Scientific not'n avoids writing lots of zeroes. Recall these rules:
1. SHIFT the decimal until it's after the left-most non-zero digit, and drop the zeroes; this
is the base
2. REWRITE each decimal place you shifted as a power of ten, in the exponent:
a. ea. shift made to the left becomes +1 power of ten: 721. = 7.21 x 102
b. ea. shift to the right becomes -1 power of ten: .0049 = 4.9 x 10-3
3. when multiplying/dividing #'s, treat bases and exponents SEPARATELY:
(1.2 x 10-6) x (3.5 x 103) = (1.2 x 3.5) x
(10-6 x 103)
4. to MULTIPLY exponents (the power to which 10 is raised), just add them
10-6 x 103 = 10-6+3 = 10-3
5. to DIVIDE exponents, flip sign of denominator's exponent, then mulitply
10-8 / 103 = 10-8 x 10-3
= 10-8 -3 = 10-11
EXAMPLE:
Q: How many H (hydrogen) atoms are in the Sun, approximately?
A: Divide the mass of the Sun by the mass of one H atom: NH = MSun/MH
masochists write
NH = 2,000,000,000,000,000,000,000,000,000,000,000 /
.000 000 000 000 000 000 000 001 67
YUCK!
WE write
NH = 2 x 1033 / 1.67 x 10-24
= (2 / 1.67) x (1033/10-24)
= (1.2) x (1033 x 10+24)
= 1.2 x 1057
This should be a review for you. If it's not, see p.4 in the text,
Appendix 4 (p.A-18) in the text, or try these web pages:
http://www.nyu.edu/pages/mathmol/textbook/scinot.html,
http://library.advanced.org/20991/textonly/alg/sci_not.html, or
http://janus.astro.umd.edu/astro/scinote.html.