Prefixes

1. Prefixes • Kilo (k) – 1000 • Hecto (h) – 100 • Deca (da) – 10 • No Prefix – 1 • Deci (d) – 1/10 • Centi (c) – 1/100 • Mili (m) – 1/1000

2. Conversion Staircase

3. Example • Convert 50 centimetres to kilometres. • First convert cm to m than m to km. • Centimetres to Metres (1 m = 100 cm) 50 cm ÷ 100 = 0.5 m • Metres to Kilometres (1 km = 1000 m) 0.5 m ÷ 1000 = 0.0005 km • So 50 cm is the same as 0.0005 km

4. Squares and Cubes • Square • 1 square metre (m2) has a length of 1m and a width of 1m. (1m)×(1m) = 1m2 • Cube • 1 cube metre (m3) has a length of 1m, a width of 1m and a height of 1m. (1m)×(1m)×(1m) = 1m3 • When converting squares and cubes remember to convert each measure before multiplying.

5. Converting Time • 60 minutes in 1 hour • 60 seconds in 1 minute • 1000 milliseconds in 1 second • Example: 1.5 hours to milliseconds. • 1.5 h (60min/1h) = 90 min • 90 min (60s/1min) = 5400 s • 5400 s (1000ms/1s) = 5400000 ms

6. Worksheet • Do # 1 on the Unit Conversions Worksheet. • Answers: #1 a) 0.00034 m b) 17900 cg c) 0.179 kg d) 99.0 mm e) 150 g f) 300 s g) 0.083 h h) 70000 mL i) 0.25 L j) 11520 s

7. Worksheet Answers • Question 2 a) 100 cm2 b) 0.10 m c) 0.01 m2 d) ÷ 1002 e) 10000 mm2 f) g) i. 0.0025 m2 ii. 4200 cm2 iii. 530000 mm2 iv. 0.00042 m2

8. Worksheet Answers • Question 3 a) 1000 cm3 b) 0.1 m c) 0.001 m3 d) ÷ 1003 e) 1000000 mm3 f) × 10003 g) i. 0.000025 m3 ii. 420000 cm3 iii. 530000000 mm3iv. 0.000000420 m3

9. Accuracy and Precision • Accuracy is how close repeated measurements of a quantity are to the actual (true) value. • Precision is how close repeated measurements of a quantity are to each other. • Can be seen easier by looking at targets and how close you are to the bulls-eye and how close each shot is to each other.

10. Visual Explanation High Accuracy but Low Precision Low Accuracy but High Precision

11. Other Possibilities • What might a target look like if both the accuracy and precision were low? • What about if both were high? • Why might it be important to be accurate? • Why might it be important to be precise? • Both Accuracy and Precision are important when we take a measurement.

12. Measurement • When we measure something we are obtaining the magnitude of a quantity, such as length or mass, relative to a unit of measurement, such as a metre or gram. • Measurements answer the questions “how many” or “how much” of something we have. • Often our measurements must be more precise than the instrument used to measure.

13. How to Measure • Always take one more digit than the instrument reads byestimating the value between the two marks that are certain. • Metre stick has two certain digits which are centimetres and millimetres. • To obtain a third digit (uncertain) we must estimate the value between the millimetre marks on the metre stick

14. Example #1 • What value would you record for this measurement? • Know it is between 6 and 7 cm markings • Also know it is between 3 and 4 mm markings • Closer to the 4 mm mark so we estimate the value is about 6.36 cm

15. Example #2 • How much liquid is in the test tube? • Between 60 and 70 mL. • When reading volume take the measurement from the Meniscus. • So the measurement will be about 63 mL.

16. Worksheet • Do questions on the Measurement Worksheet • Remember for #3 you take the measurement from the bottom of the “Meniscus” • The Meniscus is the bottom of the curve

17. Example of Digits • Measurement could be read as 6.36 cm or even 63.6 mm which both have 3 digits. • What about if we recorded the measurement as 0.0636 m. • This now has 5 digits but only 3 are significant

18. Significant Digits • When we take a measurement all digits are considered significant. • When taking a measurement with a metre stick there are three significant digits in the reading we obtain. • The number of significant digits is determined by following rules that help you decide whether or not a digit is considered significant

19. Counting Significant Digits • All nonzero digits are • All zeros between nonzero digits are • All zeros to the right of a decimal place are • Zeros to the left of non zero digits are not • If no decimal place, trailing zeros are not • If decimal place than all digits are • Line can specify the numbers that are

20. Worksheet • Do #1 on the Significant Digits Worksheet a) 3 b) 2 c) 5 d) 4 e) 2 f) 4 g) 3 h) 4 i) 5 j) 5 k) 2 l) 4

21. Adding Significant Digits • Measurements can only have 1 uncertain digit so when measurements are added the sum can only have 1 uncertain digits. • The measurement with the least number of digits after the decimal will determine were the uncertain digit is in the sum. • Addition Rules also apply to Subtraction

22. Worksheet • Do #2 i-r on the Significant Digits Worksheet • Answers i) 12.5 j) 3.9 k) 2.3 l) 19 m) 100 n) 110 o) 100 p) 124 q) 124 r) 0.026

23. Multiplying Significant Digits • When multiplying measurements together the final product can not have more significant digits than the measurement that had the least to begin with • Multiplication Rules also apply to Division • Rounding - Look at first non sig-dig • If digit is 0, 1, 2, 3 or 4 than round down • If digit is 5, 6, 7, 8 or 9 than round up

24. Worksheet • Do #2 a-h on the Significant Digits Worksheet • Significant Figures Sheet #1-7 • Answers