Scientific Notation
1. Why use scientific notation?
a. Primarily because physics often deals with very large and
very small numbers.
b. For example, the distance from the earth to the sun is
150,800,000,000 m and the distance between carbon
atoms in diamond is 0.00000000142 m.
c. The other reason is that it allows us to write measurements
with a precise number of significant figures (More on this
later).
2. Numbers greater than 1
a. When a number greater than 1(ex. 150,800,000,000 m) is
converted to scientific notation the following rules apply:
b. First, move the decimal point until exactly one non-zero
digit (a 1-9) appears to the left of the decimal.
c. Second, write the new number down while dropping the
trailing zeroes. (ex. 1.508)
d. Third, write the symbol “x10” after the number.
(ex. 1.508 x10)
e. Finally, write how many times you moved the decimal as a
positive exponent. (ex. 1.508 x1011)
3. Numbers smaller than 1
a. When a number smaller than 1(ex. 0.00000000142 m) is
converted to scientific notation the following rules apply:
b. First, move the decimal.
c. Second, write the new number down while dropping
zeroes. (ex. 1.42)
d. Third, write the symbol “x10” after the number.
(ex. 1.428 x10)
e. Finally, write how many times you moved the decimal as a
negative exponent. (ex. 1.42 x10-9)
4. A useful mnemonic
a. When trying to remember whether to make an exponent
positive or negative a mnemonic is useful.
b. The correct association in you head should be:
(left = positive) and (right = negative).
c. Remember this by associating “g = g” from the words
“right” and “negative”.
5. Some practice
a.
b.
c.
d.
e.
f.
Write the following numbers in scientific notation:
1200
0.005
177,000
0.00000253
8.35