Scientific Notation

Scientific Notation How to write in scientific notation.

Move the decimal… until it is on the right side of the first nonzero number. Example: 123 000 000 000 The decimal will be between 1 & 2 1.23 000 000 000

Drop non significant zeros. • 123 000 000 000 has 3 significan digits, therefore the zeros are not significant therefore you may drop these. • Therefore, 1.23 000 000 becomes 1.23

Find the exponent. • Count how many places you moved the decimal point. • This will be your exponent. • If you do not see a decimal point, assume it is at the end of the number • In the number 123 000 000 000. you will need to move the decimal point 11 places to get it between 1 & 2.

Put it all together. • 123 000 000 000 = 1.23 x 1011 Always use the power of 10.

Follow the same steps for small numbers Example: 0.00000123 Move decimal point = 0000001.23 Drop non significant zeros = 1.23 Count number of places moved = 6 Add a negative to the exponent = -6 Final answer: 1.23 x 10-6

Practice Problems I. Writing in scientific notation • 20 000 Hz = 2 x 104 Hz • 105 000 g = 1.05 x 105 g • 0.005 cm/h = 5 x 10-3 cm/h • 0.02 cm/s = 2 x 10-2 cm/s • 160 050 000 km = 1.6005 x 108 km • 0.000003050 kg = 3.050 x 10-6 kg

Practice Problems • Write the following numbers in standard notation. • 1.47 x 103 m/s = 1470 m/s • 1 x 10-8 mm = .00000001 mm • 2.5 x 100 N = 2.5

Scientific Notation