M EASURES : S IGNIFICANT FIGURES, PRECISION AND ACCURACY Dr. Chin Chu Chemistry River Dell High School

M EASUREMENTS Temperature demonstration What have been learned here? Human senses are not reliable indicator of physical properties. We need instruments to give us unbiased determination of physical properties. A system must be established to properly quantify the measurements. Scales and units.

M EASUREMENTS Definition – comparison between measured quantity and accepted, defined standards (SI). Quantity: Property that can be measured and described by a pure number and a unit that refers to the standard.

M EASUREMENT R EQUIREMENTS Know what to measure. Have a definite agreed upon standard. Know how to compare the standard to the measured quantity. Tools such as ruler, graduated cylinder, thermometer, balances and etc…

M EASUREMENTS – U NITS SI Units – (the metric system) Universally accepted Scaling with 10 Base Units: Time (second, s) Length (meter, m) Mass (kilogram, kg) Temperature (Kelvin, K) Amount of a substance (mole, mol) Electric current (ampere, A) Luminous intensity (candela, cd)

M EASUREMENTS - T EMPERATURE Temperature Scales: Celsius (°C, centigrade) Water freezing: 0 °C Water boiling: 100 °C Kelvin (K, SI base unit of temperature) Same spacing as in Celsius scale. Conversion: Celsius = Kelvin Fahrenheit (°F) Not the same spacing as the other two. Conversion: Fahrenheit = (5/9)(Celsius -32)

M EASUREMENTS – U NITS Derived Units: Volume Units: (length) 3, such as cm 3,m 3, dm 3 (liter) Density Defined as mass per unit volume the substance occupies.

H OW R ELIABLE ARE M EASUREMENTS ?

Let’s use a golf anaolgy

Accurate?No Precise?Yes

Accurate?Yes Precise?Yes

Precise?No Accurate?Maybe?

Accurate?Yes Precise?We cant say!

I N TERMS OF MEASUREMENT Three students measure the room to be 10.2 m, 10.3 m and 10.4 m across. Were they precise? Were they accurate?

A SSESSING U NCERTAINTY The person doing the measuring should asses the limits of the possible error in measurement

S IGNIFICANT FIGURES ( SIG FIGS ) How many numbers mean anything When we measure something, we can (and do) always estimate between the smallest marks

S IGNIFICANT FIGURES ( SIG FIGS ) The better marks the better we can estimate. Scientist always understand that the last number measured is actually an estimate object mm

S IGNIFICANT D IGITS AND M EASUREMENT Measurement Done with tools The value depends on the smallest subdivision on the measuring tool Significant Digits (Figures): consist of all the definitely known digits plus one final digit that is estimated in between the divisions.

S IGNIFICANT F IGURES Only measurements have significant figures. Counted numbers and defined constants are exact and have infinite number of significant figures. A dozen is exactly mL = 1 L Being able to locate, and count significant figures is an important skill.

Measured Value Uncer- tainty Ruler Division Known digits Estimated digit 1.07 cm+/-0.01 cm 0.1 cm1, cm+/ cm 0.01 cm3,5, cm+/- 0.1 cm1 cm2, 27 Significant Figures: Examples

S IGNIFICANT F IGURES : E XAMPLES What is the smallest mark on the ruler that measures cm? ____________________ 142 cm? ____________________ 140 cm? ____________________ Does the zero count? We need rules!!!

R ULES OF S IGNIFICANT F IGURES Pacific: If there is a decimal point present start counting from the left to right until encountering the first nonzero digit. All digits thereafter are significant. Atlantic: If the decimal point is absent start counting from the right to left until encountering the first nonzero digit. All digits are significant.

R ULES OF S IGNIFICANT F IGURES - E XAMPLES Pacific Ocean Atlantic Ocean Example 1 Example decimal point No decimal point 78638

R OUNDING R ULES Rounding is always from right to left. Look at the number next to the one you’re rounding : leave it : round up With one exception: when the number next to the one you’re rounding is 5 and not followed by nonzero digits (a.k.a. followed by all zeros) – round up if the number (rounding to) is odd; don’t do anything if it is even.

2.536 R OUNDING R ULES - E XAMPLES Example Last significant digit < leave it Example Last significant digit > 5 round up Example Last significant digit > 5 round up Example Last significant digit the exception round up 2.54 odd

M ATHEMATICAL O PERATIONS I NVOLVING S IGNIFICANT F IGURES Addition and Subtraction The answer must have the same number of digits to the right of the decimal point as the value with the fewest digits to the right of the decimal point. Why? The result from the addition or subtraction would have the same precision as the least precise measurement.

M ATHEMATICAL O PERATIONS I NVOLVING S IGNIFICANT F IGURES Addition and Subtraction Example: 28.0 cm cm cm cm 28.0 cm cm cm 1.Arrange the values so that decimal points line up. 4.Round the answer to the same number of places. 2.Do the sum or subtraction. 3.Identify the value with fewest places after decimal point cm

M ATHEMATICAL O PERATIONS I NVOLVING S IGNIFICANT F IGURES Multiplication and Division The answer must have the same number of significant figures as the measurement with the fewest significant figures.

M ATHEMATICAL O PERATIONS I NVOLVING S IGNIFICANT F IGURES Multiplication and Division Example: cm 3 1.Carry out the operation. 2.Identify the value with fewest significant figures. 3.Round the answer to the same significant figures cm cm cm 28.0 cm cm cm cm 3 3