1. MEASUREMENT AND CALCULATIONS Chapter 9.2

2. Significant Digits When we measure and calculate values, we can only use a number of digits in our answer that has been accurately measured. “certain plus one”

3. SIGNIFICANT DIGITS All digits 1-9 are significant digits. Rule……Start counting at the first non-zero digit. Count until you run out of numbers. Examples: 30.95 – 4 sig figs 4.03 – 3 sig figs 0.04 – 1 sig fig ( leading zeros don’t count) 0.5060 – 4 sig figs 120 – 2 sig figs 120. – 3 sig figs

4. PRACTICE Significant Digits 1) 1.02 Km = _______ significant Digits 2) 0.32 cm = _______ significant Digits 3) 3600. kg = _______ significant Digits 4) 20.060 L = ______ significant Digits 5) 0.0030 g = ______ significant Digits

5. ROUNDING NUMBERS If the digit after the digit to be rounded is 5 or larger, round up. If not leave the number as is. Example: 9.147 cm rounded to three Sig. Digits is 9.15 cm. 7.23 g rounded to two Sig. Digits is 7.2 g.

6. TRY THESE ROUNDING QUESTIONS 0.0327 rounded to two s.d. 15.430 rounded to three s.d We now can apply these two concepts to basic mathematical calculations.

7. ADDING OR SUBTRACTING SIGNIFICANT DIGITS When adding or subtracting, you round to the value with the least number of places after the decimal. EXAMPLE: 1.2 + 3.08 + 7.60 = 11.88 = 11.9 10.013 – 1.07 = 8.943 = 8.94

8. Multiplying or Dividing SIGNIFICANT DIGITS When multiplying or dividing significant digits, you round to the value with the least total number of sig. figs. Example: 4.62 x 0.035 = 0.1617 = 0.16 107.45 ÷ 6.40 = 16.7890 = 16.8

9. PRACTICE 1) (2.4)(6.16) = ______ = _____ 2) 16.1 – 2.4 = ______ = _____ 3) 4.1 ÷ 8.6 = ______ = _____ 4) 6.105 + 0.12 = ____ = _____

10. CONVERTING UNITS You must understand the metric system to effectively convert. Nano Micro Milli Centi Basic Symbols: m, g, L deca hecta kilo mega Examples: 1 m = 100 cm 1 m = 1000 mm Examples: 1 g = 0.001 kg 1 g = 0.000001 mega grams Multiply Divide

11. However, you may have to use the conversion factor method that does not involve the metric system or has more than one unit. Example: 1) How many hours is 20.5 minutes? 20.5 min x 1 hour = 0.34166 = 0.342 h 60 min 2) How many m/s is 5km/h? 5 km x 1 h x 1000 m = 5000 m=1.388 1m/s h 3600s 1 km 3600 s

12. REARRANGING FORMULAS You must isolate the variable you are trying to solve for. To accomplish this you need to use the opposite operation that is indicated. EXAMPLE: d = vt ( rearrange for v ) Divide by t because vt is multiplication. d = v t

13. There is an easy way to rearrange three part equations using the pie method. EXAMPLE: This does not work for equations such as: a = v f – v i OR c = 2πr T D VT v = d / t t = d / v d = vt

14. PRACTICE 1) c = m / v ( rearrange for m ) 2) a = ½ bh ( rearrange for h) ANSWER: 1) m = cv 2) h = 2a/b

15. STEPS FOR SOLVING WORD PROBLEMS 1) List all the known and the unknown from the problem. 2) Select the best formula which uses the known and unknown. (be careful of extraneous info.) 3) Substitute the information into the equation. 4) calculate 5) round with appropriate significant digits. 6) Write a sentence answer.

16. QUESTIONS Text Page 349 #1,3,4,6,7,8,9