Scientific Notation

1. Scientific Notation

2. 1. Why use scientific notation? • Primarily because physics often deals with very large and very small numbers. • 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. • The other reason is that it allows us to write measurements with a precise number of significant figures (More on this later).

3. 2. Numbers greater than 1 • When a number greater than 1(ex. 150,800,000,000 m) is converted to scientific notation the following rules apply: • First, move the decimal point until exactly one non-zero digit (a 1-9) appears to the left of the decimal. • Second, write the new number down while dropping the trailing zeroes. (ex. 1.508) • Third, write the symbol “x10” after the number. (ex. 1.508 x10) • Finally, write how many times you moved the decimal as a positive exponent. (ex. 1.508 x1011)

4. 3. Numbers smaller than 1 • When a number smaller than 1(ex. 0.00000000142 m) is converted to scientific notation the following rules apply: • First, move the decimal. • Second, write the new number down while dropping zeroes. (ex. 1.42) • Third, write the symbol “x10” after the number. (ex. 1.428 x10) • Finally, write how many times you moved the decimal as a negative exponent. (ex. 1.42 x10-9)

5. 4. A useful mnemonic • When trying to remember whether to make an exponent positive or negative a mnemonic is useful. • The correct association in you head should be: (left = positive) and (right = negative). • Remember this by associating “g = g” from the words “right” and “negative”.

6. 5. Some practice • Write the following numbers in scientific notation: • 1200 • 0.005 • 177,000 • 0.00000253 • 8.35