Significant Figures & Rounding

Chemistry A

IntroductionPrecision is sometimes limited to the tools we use to measure.

For example, some digital clocks display only hours and minutes (12:00), so you can only read it to the nearest minute.

With a stopwatch we can read up to the nearest hundredth of a second.

So scientists indicate the precision of measurements by the number of digits they report.

For example, a value of 3.25g is more precise than a value of 3.3 g.

The digits that are reported are the Significant Figures.

Significant Figures

Significant Figures include all known digits plus one estimated digit.

There are rules we need to follow when dealing with Significant Figures.

Rules for Recognizing Sig. Figs.1. Non-zero numbers are always

significant.7.23 has three

2. Zeros between non-zero numbers are always significant.

60.5 has three

3. All ending zeros to the right of the decimal are significant.

6.20 has three

Rules for Recognizing Sig. Figs.

4. Zeros that act as placeholders not significant. Convert to sicentific notation

0.000253 & 432000 each have three

5. Counting numbers and defined constants have an infinite number of significant figures. π = 3.14

PracticeDetermine the Significant Figures in the

following numbers.

508.04 sig. figs.

8070003 sig. figs.

0.0004823 sig. figs.

3.1587 x 10-8 5 sig. figs.

Rounding NumbersSuppose you divide 22.44 by 14.2 on you calculator. The answer you get is 1.5802817.

Do you write all of that number down as your answer?

No, because your answer should have no more significant figures than the data with the fewest sig. figs.

So your answer should be 1.58

Rules for Rounding Numbers

If the number right next to the last sig. fig. is less than 5, don’t change the last significant figure.

2.532 2.53

If the number right next to the last sig. fig. is greater than 5, round up the last significant figure.

2.536 2.54

Rules for Rounding Numbers

If the number right next to the last sig. fig. is equal to 5 and is followed by a non-zero, round up the last significant figure.

2.5351 2.54

Rules for Rounding Numbers

If the number right next to the last sig. fig. is equal to 5 and is not followed by a non-zero, look at the last significant figure.

If odd, round up.

If even, don’t round up.

2.5350 2.54 but 2.5250 2.52

PracticeRound to 4 significant figures

8479184790

38.543238.54

256.75256.8

4.93564.936

Adding & SubtractingWhen adding or subtracting, answer must have the same amount of numbers to the right of the decimal point as the value with the fewest numbers to the right of the decimal.

28.0

23.538

+ 25.68

77.218 77.2

Practice

43.2 + 51.0 + 48.7 =

142.9

93.26 – 81.14 =

12.12

258.3 + 257.11 + 253 =

768

Multiplying & Dividing

Your answer must have same amount of numbers as the value with the fewest significant figures.

3.20 x 3.65 x 2.05 = 23.944

23.944 23.9

Practice

24 x 3.26 = 78

120 x 0.10 = 12

4.84/ 2.4 =2.0

168/ 58 =2.9