Ch1 – S2

Measurements in Experiments

Measurements & Units

• When scientists make measurements, they report their results as numbersnumbers and unitsunits.

• Units are standard measurements or standard quantities used to compare, like foot, cup....

The platinum-iridium cylinder shown here is the primary kilogram standard for the United States.

• As a physical quantity is measured, the number describing it, depends on the unit used (e.g. the classroom height equals 33 meters or 300300 centimeters).

• Three basic things can be measured: mass, length (or distance), and time.

• When scientists do research, they must communicate the results of their experiments with each other and agree on a system of units for their measurements.

• In 1960, an international committee agreed on a system of standards.

• This system of units is called the Système International d’Unités (SI).

Physical Quantity SI Unit Abbreviation of Unit

MassMass kilogramskilograms KgKg

Distance or lengthDistance or length metersmeters mm

Time Time secondsseconds ss

• Physics is a science that describes a broad range of topics and requires a wide range of measurements, from very largevery large to very smallvery small.

• For example, distance measurements can range from the distances between stars (about 100 000 000 000 000 000 m) to the distances between atoms in a solid (0.000 000 001 m).

• Because these numbers can be extremely difficult to read and write, an approach commonly used in SI is to combine the units with prefixes that symbolize combine the units with prefixes that symbolize certain powers of 10certain powers of 10. Example:

The mass of this insect can be expressed several different ways: 0.00001 kg, 0.01 g, or 10 mg.

Precision, accuracy, & significant figures.

• No measurement is perfect; every measurement is done with some error. And this error must be minimized.

• This error may be due to:– Lack of calibration.– The way the measurement is done.– The scale error:

Lack of calibration

• For example, a digital balance must read zero when empty.

• Also the balance has to read 1 Kg when a standard one kilogram-mass is put on.

• A stopwatch must be reset ( read zero) at the beginning of time counting; else the initial non-zero reading must be taken in consideration.

Precision, accuracy, & significant figures.• No measurement is perfect; every

measurement is done with some error. And this error must be minimized.

• This error is due to:– Lack of calibration.– The way the measurement is done.– The scale error:

As you can see from fig, we have chosen three position at which you can place your eye.Clearly at these three position we can have the following readingReading at A = 6.2 cmReading at B = 5.8 cmReading at C = 5.5 cmWhat you you think would be the correct reading?The correct reading is would be obtained when the eye is placed at B.

• In addition the working status of a measuring tool affects the error in measurements. For example If a meterstick or balance is not in good working order, this will introduce error into any measurements made with the device.

• For this reason, it is important to be careful with lab equipment.– Rough handling can damage balances. – If a wooden meterstick gets wet, it can warp, making

accurate measurements difficult.– Because the ends of a meterstick can be easily damaged or

worn, it is best to minimize instrument error by making measurements with a portion of the scale that is in the middle of the meterstick. Instead of measuring from the end (0 cm), try measuring from the 10 cm line.

Precision, accuracy, & significant figures.• No measurement is perfect; every measurement

is done with some error. And this error must be minimized.

• This error is due to:– Lack of calibration.– The way the measurement is done.– The scale error:

• The precision of any measurement is limited by the instrument used to measure it.

• This inherent limitation is called the scale error or scale uncertainty of the instrument.

• To get more precision, you need a more precise (more expensive and usually more difficult to use) instrument.

The scale error

In many situations, you can improve the precisionimprove the precision of a measurement. This can be done by making a by making a reasonable estimationreasonable estimation of where the mark on the instrument would have been.

• It is important to record the precision of your measurements so that other people can understand and interpret your results. A common convention used in science to indicate precision is known as significant figures.

• In the case of the measurement of the pencil as about 18.2 cm, the measurement has three significant figures.

• The significant figures of a measurement include all the digits that are actually measured (18 cm), plus one estimated digit.

• Note that the number of significant figures is determined by the precision of the markings on the measuring scale.

Scientific Notation

To learn about:1) scientific notation definition, and2) writing numbers in scientific notation, and3) do a quiz about scientific notation Please go through:

http://www.nyu.edu/pages/mathmol/textbook/scinot.html

For doing the assessment go through:

http://www.edinformatics.com/math_science/scinot6.htm

• Recall that significant digits in an answer show its precision.

• When you perform any arithmetic operation, it is important to remember that the result never can be more precise than the least-precise measurement.

Arithmetic with significant digits

• To add or subtract measurements, first perform the operation, then round off the result to correspond to the least-precise value involved.

• For example, 3.86 m + 2.4 m = 6.3 m because the least-precise measure is to one-tenth of a meter.

• To multiply or divide measurements, perform the calculation and then round to the same number of significant digits as the least-precise measurement.

• For example, 409.2 km/11.4 L = 35.9 km/L, because the least-precise measure has three significant digits.

• Some calculators display several additional digits while others round at different points.

• Be sure to record your answers with the correct number of digits.

When dividing 3.93.9 by 7.27.2 the calculator shows the answer as 0.541666666……0.541666666……

Since 3.93.9 and 7.27.2 each has 22 significant figuressignificant figures so the answer of this division should be reported as 0.540.54 (2 s.f.).