Here are a few examples of scientific notation, using powers of ten:
one thousand = 1,000
103 = 10 × 10 × 10 = 101 × 101 × 101 = 101+1+1 = 1e3
one million = 1,000,000
106 = 10 × 10 × 10 × 10 × 10 × 10 =
101 × 101 × 101 × 101 × 101 × 101 = 101+1+1+1+1+1 = 1e6
one million = one thousand × one thousand
106 = 103 × 103 = 103+3 = 1e6
when multiplying powers of ten, add the exponents
103 × 102 = 103+2 = 105 = 1e5
when dividing powers of ten, subtract the exponents
103 ÷ 102 = 103-2 = 101 = 10 = 1e1
when raising powers of ten to a power, multiply the exponents
(104)2 = 104 × 2 = 108 = 1e8
a negative exponent means that you divide, rather than multiplying, by the powers of ten
10-4 = 1 ÷ 104 = 0.0001 = 1e-4
negative numbers are smaller than positive ones
-104 < -102 < -101 < -100 < 0 <
100 < 101 < 102 < 104
-10,000 < -100 < -10 < -1 < 0 <
1 < 10 < 100 < 10,000
