Measurement in Science

1
Measurement in Science

• Two kinds of numbers
• Exact numbers the value is known exactly-by
  definition, there is exactly 1000 g in a kg
• Inexact numbers obtained by measurement
  always some uncertainty in the last digit
• All digits in a measurement are significant the
  number of significant figures indicates the
  exactness of the measurement

2
Rules for assigning of significant digits

• 1 all nonzero digits are significant e.g.
  12.5, 132.6
• 2 zeros in front of a number are not
  significant e.g. 0.0032, 0.0125
• 3 zeros between non-zero digits are
  significant e.g. 107.5, 0.05008
• 4 zeros at end of a number are significant if
  there is a decimal point in number e.g. 100 ,
  .0800 , 5000.

3
How to calculate addition/subtraction

• The answer should have the same number of decimal
  places as of the quantity with the least number
  of decimal places
• Example add 13.3 467.78 which number has the
  least number of decimal places and what is it
• 13.3 1 decimal therefore answer as one
  decimal therefore 481.1

4
How to calculate multiplication/division

• The answer (product/quotient) should have the
  same number of significant digits as the quantity
  with the least number of significant digits
• Example 230 x 13.67
• Answer has 2 sig figs, therefore 3144.11 ? 3100

5
Rules for scientific notation

• Main idea a number can be expressed as the
  product of a decimal number between 1 and 10, and
  some integer power of 10
• We shift the decimal point to get the power of 10
• Eg 271. ? 2.71 x 102 4326 ?
• 4.326 x 103
• .00065 ? 6.5 x 10-4 .00569 ?
• 5.69 x 10-3