Powers of 10 and scientific notation

The link between prefixes and powers of 10

Each prefix corresponds to a power of 10. For example, kilo corresponds to 10^3 (that is, 1000), and milli corresponds to 10^-3 (that is, 1/1000 = 0.001).

Prefix	Power of 10
kilo (k)	10^3
hecto (h)	10^2
deca (da)	10^1
deci (d)	10^-1
centi (c)	10^-2
milli (m)	10^-3

Writing a number in scientific notation

Scientific notation consists of writing a number in the form a x 10^n, where a is between 1 and 10 (1 <= a < 10). For example:

• 3,200,000 m is written 3.2 x 10^6 m
• 0.000045 s is written 4.5 x 10^-5 s

This method is very useful in physics because it avoids writing long strings of zeros and makes calculations easier.

Concrete example

The Earth-Sun distance is about 150,000,000 km, i.e. 1.5 x 10^8 km. The diameter of an atom is about 0.0000000001 m, i.e. 1 x 10^-10 m. Scientific notation clearly makes these numbers much more readable.

Common pitfall

Watch the sign of the exponent: a positive exponent (10^3) corresponds to a large number, a negative exponent (10^-3) corresponds to a small number. Many students mix the two up at first: remember to check with a simple example like 10^1 = 10 (large) and 10^-1 = 0.1 (small).