Multiplication & Division and Significant Digits
A square has a length of 12.7 cm and a width of 8.8 cm. What is its area? 12.7 cm x 8.8 cm = cm 2 Does this answer make sense? The answer has 5 significant digits! The factors have 3 and 2 sig dig respectively We know that the number of sig dig represents accuracy. Can the answer be more accurate than the question?
A car travels 486 km in 5.7 hours. What is its average speed? 486km/5.7h = km/h (on an 8- digit display calculator) Does this answer make sense? The answer has 8 significant digits! The dividend and divisor have 3 and 2 sig dig respectively – once again the answer is more accurate than the question.
It makes no sense that the answer could be more accurate! Thus we look to the least accurate value in the question. THE RULE IS: The answer has the same number of significant digits as the least number of significant digits used in the calculations.
12.7 cm x 8.8 cm = cm 2 The least accurate value in the question has 2 significant digits. Therefore the answers should be rounded down to 2 sig dig cm 2 ⇒ 110 cm 2 486km/5.7h = km/h The least accurate value in the question has 2 significant digits. Therefore the answers should be rounded down to 2 sig dig km/h ⇒ 85 km/h
If the digit after the one you want is greater than 5, then round up For example: To obtain 2 significant digits: 3.47 rounds to 3.5 and rounds to 3.5 If the digit after the one you want is less than five then the preceding number stays the same For example: To obtain 2 significant digits: 3.44 rounds to 3.4 and rounds to 3.4 If the single digit after the one you want is 5, round to the closest even number For example: To obtain 2 significant digits: 2.55 is rounded to 2.6 and 2.25 is rounded to 2.2
Round-off the following to 3 significant digits: 1) cm 2) km 3) mm 4) km 5) m
Numbers obtained from counting are not measured. They do not affect the number of significant digits in the answer! Ex.Each section of a bridge weighs 2430 tonnes. The bridge has 24 sections, what is the weight of the bridge? Since the 24 is a counted number, we still use the 3 significant digits in the first number to obtain the number of sig dig in the answer. 24 x 2430 tonnes = tonnes ⇒ tonnes
All answers must have the correct number of significant digits and the correct units. 1) 8.75 mol/ 2.18 L 2) 120 km/h x 2.25 h 3) m / s 4) mm x mm 5) m x 24 6) L/ 27.3 h 7) 2002 m x 178 m 8) g/ 31.4 cm 3
6)Numbers obtained from counting are not measured. They do not affect the number of significant digits in the answer! Ex.Each section of a bridge weighs 2430 tonnes. The bridge has 24 sections, what is the weight of the bridge? Since the 24 is a counted number, we still use the 3 significant digits in the first number to obtain the number of sig dig in the answer. 24 x 2430 tonnes = tonnes ⇒ tonnes