Wks Full Pack L2

Significant Digits Overview All measurements have uncertainty. In science, it is important to indicate the uncertainty when you are reporting numbers since this indicates the reliability of the data and the quality of instruments being used. When a scientist takes a measurement, she records all the digits she is certain of and includes one digit that has some uncertainty. For instance, if a standard metric ruler were used to find the length of a pen, the reading may fall between 15.4cm and 15.5cm. The scientist may estimate that the length is closer to the 15.5 mark and report the value as 15.47cm. In this measurement, only the 7 is uncertain and is probably off by 1 or 2 at the most. Sometimes the uncertainty will be reported using the ± symbol. For example, 244 ± 3. When the ± symbol is not used, expect that the right-most digit is uncertain and could be off by 2. For example, a value of 34.23mL means that the scientist is fairly certain the value is between 34.21 and 34.25mL with the best guess being 34.23mL. Besides measurements, scientists also report calculated values (like density). There is a two-part rule that indicates how to round calculated numbers so that they show the same degree of uncertainty as the measurements they were calculated from. To use the rule for multiplication and division you will need to know how many significant digits each factor has. The number of significant digits is the number of digits that indicate precision. It is the number of digits you are certain of and the one uncertain digit. The number of significant digits in 15.47cm (length of the pen) is 4. Determining the number of significant digits Atlantic-Pacific Rule: Draw a map of the US and label the Atlantic and Pacific oceans. When the decimal point is Present, count the digits starting with the first non-zero digit from the Pacific side (left side). When the decimal point is Absent, count the digits starting with the first non-zero digit from the Atlantic side (right side). Examples: 1. 34000 Decimal is absent. Starting from the right, the 1st non-zero digit is the 4. There are 2 significant digits. 2. 0.005030 Decimal is present. Starting from the left, the 1st non-zero digit is the 5. There are 4 significant digits. As you can see from the examples, some of the zeros get counted and some don’t. On the other hand, all non-zeros are counted all of the time. Reporting calculated numbers to the correct significant digits Many-Places Rule: When doing Multiplication or division, report your answer to as Many significant digits as the factor with the least significant digits. When doing Plus or minus (i.e., addition or subtraction), report your answer to the same number of Places as the factor with the least. Another way of saying the rule for adding and subtracting is that the answer should show imprecision in the same place as the factor with the largest uncertainty. Examples: 1. 0.4563 x 13 = 5.9 (5.9319 before rounding) 2. 28.432 + 37.2 = 65.6 (65.632 before rounding)

Chemistry Worksheet: Significant Figures #1 Enter the number of significant figures for each of the numbers below. Laliberte, 9/9/08

1. 2.234 _________________

6. 124.3 _________________

2. 0.0005 ________________

7. 0.00210 _______________

3. 5400 _________________

8. 3.1415926 _____________

4. 7603 _________________

9. 4009.20 _______________

5. 12 apples ______________

10. 1.0045 ________________

Perform the following addition and subtraction calculations and express your answer to the correct number of significant figures. 11. 2.01 + 4.23 + 16.0057 = 12. 45 + 25 + 0.006 = 13. 1256 + 23.04 + 84.942 = 14. 36.72 - 9.627 = 15. 183 - (26.9 + 7.32) = Perform the following multiplication and division calculations and express your answer to the correct number of significant figures. 16. 23.5 x 9.1 = 17. 7033.0 x 34.3 = 18. 23 x 74.2 x 503.04 = 19. 674 / 30.00 = 20. 63556 / 12 =

Chemistry Worksheet: Significant Figures #2 Part1: Enter the number of significant figures for each of the numbers below. 1. 8.03 _________________

6. 0.004800 _________________

2. 12.500 ________________

7. 2.6 x 109 _______________

Laliberte, 9/9/08

3. 6000 _________________

8. 656,000 _____________

4. 712 _________________

9. 6 pizzas _______________

5. 1002.2 ______________

10. 23.45 ________________

Part 2: Perform the following addition and subtraction calculations and express your answer to the correct number of significant figures. 11. 112.5 + 19.27 + 84.5207 = 12. 71 + 22 + 0.019 = 13. 1.0058 + 19.74 + 0.652 = 14. 8500 – 189.4 = 15. 96.874 – (17.2 + 9.71) = Part 3: Perform the following multiplication and division calculations and express your answer to the correct number of significant figures. 16. 72.5 x 68.1 = 17. 7.25x1011 x 34.3 = 18. 68.5 x 0.0762 x 143.1 = 19. 809.9 ÷ 17.200 = 20. 56 ÷ 12345 =

Chemistry Worksheet: Significant Figures #3 Answer each problem using significant figures. ADDITION 1.

3.84 + 2.74 + 0.07 =

4.

6.75 + 2.73 + 2.8634 =

2.

4.7 + 4.876 + 2 =

5.

1.350 + 3.5 + 2.79 =

3.

0.96 + 2.348 + 2.84 =

6.

2.222 + 7.54 + 0.056 =

Laliberte, 9/9/08

SUBTRACTION 7.

34.89 – 45.739 =

10. 8.76 – 4.5 =

8.

0.008 – 0.76 =

11. 3.65 – 2.7 =

9.

97.747 – 7.8 =

12. 4.7 – 9.752 =

MULTIPLICATION 13. 0.096 x 0.63 =

16. 2.86 x 3.8 x 3 x 0.8 =

14. 2.74 x 3.7 =

17. 0.008 x 2.7 x 2 x 4.0 =

15. 2.85 x 2.5234 =

18. 1.11 x 2.4 x 3.9 =

DIVISION 19. 8.4 ÷ 18.2 =

22. 2.65 ÷ 5.7 =

20. 22.5 ÷ 6.3 =

23. 5.5 ÷ 2.43 =

21. 4.86 ÷ 8.8 =

24. 1.23 ÷ 5.3 =

Chemistry Worksheet: Conversions #1 1. 12 L = __________qts

6.

19.4 L = __________qts

2. 142 cm = ___________m

7.

16.3 in = ___________cm

3. 5.5 kg = __________lbs

8.

175 lbs = __________ kg

Laliberte, 9/9/08

4. 155 mL = __________L

9.

1.5 L = __________mL

5. 1.7 kL = ___________ mL

10. 671.7 mL = ___________ L

11. How many liters of gasoline can be held in a gas tank with capacity 12.5 gallons?

12. If you donate 1.00 pints of blood, how much blood have you given in mL?

13. How many fluid ounces are in a 2.00 liter soda bottle?

14. If your car's gas mileage is 32 miles/gallon, what would it be in km/L?

15. How long is a 10.0 km road race in miles?

Laliberte, 9/9/08