A power of ten does exactly one thing to a number: it walks the decimal point. Drag the exponent and watch the point travel. Then step through converting real numbers into scientific notation — and doing arithmetic with them without ever writing out the zeros.
Where the point lands
How big is that?
6.02 × 103= 6,020
Exponent — drag me103
10−9100109
Coefficient a6.02
1.009.99
Or jump to a real measurement
The definition. A number is in scientific notation when it reads a × 10n with 1 ≤ |a| < 10 and n an integer. Exactly one nonzero digit in front of the point — no more, no fewer.
The trap. A negative exponent does not make a negative number. 3 × 10−4 = 0.0003, which is positive. The exponent's sign says which way the point moved; the coefficient's sign says whether the number is negative. The two are unrelated.