1. MEASUREMENT AND CALCULATIONS Chapter 9.2

2. Significant Digits ► The international agreement about the correct way to record measurements: ► Record all those digits that are certain plus one uncertain digit, and no more. ► These “certain-plus-one” digits are called significant digits. ► The certainty of a measurement is determined by how many certain digits (plus one) are obtained by the measuring instrument.

3. SIGNIFICANT DIGITS ► All digits included in a stated value ( except leading zeros) are significant digits. ► The position of the decimal point is not important when counting significant digits. ► 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. – 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. 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

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

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

8. ORDER OF OPERATIONS Significant Digits ► You will come across problems involving both x / ÷ and + / -. This is done step by step using the above rules. ► EXAMPLE: ► 4.3 ÷ 1.2 – 6.1 = 3.58333 – 6.1 ► 3.6 – 6.1 ► 2.5

9. PRACTICE 1) (6.2)(4.3) – 12 6.1 6.1 2) 42 – (2.2)(1.3)

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

11. TRY THESE ROUNDING QUESTIONS ► 0.0327 rounded to one Sig. Fig. Digit ► 15.430 rounded to three Sig. Fig. Digits ► We now can apply these two concepts to basic mathematical calculations.

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►t►t►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. CONVERTING UNITS ► You must understand the metric system to effectively convert. ► Nano ► Micro ► Milli ► Centi ► Basic Symbols: m, g, L ► Kilo ► Mega ► Giga Examples: 1 m = 100 cm 1 m = 1000 mm Examples: 1 g = 0.001 kg 1 g = 0.00001 mega grams Multiply Divide

16. ► 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

17. 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.

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