UNIT

3

MEASUREMENT AND D

ATA

PROCESSIN

G

TIER 3

Identify the uncertainties in a particular experiment

Construct ways to reduce random errors

Apply the rules of significant figures (sig figs) to determine the number of sig figs in a given number

State the results of calculations to the appropriate number of significant digits

Identify the uncertainties in a particular experiment

Each instrument has a degree of uncertainty . For example:

A digital instrument has a degree of uncertainty of +/- the smallest scale division

An analogue instrument such as a graduated cylinder, thermometer etc has a degree of uncertainty of +/- half the smallest division

DIGITAL BALANCE

THIS BALANCE IS CAPABLEOF READING TO THE HUNDREDTH PLACE SO THE MEASUREMENT WOULD BE WRITTEN AS:

12.58 +/- .01 g

ANALOGUE INSTRUMENTS

THIS GRADUATED CYLINDER IS MARKED OFF BY EVERY 2 ml . THEREFORE THE UNCERTAINTY WOULD BE +/- 1ml

HOW WOULD YOU EXPRESS THIS MEASUREMENT

38.2 +/- .5 cm3

Each division is 1 cm3 so the uncertainty would be ½ = .5.

Always express your data to one estimated digit.

Since it is just past the 38 cm3 mark, one person may read it as 38.2 +/- .5 cm3 whereas someone else might read it as 38.3 +/- .5 cm3

ANSWER:

Construct ways to reduce random errors

Because random errors have an equal probability of being too high or too low, the best way to reduce this errors is to repeat the measurement as many times as possible.

The rule of thumb is to do at least 3 trials if not more. If the same person duplicates the experiment with the same results then it is considered repeatable.

If several experimenters duplicate the results then it is considered reproducible.

SIGNIFICANT FIGURES

Apply the rules of significant figures (sig figs) to determine the number of sig figs in a given number

RULES FOR DETERMINING NUMBER OF SIGNIFICANT DIGITS

ADDING AND SUBTRACTING

When adding or subtracting, the answer should be quoted to have the same number of digits to the right of the decimal point as there are in the measurement having the fewest digits to the right of the decimal point.

SIGNIFICANT FIGURES

MULTIPLICATION AND DIVISION

When multiplying or dividing numbers, the answer should be quoted to have the same number of significant figures that are in the measurement with the fewest number of significant figures

Rounding off rule #1If the first digit to be dropped is less than 5, that digit and all the digits that follow it are simply dropped.

Rounding off rule #2

If the first digit to be dropped is a digit greater than 5, or if it is a 5 followed by digits other than zero, the excess digits are all dropped and the last retained digit is increased in value by one unit.

Rounding off rule #3

If the first digit to be dropped is a 5 not followed by any other digit, or if it is a 5 followed only by zeros, an odd0even rule is applied.

Odd-Even rule for rounding off:

If the last retained digit is even, its value is not changed, and the 5 and any zeros that follow are dropped. If the last digit is odd, its value is increased by one.

Intention of the odd-even rule for rounding off:The intention of this odd-even rule is to average the effects of rounding off.

ROUNDING RULES

How many significant figures do the following numbers have?1) 1234 _____2) 0.023 _____3) 890 _____4) 91010 _____5) 9010.0 _____6) 1090.0010 _____7) 0.00120 _____8) 0.00030 _____9) 1020010 _____10) 780. _____11) 1000 _____12) 918.010 _____13) 0.0001 _____14) 0.00390 _____15) 8120 _____16) 72 _____

Solutions to the Significant Figures Practice Worksheet1) 42) 23) 24) 45) 56) 87) 38) 29) 610) 311) 112) 613) 114) 315) 316) 2

583.00 ÷ 83=7.0(57.6 X 3) ÷ (34 X 3.00 X

87.507)=0.02

567.000 - 12=5558597 - 0.l=8597

(3.50 X 105)  X [2.8 ÷ (5.4  - 4.09)]=750000

(6.10 X 107 ) + (3 X 107 )=9 X 107

787  X 3.0=2400

Answers are in RED

THE END