Scientific Notation and Significant Figures ( a short review )
Scientific Notation Expresses a value as a product of number between 1 and 10 and the appropriate power of 10 ex: 27000 = 2.7 x10 3 0.000167 = 1.67 x10 4 5 = 5x10 0
Significant Figures (SF) 231 (3 SF) 3.6547 (5 SF) non zero digit are always significant 1.3 x10 5 (2 SF) 2.0004 (5 SF) 9.901 x10 2 (4 SF) trapped zeroes are always significant 1000001 (7 SF) 073 (2 SF) leading zeroes are never significant 0.00274 (3 SF) 96 00 (ambiguous) 9600 . (4 SF) trailing zeroes are significant ONLY when 12000.0 (6 SF) there is a decimal point in the number. 12.00 x10 3 (4 SF) 0.001000 (4 SF) exact number and conversion factor are regarded as infinitely precise
Significant figures in calculation
Multiplication / Division : The final answer must have the smallest number of significant figures among the numbers involved in the calculation 24.015 x 6.05 = 145 3.105 x10 3 x 1.43 x 10 2 = 4.44 (5 SF) (3 SF) (3 SF) (4 SF) (3 SF) (3 SF) Addition / Subtraction : The final answer must have the smallest number of decimal places among the numbers involved in the calculation 493 + 2.3 = 495 6.500 x10 5 2.3 x10 6 = 6.27 x10 5 (3 SF) (2 SF) (3 SF) (4 SF) (2 SF) (3 SF)
Rounding off Use the digit immediately to the right of the last significant digit (the others do not count!) ex: round off the following set of numbers to 3 SF 0.12748 The number after the last SF (here 4) is less than 5: no round up. → 0.127 0.0352 95 The number after the last SF (here 9) is more than 5: round up. → 0.0353 In the case when the number following the last SF is a 5 2.14 58 If the last SF is even (here 4) followed by a 5, no round up. → 2.14 4 443 51 If the last SF is odd (here 3) followed by a 5, increase last SF by one. → 4.44x10
http://place.dawsoncollege.qc.ca/~dbaril/ Problem set: Significant figures
Question 1 Which number has the most significant figures? a. 5.61 km c. 1.000 m 4 b. 0.00021 L d. 2.3x10 m
Question 2 How many significant figures are in each of the following? a. 203 K d. 6.30x10 2 km
b. 300.00 g e. 1000°C
c. 2.11x10 3 M f. 0.0100 L
Question 3 Perform the operations indicated and express your answer to the correct number of significant figures. a. 27 + 37.2 9.06 =
b. 28.763 0.763 =
c. 22.31 + 120.6542 + 0.002 =
d. (65.2 – 63.6) x 283 =
e. 2.1 x10 4 x 2.38x10 4 =
f. 5.23x10 3 2.3x10 4 =
Question 4 Round up the following numbers to three significant figures. Use the scientific notation if required. a. 10002 d. 1.040x10 5
b. 56.078 e. 0.066559
c. 302.59 f. 2030
Answers Q1: c Q2: a. 3 b. 5 c. 3 d. 3 e. ambiguous f. 3 2 -3 Q3: a. 55 b. 28.000 c. 142.97 d. 4.5x10 e. 5.0 f. 5.00x10 4 5 -2 3 Q4: a. 1.00x10 b. 56.1 c. 302 d. 1.04x10 e. 6.66x10 f. 2.03x10
http://place.dawsoncollege.qc.ca/~dbaril/