 cm)3 = (102 cm)3 = 106 cm3V = l w h = (100 cm)3 = (1 m)3 = 1 m3 Therefore, 106 cm3 = 1 m3
How many m3 are present in a cube having a volume of 1000 cm3? 1000 cm3 = 103 cm3 = ? m3 using the answer to Example #4 we know that 106 m3 = 1 m3 103 cm3 = 10(-3+6) cm3 = ? m3 remember that adding exponents means multiplying powers of 10 (10-3 × 106) cm3 = ? m3 10-3 × (106 cm3 ) = 10-3 m3