Measurement in Science

What do you need to understand about measurements in science? Quantitative versus qualitative measurements The metric system Use of official scientific units (SI units – standard international units) Use of scientific notation (105 etc) Accuracy versus precision versus error Use of significant figures

Qualitative versus quantitative measurements Qualitative measurements Use words (not numbers) to describe what happened Words may be descriptive and not necessarily specific Quantitative measurements Uses NUMBERS Uses UNITS Can be accurate or inaccurate Can be precise or imprecise

Science (usually) uses the METRIC system

Essential metric prefixes Kilo (k) = 1000 (one thousand, 103) Deci (d) = 1/10 (one tenth, 10-1) Centi (c) = 1/100 (one hundredth, 10-2) Milli (m) = 1/1000 (one thousandth, 10-3) Micro () = (one millionth, 10-6) Nano (η) = (one billionth, 10-9)

1 metre = = 10 dm = 100 cm = 1000 mm 1 mm = = 0.1 cm = 0.001 m 1 kg = = 10 dg = 1000 g = 1 000 000 mg 1 mg = = 0.001 g = 0.000 001 kg

Standard International Units

Measuring distance-length: METRE

Time is measured in SECONDS

MASS is measured in kilograms (g) Mass is a measure of the quantity of matter Mass is constant, regardless of location Measured in kg (NB: Weight is a force that measures the pull by gravity- it changes with location)

Mass is not equivalent to weight! Is measured in kg Reflects how much matter something contains Is closely related to inertia Cannot be measured directly WEIGHT Is measured in NEWTONS (= 1 kg.ms-1) Is a force measurement which measures how strongly gravity is pulling on an object

Scales show an estimate of your mass based on the force your body exerts on it. And to find out how much force your body is exerting on the scales, multiply by 9.8 (to convert kg into Newtons).

Measuring Temperature: KELVIN Kelvin scale (or absolute scale) Named after Lord Kelvin K = oC + 273 A change of one degree Kelvin is the same as a change of one degree Celsius No degree sign is used

Temperature Scales Water freezes at 273 K Water boils at 373 K 0 K is called absolute zero, and equals –273 oC Absolute zero is the temperature at which gas molecules stop moving

Non SI temperature scale - CELSIUS Celsius scale- named after Swedish astronomer Anders Celsius Uses the freezing point (0 oC) and boiling point (100 oC) of water at atmospheric pressure as references Divided into 100 equal intervals, or degrees Celsius

Scientific notation Simple – it’s the method scientist use to neatly write very BIG or very small numbers.

Scientific notation

Significant Figures

How sure can we be about our measurements? We seek to make our measurements as accurate and precise as possible Accuracy – how close a measurement is to the true value Precision – how close the measurements are to each other (reproducibility)

Precision or accuracy?

21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 30.5 31.5 nearest to 30.5 measure to 1 dp; one more dp than smallest division 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 30.55 30.65 nearest to 30.55 measure to 2 dp; one more dp than smallest division

Applying Precision Scientists use significant figures to show precision of a measured quantity Significant figure: ‘each of the digits of a number that are used to express it to the required degree of accuracy, starting from the first nonzero digit’ In science, numbers are always rounded to a defined number of significant figures

Significant Figures – Counting Rules Non-zero digits are ALWAYS Significant Leading zeros are NEVER significant 0.000036 has TWO Significant Figures Trailing zeros may or may not be significant 2500 may have TWO or FOUR Significant Figures 2.5 X 103 has 2 s.f., while 2.500 X 103 has 4 s.f. Zeros ‘in between’ Non-Zeros are significant 2501 and 2003 have FOUR Significant Figures Zeros after a decimal point ARE SIGNIFICANT They do not begin the number 25.00 and 15.10 have FOUR Significant Figures

How many significant figures are there in a number? An EASY way to decide is to convert the number to SCIENTIFIC NOTATION (but keep and consider any zeros following a decimal point)… The number of digits in your ‘mantissa’ is your number of significant figures For example: 32701.00 = 3.270100 X 104 Note that in this example, the two zeros following the decimal point are also considered as significant…

Decimal places versus significant figures When we round to decimals, we start counting as soon as we reach the decimal point. Round 17.46789 to 2 decimal places 1 decimal place 2 decimal places, this will stay a 6 or go to a 7 depending on what the next number is

Significant Figures When we round to significant figures, we start counting as soon as we reach a number that is not zero Round 17.46789 to 2 significant figures 1 significant figure 2 significant figures, this will stay a 7 or go to a 8 depending on what the next number is All the numbers after will become zero Round 17.46789 to 2 decimal places=17.00

It’s more than 4 so we round up! Round to 1 sf 3 7 8 5 4 3 7 Look at the next number It’s more than 4 so we round up!

It’s less than 5 so we round down! Round to 3 sf 3 7 8 4 3 7 Look at the next number It’s less than 5 so we round down!

It’s more than 4 so we round up! Round to 2 sf . 2 9 8 9 Look at the next number It’s more than 4 so we round up!

It’s more than 4 so we round up! Round to 3 sf . 2 9 8 7 Look at the next number It’s more than 4 so we round up!

Rounding to Significant Figures Main When you are rounding to decimal places you start counting after the decimal point, but with significant figures you start counting at the first non zero number 1000 1500 1460 200 160 157 40 37 37.1 6 6.1 6.09 0.006 0.0064 0.00640 4.7 0.058 0.19 540

Significant Figures – Adding/Subtracting The answer cannot have more decimal places than the least number of decimal places in the calculation Add 15.1 to 3 The answer is 18

Significant Figures – Multiplication/Division Based on the given values, or what you think are measured values, round your answer so that it has the same number of significant figures as the input (or given) with the least number of significant figures Multiply 2.0 and 3.01 Answer in correct significant figures is 6.0

27 26.5≤x<27.5 27.0 26.95≤x<27.05 27.00 26.995≤x<27.005 Which is the measurement with the highest precision and probably the most accurate?

Rounding to Significant Figures (sig fig or s.f) 10 multiple choice questions

Round- 0.23 to 1 s.f 0.3 2 A) B) 0.2 3 C) D)

Round- 0.045 to 1 s.f 0.04 0.1 A) B) 0.0 0.05 C) D)

Round- 623 to 1 s.f 600 620 A) B) 630 700 C) D)

Round- 5328 to 1 s.f 5300 5000 A) B) 5330 6000 C) D)

Round- 0.005136 to 2 s.f 0.01 0.0050 A) B) 0.00514 0.0051 C) D)

Round- 426.213 to 2 s.f 426.21 430 A) B) 400.00 420 C) D)

Round- 3002.01 to 3 s.f 300 3000 A) B) 3010 3002.0 C) D)

Round- 983.4 to 1 s.f 100 900 A) B) 980 1000 C) D)

Round- 0.00456 to 2 s.f 0.0045 0.004 A) B) 0.0046 0.00 C) D)

Round- 36345.3 to 3 s.f 36300 4000 A) B) 36000 45300 C) D)

A duck is exactly 10. 0 cm tall A duck is exactly 10.0 cm tall. The duck was measured several times by several people. Which of the following data sets is most precise? 8.1, 8.0, 8.2, 8.0 9.7, 10.0, 10.9, 10.3 9.1, 9.0, 10.8, 10.6 7.9, 10.0, 11.4, 10.5

The dart thrower is accurate but not precise precise but not accurate both accurate and precise neither accurate nor precise

The dart thrower is accurate but not precise precise but not accurate both accurate and precise neither accurate nor precise

The dart thrower is accurate but not precise precise but not accurate both accurate and precise neither accurate nor precise

What is the correct reading on this cylinder? 30 cm3 32 cm3 32.0 cm3 34 cm3 34.0 cm3

What is the uncertainty in this reading? ± 0.05 cm ± 0.10 cm ± 0.20 cm ± 1.00 cm

What is the sum 3.041 + 0.81? 3 4 3.9 3.85 3.851

What is 31 times the answer to the previous problem? What is the product 8.2 x 13.7? What is 31 times the answer to the previous problem? 100 110 112 112.3 112.34 3400 3410 3482.54 3500