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Appendix A: Miscellany
4.

Scientific Notation

Physicists deal with really big and really small numbers sometimes, and it can get tiresome (and risky) to count all of those zeroes. That's why scientific notation was born! It looks like this

5.2mantissa×103exponent

The mantissa is typically (but not always! See Formal Scientific Notation*) a number between 1 (inclusive) and 10 (exclusive): that is, a single nonzero digit, followed by a decimal point and any number of other digits. The exponent is always an integer: if it's nonnegative then this is a number bigger than (or equal to) 1, and if it is negative then it is less than 1.

To convert a number to scientific notation, count the number of times you would need to move the decimal point so that it is just behind the first non-zero digit. A move to the left means a positive exponent.

25+34+26+1.=2.546×1030.01324=3.4×102

Don't confuse the E or EE key with the ex key.
Many calculators have a specific way to enter a number in scientific notation, usually a button labelled E or EE. A number like 45×104 should be entered as 4 5 E 4. Some people use this notation in writing as well, writing "4.6E-6" or "4.6e-6" when they mean 4.6×106.

Sometimes we need to change a number in scientific notation so that it has a different exponent: for example, 2.3×103 is the same as 23×102. Every change of the exponent must also be accompanied by moving the decimal point one place. For example: 2.3+10+2×1072=230×109 21.3×105+1=0.23×106

Or in other words

If you make the exponent bigger, make the mantissa smaller.
If you make the mantissa bigger, make the exponent smaller.