Basic Math Concepts Needed for Chemistry

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 = 111.76 cm2

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?

Thought Question

A car travels 486 km in 5.7 hours. What is its average speed?

486km/5.7h = 85.263157 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.

Thought 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.

Multiplication and Division Rule

12.7 cm x 8.8 cm = 111.76 cm2

The least accurate value in the question has 2 significant digits.

Therefore the answers should be rounded down to 2 sig dig

111.76 cm2 ⇒ 110 cm2

486km/5.7h = 85.263157 km/h The least accurate value in the question has 2

significant digits. Therefore the answers should be rounded down

to 2 sig dig 85.263157 km/h ⇒ 85 km/h

Let’s Revisit our questions!

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 3.494 rounds to 3.5

If the digit after the one you want is less than five then the preceding number stays the sameFor example: To obtain 2 significant digits: 3.44 rounds to 3.4 and 3.449 rounds to 3.4

If the single digit after the one you want is 5, round to the closest even numberFor example: To obtain 2 significant digits: 2.55 is rounded to 2.6 and 2.25 is rounded to 2.2

It helps to know rounding rules for this!

Round-off the following to 3 significant digits:

1) 3.4752 cm2) 123 453 km3) 0.00472 mm4) 109 995 000 km5) 0.000003485 m

Rounding

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 = 58320 tonnes ⇒ 58300 tonnes

Multiplying by numbers without units

All answers must have the correct number of significant digits and the correct units.1) 8.75 mol/ 2.18 L2) 120 km/h x 2.25 h3) 67200000000 m / 8.256 s4) 0.0074 mm x 0.0348 mm5) 9.050 m x 246) 12000 L/ 27.3 h7) 2002 m x 178 m8) 12.75 g/ 31.4 cm3

Practice with Multiplication and Division

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 = 58320 tonnes ⇒ 58300 tonnes

The 6 Significant Digits Rules