Multiplication & Division and Significant Digits.

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Presentation transcript:

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