2. Scientific Notation, Significant Figures & Significant Digits SCH3U

3. Learning Goals By the end of this lesson you should be able to: 1. Write numbers, large or small in scientific notation 2. distinguish between certain and measured numbers 3. Determine the number of significant digits in a measurement 4. Round to the specified number of significant digits 5. Explain the difference between accuracy & precision 6. Determine the correct significant digits based on lab equipment

4. Certain Numbers O All counted quantities are exact and contain an infinite number of significant digits. O Only whole numbers are possible O Eg. The number of students in the class O Numbers obtained from definitions are exact. O Eg. 1 km has exactly 1000m

5. Measurements O Measurements are not exact. O Are comparisons to a standard O When measuring there is some level of error or uncertainty O Eg. What is the length of the clownfish?

6. Accuracy O Every measurement has a degree of certainty or uncertainty O For any measurement, you need to record all certain digits and one uncertain digit

7. Precision O Is the place value of the last measurable digit O The more decimal places, the more precision O No matter how precise a measurement, it may still not be accurate.

9. Significant Digits O Defn: Those numbers that result from directly measuring an object. It shows the precision of the measurement. O Units must be included (no units no sd) O The precision of the measurement depends upon the measuring instrument O Use the following PRIORITIZED list to determine the number of sd’s in a measurement, calculation, or conversion

10. Rule 1: All nonzero digits are significant (they were measured) O Samples O a. 234 m O b. 1678 cm O c. 0.23 g O SD’s and precision O a. 3 sd to the m O b. 4 sd to the cm O c. 2 sd to the cg

11. Rule 2: All zeros between nonzero (or significant) digits are significant O Samples O a. 202 mm O b. 1003 cm O c. 0.200105 m O SD’s and precision O a. 3 sd to the mm O b. 4 sd to the cm O c. 6 sd to the  m Translation: In between 0s must be measured

12. NOT Rule 3: Zeros to the right of a nonzero digit but to the left of an understood decimal are NOT significant unless otherwise indicated. O a. 200 cm O b. 109,000 m O c. 1,000,000 mm O d.200 cm O e.200 cm O a. 1 sd to the m O b. 3 sd to the km O c. 1 sd to the km O d. 3 sd to the cm O e. 2 sd to the dm Translation: 0s at the end of a whole number are NOT measured unless marked. (a bar over a zero indicates the last measured zero)

13. NOT Rule 4: All zeros to the right of a decimal point but to the left of a nonzero digit are NOT significant. O Samples O a. 0.0032 m O b. 0.01294 g O c. 0.00000002 L O SD’s and precision O a. 2 sd to the.1 mm O b. 4 sd to the.01 mg O c. 1 sd to the.01  L Translation: 0s in front of a number less than 1 are NOT measured.

14. Rule 5: All zeros to the right of a decimal point and following a nonzero digit are significant O Samples O a. 20.00 g O b. 0.07080 mm O c. 1.0400 cm O d. 45.00 O SD’s and precision O a. 4 sd to the cg O b. 4 sd to the.01  m O c. 5 sd to the  m O d. 0 sd Translation: 0s at the end of a decimal number are measured.

15. How to use SD rules when multiplying/dividing O Rule: Your calculation (answer) must have the same precision as the LEAST precise original measurement O Find the number of significant digits in each of the starting numbers and note the lowest number of significant digits O ex. 2.40 cm x 3 cm (lowest # of sd is 1) O Calculate your answer O Round the answer to the lowest # of sd found in #1 O 2.40 cm x 3 cm = (7.2 cm 2 ) = 7 cm 2

16. Learning Check MeasurementSignificant FIgures 32.07 m 0.0041 g 6400 s 10.0 kJ 100 people (counted) 2. 77.8 km/h x 0.8967 h = 3. 35 000/1.20 L

17. Rounding O If you are rounding from a number below 5 O If you are rounding from a number above 5 O If you are rounding from 5 ROUND DOWN ROUND UP ROUND TO THE EVEN

18. Learning Check O Round to the nearest integer: 1. 1.1 2. 1.6 3. 1.5 4. 2.5 5. 2.5137

19. Scientific Notation O Used to express very large numbers or very small numbers in an easier format ExpressionCommon Decimal Notation Scientific Notation 124.5 million kilometres = 124.5 billion meters 124 500 500 km = 124 500 000 000m 1.245 x 10 8 km = 1.245 x 10 11 m 154 thousand nanometres 154 000 nm = 0.000154 m 1.54 x 10 5 nm =1.54 x 10 -4 m

20. Learning Check O Write the following values in scientific notation: a. 35 000 b. 0.00000492 c. 35 d. 1240