Measuring, Precision vs. Measuring, Precision vs. Accuracy, and Intro to Accuracy, and Intro to

Significant FiguresSignificant Figures

What do we measure?What do we measure?

VolumeVolume – the amount of space taken up – the amount of space taken up by a substanceby a substance

MassMass – the amount of matter in an object – the amount of matter in an object

TemperatureTemperature – measure of how much – measure of how much thermal energy a substance has compared thermal energy a substance has compared to a reference pointto a reference point

LengthLength – straight line distance between 2 – straight line distance between 2 pointspoints

What do you measure with?What do you measure with?

Units of MeasurementUnits of Measurement

You cannot just record a number for a You cannot just record a number for a measurement. A measurement. A unit must also be indicatedunit must also be indicated. . For example, a measurement is taken for the For example, a measurement is taken for the

length of the laboratory table and recorded as 183 length of the laboratory table and recorded as 183 is not correct. A correct recording would be 183 is not correct. A correct recording would be 183 centimeters (cm). centimeters (cm).

All measurements should be made in All measurements should be made in metric metric unitsunits, or converted to metric. , or converted to metric.

Measuring Liquids – Volume!Measuring Liquids – Volume!When you measure the volume of When you measure the volume of a liquid it is important to make a liquid it is important to make sure that you use the appropriate sure that you use the appropriate kind and size of instrument. kind and size of instrument.

When you put a sample of a liquid When you put a sample of a liquid into one of these instruments you into one of these instruments you will notice a curve at the surface of will notice a curve at the surface of the liquidthe liquid. This curve, which is . This curve, which is called a called a meniscus.meniscus.

Adjust your body and head so Adjust your body and head so that you are that you are eye leveleye level with the with the instrument and the meniscus. instrument and the meniscus. Read the volume of the liquid Read the volume of the liquid at the at the bottombottom of the meniscus of the meniscus. .

Measuring MassMeasuring Mass

The triple beam balanceThe triple beam balanceCarrying the BalanceCarrying the Balance1.1. Be sure all movable masses are Be sure all movable masses are

back to the zero point.back to the zero point.2.2. Place one hand under the balance Place one hand under the balance

and the other hand on the support and the other hand on the support (arm) to carry the balance. (arm) to carry the balance.

Using the BalanceUsing the Balance1.1. Zero the balanceZero the balance before you before you

determine the mass of any determine the mass of any substance.substance.        a) Slide all of the movable         a) Slide all of the movable

masses back to the zero masses back to the zero point.point.

        b) Check to see that the         b) Check to see that the pointer swings freely along pointer swings freely along the scale.the scale.

            

Mass cont.Mass cont.Never put a hot object directly on the balance panNever put a hot object directly on the balance pan. .

Any dry chemical that is to be massed should be Any dry chemical that is to be massed should be placed on paper or in a container. placed on paper or in a container.

Never pour chemicals directly on the balance panNever pour chemicals directly on the balance pan. . Remember to mass the paper or container before adding the Remember to mass the paper or container before adding the

substance.substance.

Once you have placed the object to be massed on Once you have placed the object to be massed on the pan, move the riders along the beams the pan, move the riders along the beams beginning with the largest mass first. If the beginning with the largest mass first. If the beams are notched, make sure all riders are in beams are notched, make sure all riders are in a notch before you take a reading.a notch before you take a reading.

What is the mass?What is the mass?

Answer!Answer!

Measuring TemperatureMeasuring Temperature

We will use degrees Celsius in this class!We will use degrees Celsius in this class!

Never stir with a thermometer.Never stir with a thermometer.

Never read a temperature with a Never read a temperature with a thermometer leaning against a side of a thermometer leaning against a side of a beaker.beaker.

NO WAY! ->NO WAY! ->

Measuring LengthMeasuring Length

Meter sticksMeter sticks are carefully calibrated in are carefully calibrated in centimeters with a millimeter least count. centimeters with a millimeter least count. That is, the millimeter is the smallest That is, the millimeter is the smallest subdivision on the meter stick. subdivision on the meter stick. This means the millimeter is the unit of the This means the millimeter is the unit of the

smallest reading that can be made without smallest reading that can be made without estimating. estimating.

Figure 1.Figure 1. This meter stick is This meter stick is calibrated in centimeters calibrated in centimeters (shown as the numbered (shown as the numbered major divisions) with a major divisions) with a least count of millimeters.least count of millimeters.

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Reading instruments to significant Reading instruments to significant figuresfigures

The least count of this meter stick The least count of this meter stick is one millimeter, so we know is one millimeter, so we know with absolute certainty that the with absolute certainty that the object is between 41.6 cm and object is between 41.6 cm and 41.7 cm. 41.7 cm.

We then estimate the object's We then estimate the object's length to the fractional part length to the fractional part (doubtful figure) of the least (doubtful figure) of the least count subdivision… 41.64 cm. count subdivision… 41.64 cm.

Let’s do this again…What is the Let’s do this again…What is the mass?mass?

Answer = 216.49 cmAnswer = 216.49 cm

Sig FigsSig Figs

Significant digits or significant figuresSignificant digits or significant figures are digits read from the measuring are digits read from the measuring instrument plus one doubtful digit instrument plus one doubtful digit estimated by the observer. estimated by the observer.

Examples:Examples: 203.4 cm: least count of ruler was 1 cm, 203.4 cm: least count of ruler was 1 cm,

tenth of centimeter was estimated.tenth of centimeter was estimated. 4.07 cm: least count was 0.1 cm. 4.07 cm: least count was 0.1 cm.

hundredth of centimeter was estimated.hundredth of centimeter was estimated.

Rules for Sig FigsRules for Sig Figs

Digits from 1-9 are always significant. Digits from 1-9 are always significant. Zeros between non-zeros are always significantZeros between non-zeros are always significantZeros at the beginning of a number are never significant, Zeros at the beginning of a number are never significant, they merely indicate the position of the decimal pointthey merely indicate the position of the decimal pointZeros that fall both at the end of the number Zeros that fall both at the end of the number ANDAND after after the decimal point are always significantthe decimal point are always significantWhen a number ends in zeros but contains NO decimal When a number ends in zeros but contains NO decimal point the zeros may or may not be significant….if this is point the zeros may or may not be significant….if this is the case, we use scientific notation!the case, we use scientific notation!

ExamplesExamples

EXAMPLESEXAMPLES # OF SIG. DIG.# OF SIG. DIG. COMMENTCOMMENT

453 kg453 kg 33 All non-zero digits are All non-zero digits are always significant.always significant.

2004 L2004 L 44 Zeros between 2 sig. Zeros between 2 sig. dig. are significant.dig. are significant.

5.005.00 33 Additional zeros to the Additional zeros to the right of decimal right of decimal andand a a

sig. dig. are sig. dig. are significant.significant.

0.0070.007 11 Placeholders are notPlaceholders are not

Practice problemsPractice problems

What is the number of sig figs in each of the What is the number of sig figs in each of the following: following:

a)a) 1282 kg1282 kg

b)b) 0.00296 s0.00296 s

c)c) 8.070 mm8.070 mm

d)d) 0.0105 L0.0105 L

e)e) 9.7750 x 109.7750 x 10-4 -4 mm

Accuracy and PrecisionAccuracy and Precision

Accuracy-the closeness of a measurement Accuracy-the closeness of a measurement is to the true value of what is measuredis to the true value of what is measuredPrecision- a gauge of how exact a Precision- a gauge of how exact a measurement ismeasurement is

Which is more precise…a glug ruler or a Which is more precise…a glug ruler or a 0.01 glug ruler? Why?0.01 glug ruler? Why?With which ruler can you report more With which ruler can you report more significant figures?significant figures?

Accuracy vs. PrecisionAccuracy vs. Precision

Clock ExampleClock Example

Digital vs. analogDigital vs. analog