Presentation on theme: "Significant figures or Significant digits"— Presentation transcript:
1 Significant figures or Significant digits 4/17/2017 8:00 AMSignificant figures or Significant digitsANY numbers generated by means of a measurement (length, volume, time, etc) should be expressed in the correct number of significant figures.This reflects how close the measured values are to the true values.
2 Significant Figures (digits) = reliable figures obtained by measurement= all digits known with certainty plus one estimated digit
3 Taking the measurement Is always some uncertaintyBecause of the limits of the instrument you are using
4 EXAMPLE: mm rulerIs the length of the line between 4 and 5 cm? Yes, definitely. Is the length between 4.0 and 4.5 cm? Yes, it looks that way. But is the length 4.3 cm? Is it 4.4 cm?
5 It is important to be honest when reporting a measurement, so that it does not appear to be more accurate than the equipment used to make the measurement allows.We can achieve this by controlling the number of digits, or significant figures, used to report the measurement.
6 As we improve the sensitivity of the equipment used to make a measurement, the number of significant figures increases.Postage Scale3 g1 g1 significant figureTwo-pan balance2.53 g0.01 g3 significant figuresAnalytical balance2.531 g0.001g4 significant figures
7 Which numbers are Significant? 5,551,21355.00 mmWhich numbers are Significant?How to count them!9000 L0.003g
8 Non-Zero integers Always count as significant figures has 4 significant digits
9 Zeros – there are 3 types Leading zeros (place holders) The first significant figure in a measurement is the first digit other than zero counting from left to right0.0045g(4 is the 1st sig. fig.)“0.00” are place holders.The zeros are not significant
10 Captive zerosZeros within a number at always significant – gAll digits are significant
11 Trailing zeros – at the end of numbers but to the right of the decimal point 2.00 g - has 3 sig. digits (what this means is that the measuring instrument can measure exactly to two decimal places.100 m has 1 sig. digitZeros are significant if a number contains decimals
12 Exact Numbers Are numbers that are not obtained by measuring Referred to as counting numbersEX : 12 apples, 100 people
13 Exact Numbers Also arise by definition 1” = 2.54 cm or 12 in. = 1 foot Are referred to as conversion factors that allow for the expression of a value using two different units
14 Significant Figures Rules for sig figs.: Count the number of digits in a measurement from left to right:Start with the first nonzero digitDo not count place-holder zeros.The rules for significant digits apply only to measurements and not to exact numbersSig figs is short for significant figures.
15 Determining Significant Figures State the number of significant figures in the following measurements:2005 cm40.050 cm225,000 g2g325.0 ml350.00 ml40.25 s21000 s1mol31000. mol4
16 Rounding Numbers To express answer in correctly Only use the first number to the right of the last significant digit
17 Rounding Always carry the extra digits through to the final result Then roundEX:Answer is rounds to 1.3OR1.356 rounds to 1.4
18 Rounding off sig figs (significant figures): Rule 1: If the first non-sig fig is less than 5, drop all non-sig fig.Rule 2: If the first sig fig is 5, or greater that 5, increase the last sig fig by 1 and drop all non-sig figs.Round off each of the following to 3 significant figures:12.50.60214,700192