1. Basic Math Concepts Needed for Chemistry Addition & Subtraction and Significant Digits

2. Thought Question • Add the three following masses: 12.7 cm + 8.8 cm + 7.642 cm • 12.7 cm + 8.8 cm + 7.642 cm = 29.142 cm (according to my calculator) • Does this answer make sense? • The answer has 5 significant digits! Should the answer be this accurate? • We know that the number of sig dig represents accuracy. Can the answer be more accurate than the question?

3. Thought Question • A sculptor carves a 1200 kg slab of marble. When finished the sculpture weighs 645 kg. How much marble was removed? • 1200 kg – 645 kg = 555 kg • Does this answer make sense? • The answer has more significant digits than the question!

4. Addition and Subtraction Rule • We know an answer can’t be more precise than the question! So here is the rule: • The sum or difference should have the same number of decimal places as the least precise value in the numbers being added or subtracted. • OR the sum or difference should be accurate to the same place value as the accurate numbers being added or subtracted. • NOTE that the words significant digits were NOT used!

5. Examples of the Rule 2.35 m 2.336 m + 2.2 m ⇒ this is the least precise number (1 6.886 m decimal place. Therefore the answer (6.9 m) can only have 1 decimal place) • Remember to add the numbers then round! • This is the precision rule. • Your answer can not be any more precise than the least precise measuring instrument used.

6. Let’s Revisit our questions! • 12.7 cm + 8.8 cm + 7.642 cm = 29.142 cm (according to my calculator) • The least accurate value in the question has 1 decimal place. It could also be said that the value is only accurate to the tenths column. • Therefore the answers should be rounded down to 1 decimal place. • 29.142 cm ⇒ 29.1 cm • 1200 kg – 645 kg = 555 kg • The least accurate value is only accurate to the hundreds place value. • Therefore the answers should be rounded to the closest hundred. • 555 kg ⇒ 560 kg

7. It helps to know rounding rules for this! • 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 same For 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 number For example: To obtain 2 significant digits: 2.55 is rounded to 2.6 and 2.25 is rounded to 2.2

8. Multiplying by numbers without units 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

9. Practice with Addition and Multiplication All answers must have the correct number of significant digits and the correct units. • 46.8 m + 24.17 m + 9.7612 m • 12.0 L - 2.25 L • 672000 kg + 82560 kg • 0.0074 mm - 0.0348 mm • 0.050 mm + 0.125 mm + 0.0046 mm • 462300 km – 160000 km • (202 m x 170 m) – 31000 m2 • (12.75 g – 11.1 g)/ 2.04 cm3

10. The 6 Significant Digits Rules • 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