MEASUREMENT AND CALCULATIONS Chapter 9.2

Significant Digits The international agreement about the correct way to record measurements: Record all those digits that are certain plus one uncertain digit, an 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.

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. If there is a decimal anywhere in the number, following zeros count. Examples: – 4 sig figs 4.03 – 3 sig figs 0.04 – 1 sig fig ( leading zeros don’t count) – 4 sig figs 120 – 2 sig figs 120. – 3 sig figs

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

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

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

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 = = ÷ 6.40 = = 16.8

ADDING OR SUBTRACTING SIGNIFICANT DIGITS When adding or subtracting, you round to the value with the least number of Sig. Figs. after the decimal. EXAMPLE: = = – 1.07 = = 8.94

PRACTICE 1) (2.4)(6.16) = ______ = _____ 2) 16.1 – 2.4 = ______ = _____ 3) 4.1 ÷ 8.6 = ______ = _____ 4) = ____ = _____

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 = – –

PRACTICE 1) (6.2)(4.3) – ) 42 – (2.2)(1.3)

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 = kg 1 g = mega grams Multiply Divide

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 = = h 60 min 2) How many m/s is 5km/h? 5 km x 1 h x 1000 m = 5000 m= m/s h 3600s 1 km 3600 s

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

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

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

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.

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