Significance in Measurement Measurements always involve a comparison. Measurements always involve a...

Significance in MeasurementSignificance in Measurement

Measurements always involve a Measurements always involve a comparisoncomparison..

The comparison always involves The comparison always involves some some

____________________. ____________________.


.. Which of the following Which of the following best describes the best describes the length of the beetle's length of the beetle's body in the picture to body in the picture to the left? the left?

a)a) Between 0 and 2 in Between 0 and 2 in

b)b) Between 1 and 2 inBetween 1 and 2 in

c)c) Between 1.5 and 1.6 inBetween 1.5 and 1.6 in

d)d) Between 1.54 and 1.56 Between 1.54 and 1.56 inin

e)e) Between 1.546 and Between 1.546 and 1.547 in1.547 in


The correct answerThe correct answer

is . . . is . . .

(d), between 1.54 (d), between 1.54 and 1.56 inchesand 1.56 inches


Measurements are often written as a Measurements are often written as a single numbersingle number rather than a rangerather than a range. . The beetle's length in the previous frame was The beetle's length in the previous frame was

between 1.54 and 1.56 inches long. between 1.54 and 1.56 inches long. The single number that best represents the The single number that best represents the

measurement is the center of the range, measurement is the center of the range, 1.551.55 inches.inches.

When you write the measurement as a single When you write the measurement as a single number, it's understood that the number, it's understood that the last figurelast figure (the (the second of the two 5’s in this case) had to be second of the two 5’s in this case) had to be estimated. Consider measuring the length of the estimated. Consider measuring the length of the same object with two different rulers. same object with two different rulers.


.. For each of the For each of the rulers, give the rulers, give the correct length correct length measurement for measurement for the steel pellet the steel pellet as a single as a single number rather number rather than a rangethan a range


For the ruler on the left you should For the ruler on the left you should have had . . .have had . . .

1.4 in1.4 in For the ruler on the right, you should For the ruler on the right, you should

have had . . .have had . . .

1.47 in1.47 in


A A zerozero will occur in the will occur in the last placelast place of a of a measurement if the measurement if the measured value fell measured value fell exactly on a scale exactly on a scale division.division. For example, the temperature For example, the temperature

on the thermometer should be on the thermometer should be recorded as recorded as 30.0°C30.0°C..

Reporting the temperature as Reporting the temperature as 30°C30°C would imply that the would imply that the measurement had been taken measurement had been taken on a thermometer with scale on a thermometer with scale marks 100°C apart! marks 100°C apart!

Significance in MeasurementSignificance in Measurement Use the bottom of Use the bottom of

the the meniscusmeniscus (the (the curved interface curved interface between air and liquid) between air and liquid) as a point of reference as a point of reference in making in making measurements of measurements of volume in a graduated volume in a graduated cylinder, pipet, or buret. cylinder, pipet, or buret.

In reading any scale, In reading any scale, your line of sight should your line of sight should be perpendicular to the be perpendicular to the scale to avoid 'parallax' scale to avoid 'parallax' reading errors. reading errors.


The graduated The graduated cylinder on the right cylinder on the right has scale marks 0.1 has scale marks 0.1 mL apart, so it can be mL apart, so it can be read to the nearest read to the nearest 0.01 mL. 0.01 mL.

Reading across the Reading across the bottom of the bottom of the meniscus, a reading of meniscus, a reading of 5.72 mL5.72 mL is reasonable is reasonable (5.73 mL or 5.71 mL (5.73 mL or 5.71 mL are acceptable, too). are acceptable, too).


Determine the Determine the volume readings volume readings for the two for the two cylinders to the cylinders to the right, assuming right, assuming each scale is in each scale is in mL.mL.


For the cylinder on the left, you For the cylinder on the left, you should have measured . . .should have measured . . .

3.0 mL3.0 mL For the cylinder on the right, you For the cylinder on the right, you

should have measured . . .should have measured . . .

0.35 mL0.35 mL


All of the digits up to and All of the digits up to and including the estimated digit are including the estimated digit are calledcalled ________________________________. . 142.142.77 g g ___ ___

101033 nm nm ___ ___

2.99792.997988 x 10 x 1088 m m ___ ___


Usually one can count significant digits Usually one can count significant digits simply by countingsimply by counting all of the digits up to all of the digits up to and and including the estimated digitincluding the estimated digit.. It's important to realize, however, that the position It's important to realize, however, that the position

of the decimal point has nothing to do with the of the decimal point has nothing to do with the number of significant digits in a measurement. number of significant digits in a measurement.

For example, you can write a mass measured as For example, you can write a mass measured as 124.1 g124.1 g as as 0.1241 kg0.1241 kg. .

Moving the decimal place doesn't change the fact Moving the decimal place doesn't change the fact that this measurement has that this measurement has FOURFOUR significant figures. significant figures.


Suppose a mass is given as 127 ng.Suppose a mass is given as 127 ng. That's 0.127 µg, or 0.000127 mg, or That's 0.127 µg, or 0.000127 mg, or

0.000000127 g. 0.000000127 g. These are all just different ways of These are all just different ways of

writing the same measurement, and all writing the same measurement, and all have the same number of significant have the same number of significant digits: digits: ____________. .


Determine the number of Determine the number of significant digits in the significant digits in the following series of numbers:following series of numbers:

0.000341 kg = 0.341 g = 341 mg ___0.000341 kg = 0.341 g = 341 mg ___

12 µg = 0.000012 g = 0.000000012 kg 12 µg = 0.000012 g = 0.000000012 kg ___ ___

0.01061 Mg = 10.61 kg = 10610 g ___0.01061 Mg = 10.61 kg = 10610 g ___


Any zeros that Any zeros that vanishvanish when you when you convert a measurement to scientific convert a measurement to scientific notation were not really significant notation were not really significant figures. Consider the following figures. Consider the following examples:examples:

0.01234 kg0.01234 kg

1.234 x 101.234 x 10-2-2 kg kg

______ sig figssig figs

Leading zeros (0.01234 kg) just locate the decimal point. Leading zeros (0.01234 kg) just locate the decimal point. They're never significant.They're never significant.


0.012340 kg0.012340 kg

1.2340 x 101.2340 x 10-2-2 kg kg

__sig figs__sig figs

Notice that you didn't have to move the decimal point past Notice that you didn't have to move the decimal point past the trailing zero (0.012340 kg) so it doesn't vanish and so is the trailing zero (0.012340 kg) so it doesn't vanish and so is considered significant.considered significant.

0.000011010 m0.000011010 m

1.1010 x 101.1010 x 10-5-5 m m

__ sig figs__ sig figs

Again, the leading zeros vanish but the trailing zero Again, the leading zeros vanish but the trailing zero doesn't.doesn't.


0.3100 m0.3100 m3.100 x 103.100 x 10-1-1 m m

___ sig figs___ sig figsOnce more, the leading zeros vanish but the trailing zero Once more, the leading zeros vanish but the trailing zero doesn't.doesn't.

321,010,000 miles321,010,000 miles3.2101 x 103.2101 x 1088 miles miles

___ sig figs (at least)___ sig figs (at least)Ignore commas. Here, the decimal point is moved past the Ignore commas. Here, the decimal point is moved past the trailing zeros (321,010,000 miles) in the conversion to scientific trailing zeros (321,010,000 miles) in the conversion to scientific notation. They vanish and should not be counted as significant. notation. They vanish and should not be counted as significant. The first zero (321,The first zero (321,0010,000 miles) is significant, though, 10,000 miles) is significant, though, because it's wedged between two significant digits.because it's wedged between two significant digits.


84,000 mg84,000 mg

8.4 x 108.4 x 1044 mg mg

__ sig figs (at __ sig figs (at least)least)

The decimal point moves past the zeros (84,000 mg) in the The decimal point moves past the zeros (84,000 mg) in the conversion. They should not be counted as significant.conversion. They should not be counted as significant.

32.00 mL32.00 mL

3.200 x 103.200 x 1011 mL mL

__ sig figs__ sig figs

The decimal point didn't move past those last two zeros. The decimal point didn't move past those last two zeros.


302.120 lbs302.120 lbs

3.02120 x 103.02120 x 1022 lbs lbs

___ sig figs___ sig figs

The decimal point didn't move past the last zero, so it is The decimal point didn't move past the last zero, so it is significant. The decimal point did move past the 0 between significant. The decimal point did move past the 0 between the two and the three, but it's wedged between two the two and the three, but it's wedged between two significant digits, so it's significant as well. significant digits, so it's significant as well.

All of the figures in this measurement are significantAll of the figures in this measurement are significant


All of the possibilities are All of the possibilities are covered by the following rules:covered by the following rules:

1. Zeros 1. Zeros sandwichedsandwiched between two between two significant digits are significant digits are always always significantsignificant. .

1.0001 km 1.0001 km 2501 kg 2501 kg 140.009 Mg140.009 Mg

____________

..2. 2. TrailingTrailing zeros to the right of the zeros to the right of the

decimal decimal point are point are always significantalways significant. . 3.0 m 3.0 m ___ ___12.000 µm ___12.000 µm ___1000.0 µm ___1000.0 µm ___

3. 3. LeadingLeading zeros are zeros are never significantnever significant. . 0.0003 m ___0.0003 m ___0.123 µm ___0.123 µm ___0.0010100 µm ___0.0010100 µm ___

4. Trailing zeros that all appear to the 4. Trailing zeros that all appear to the LEFT of the decimal point are not LEFT of the decimal point are not assumed assumed

to be significant. to be significant. 3000 m ___3000 m ___1230 µm ___1230 µm ___92,900,000 miles ___92,900,000 miles ___


How many significant figures are How many significant figures are there in each of the following there in each of the following measurements?measurements?

1010.010 g1010.010 g

32010.0 g32010.0 g

0.00302040 g0.00302040 g

0.01030 g0.01030 g

101000 g101000 g

100 g100 g

__________________________________

Date post:	26-Mar-2015
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