MEASUREMENT AND CALCULATIONS

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. PRACTICESignificant 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 SUBTRACTINGSIGNIFICANT 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 OPERATIONSSignificant 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 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 THESEROUNDING 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

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 = vf – vi OR c = 2πr • T v = d / t t = d / v d = vt D V T

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 Multiply Examples: 1 g = 0.001 kg 1 g = 0.00001 mega grams 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