The Return of GUSS

The Return of The Return of GUSSGUSS

Featuring Significant DigitsFeaturing Significant Digits

A Justification for “Sig A Justification for “Sig Digs”Digs”

Measurements are not perfect.Measurements are not perfect.



They always include some degree of They always include some degree of uncertainty because no measuring uncertainty because no measuring devicedevice is perfect. is perfect.

Each is Each is limitedlimited in its precision. in its precision.



They always include some degree of They always include some degree of uncertainty because no measuring uncertainty because no measuring devicedevice is perfect. is perfect.

Each is Each is limitedlimited in its precision. in its precision.

Note that we are not talking about Note that we are not talking about human errors here.human errors here.

PrecisionPrecision

We indicate the precision to which we We indicate the precision to which we measured our quantity in how we measured our quantity in how we write our measurement.write our measurement.

PrecisionPrecision

We indicate the precision to which we We indicate the precision to which we measured our quantity in how we measured our quantity in how we write our measurement.write our measurement.

For example, which measurement is For example, which measurement is more precise?more precise?

15 cm15 cm 15.0 cm15.0 cm

PrecisionPrecision

We indicate the precision to which we We indicate the precision to which we measured our quantity in how we write our measured our quantity in how we write our measurement.measurement.

For example, which measurement is more For example, which measurement is more precise?precise?

15 cm15 cm 15.0 cm15.0 cm This one, obviously. This one, obviously.

Scientists wouldn’t bother to write the .0 if Scientists wouldn’t bother to write the .0 if they didn’t mean it.they didn’t mean it.

What we meanWhat we mean

When we write 15 cm, we mean that When we write 15 cm, we mean that we’ve measured the quantity to be we’ve measured the quantity to be closer to 15 cm than to 14 cm or 16 closer to 15 cm than to 14 cm or 16 cmcm

BUTBUT

When we write 15.0 cm, we mean that When we write 15.0 cm, we mean that we’ve measured the quantity to be we’ve measured the quantity to be closer to 15 cm than to 14.9 cm or closer to 15 cm than to 14.9 cm or 15.1 cm.15.1 cm.

Significant DigitsSignificant Digits

In any measurement the In any measurement the significant significant digitsdigits are the digits that we’ve are the digits that we’ve measured:measured:

the digits we know for certain plus the the digits we know for certain plus the single last digit that is estimated or single last digit that is estimated or uncertain.uncertain.

For ExampleFor Example

The measurement 21.6 cm has The measurement 21.6 cm has threethree sig digssig digs

For ExampleFor Example

The measurement 21.6 cm has The measurement 21.6 cm has threethree sig digs, and the “6” is estimated or sig digs, and the “6” is estimated or uncertain, uncertain,

by which we mean that the by which we mean that the measurement is closer to 21.6 cm measurement is closer to 21.6 cm than to 21.5 or 21.7 cm, but may than to 21.5 or 21.7 cm, but may actually be 21.58 cm or 21.62 cm if actually be 21.58 cm or 21.62 cm if measured more precisely.measured more precisely.

The following rules are The following rules are used to determine if a digit used to determine if a digit

is significant:is significant: All non-zero digits are significantAll non-zero digits are significant

e.g. 42.5 N has three significant e.g. 42.5 N has three significant digitsdigits


is significant:is significant: All non-zero digits are significantAll non-zero digits are significant Any zeroes placed after other digits Any zeroes placed after other digits

and behind a decimal are significantand behind a decimal are significant

e.g. 0.50 kg has two significant e.g. 0.50 kg has two significant digitsdigits



and behind a decimal are significantand behind a decimal are significant Any zeroes placed between Any zeroes placed between

significant digits are significantsignificant digits are significant

e.g. 30.07 m has four significant e.g. 30.07 m has four significant digitsdigits



and behind a decimal are significantand behind a decimal are significant Any zeroes placed between Any zeroes placed between

significant digits are significantsignificant digits are significant All other zeroes are All other zeroes are notnot significant significant

e.g. both 100 cm and 0.004 kg each e.g. both 100 cm and 0.004 kg each have only one significant digithave only one significant digit

How can you say those How can you say those digits are not significant?digits are not significant?

Both 100 cm and 0.004 kg each have Both 100 cm and 0.004 kg each have only one sig dig?only one sig dig?

The zeros here are placeholders – The zeros here are placeholders – they’re just there to show in which they’re just there to show in which place the non-zeros belong.place the non-zeros belong.

If the measurements are rewritten 1 m If the measurements are rewritten 1 m and 4 g, it becomes apparent that and 4 g, it becomes apparent that there’s only one sig dig.there’s only one sig dig.

How can you say those How can you say those digits are not significant?digits are not significant?

Both 100 cm and 0.004 kg each have only one Both 100 cm and 0.004 kg each have only one sig dig?sig dig?

The zeros here are placeholders – they’re just The zeros here are placeholders – they’re just there to show in which place the non-zeros there to show in which place the non-zeros belong.belong.

If the measurements are rewritten 1 m and 4 g, If the measurements are rewritten 1 m and 4 g, it becomes apparent that there’s only one sig it becomes apparent that there’s only one sig dig.dig.

But what if you measured 100 cm exactly?But what if you measured 100 cm exactly?

Making Zeros SignificantMaking Zeros Significant

But what if you measured 100 cm exactly?But what if you measured 100 cm exactly?

You can show that a zero is significant by You can show that a zero is significant by either:either:

underscoring or overscoring the zero: 10underscoring or overscoring the zero: 1000 cmcm

(if the measurement is in a table)(if the measurement is in a table) rewriting the measurement in scientific rewriting the measurement in scientific

notation:notation:

1.00 x 101.00 x 1022 cm cm


And yes, if you And yes, if you measure a zero, measure a zero, you you mustmust write it. write it.

Your lab tables Your lab tables should not look should not look like this:like this:

Time (s)Time (s) Distance Distance (cm)(cm)

0.10.1 5.45.4

0.20.2 8.78.7

0.30.3 1010

0.40.4 13.113.1


They should look like They should look like this:this:


0.10.1 5.45.4

0.20.2 8.78.7

0.30.3 10.010.0

0.40.4 13.113.1

No ½ measurementsNo ½ measurements

Your tables also Your tables also should not look should not look like this:like this:


0.10.1 1212

0.20.2 1414

0.30.3 16.516.5

0.40.4 1818

No ½ measurementsNo ½ measurements

If you can clearly If you can clearly measure .5 in one measure .5 in one case, surely you case, surely you could measure to the could measure to the tenths place in the tenths place in the other cases too?other cases too?

We don’t use .5 to We don’t use .5 to substitute for “about substitute for “about ½”: .5 means closer ½”: .5 means closer to .5 than to .4 or .6. to .5 than to .4 or .6. Be exact. Be exact.


0.10.1 1212

0.20.2 1414

0.30.3 16.516.5

0.40.4 1818

And now for And now for some some

practice. . . .practice. . . .

How many significant digits How many significant digits are there in each of the are there in each of the

following?following? 12 m/s12 m/s 60 W60 W 305 K305 K 9.5 kg9.5 kg 2.0 T2.0 T 0.8 N0.8 N 20450 cal20450 cal


following?following? 12 m/s12 m/s 2 s.d.2 s.d. 60 W60 W 305 K305 K 9.5 kg9.5 kg 2.0 T2.0 T 0.8 N0.8 N 20450 cal20450 cal


following?following? 12 m/s12 m/s 2 s.d.2 s.d. 60 W60 W 1 s.d.1 s.d. 305 K305 K 9.5 kg9.5 kg 2.0 T2.0 T 0.8 N0.8 N 20450 cal20450 cal


following?following? 12 m/s12 m/s 2 s.d.2 s.d. 60 W60 W 1 s.d.1 s.d. 305 K305 K 3 s.d.3 s.d. 9.5 kg9.5 kg 2.0 T2.0 T 0.8 N0.8 N 20450 cal20450 cal


following?following? 12 m/s12 m/s 2 s.d.2 s.d. 60 W60 W 1 s.d.1 s.d. 305 K305 K 3 s.d.3 s.d. 9.5 kg9.5 kg 2 s.d.2 s.d. 2.0 T2.0 T 0.8 N0.8 N 20450 cal20450 cal


following?following? 12 m/s12 m/s 2 s.d.2 s.d. 60 W60 W 1 s.d.1 s.d. 305 K305 K 3 s.d.3 s.d. 9.5 kg9.5 kg 2 s.d.2 s.d. 2.0 T2.0 T 2 s.d.2 s.d. 0.8 N0.8 N 20450 cal20450 cal


following?following? 12 m/s12 m/s 2 s.d.2 s.d. 60 W60 W 1 s.d.1 s.d. 305 K305 K 3 s.d.3 s.d. 9.5 kg9.5 kg 2 s.d.2 s.d. 2.0 T2.0 T 2 s.d.2 s.d. 0.8 N0.8 N 1 s.d.1 s.d. 20450 cal20450 cal


following?following? 12 m/s12 m/s 2 s.d.2 s.d. 60 W60 W 1 s.d.1 s.d. 305 K305 K 3 s.d.3 s.d. 9.5 kg9.5 kg 2 s.d.2 s.d. 2.0 T2.0 T 2 s.d.2 s.d. 0.8 N0.8 N 1 s.d.1 s.d. 20450 cal20450 cal 4 s.d.4 s.d.


following?following? 1.40 1.40 0.075 h0.075 h 102.5 MHz102.5 MHz 2500 J2500 J 100.0 V100.0 V 40.20 A40.20 A 0.09030 km0.09030 km


following?following? 1.40 1.40 s.d.s.d. 0.075 h0.075 h 102.5 MHz102.5 MHz 2500 J2500 J 100.0 V100.0 V 40.20 A40.20 A 0.09030 km0.09030 km


following?following? 1.40 1.40 s.d.s.d. 0.075 h0.075 h 2 s.d.2 s.d. 102.5 MHz102.5 MHz 2500 J2500 J 100.0 V100.0 V 40.20 A40.20 A 0.09030 km0.09030 km


following?following? 1.40 1.40 s.d.s.d. 0.075 h0.075 h 2 s.d.2 s.d. 102.5 MHz102.5 MHz 4 s.d.4 s.d. 2500 J2500 J 100.0 V100.0 V 40.20 A40.20 A 0.09030 km0.09030 km


following?following? 1.40 1.40 s.d.s.d. 0.075 h0.075 h 2 s.d.2 s.d. 102.5 MHz102.5 MHz 4 s.d.4 s.d. 2500 J2500 J 2 s.d.2 s.d. 100.0 V100.0 V 40.20 A40.20 A 0.09030 km0.09030 km


following?following? 1.40 1.40 s.d.s.d. 0.075 h0.075 h 2 s.d.2 s.d. 102.5 MHz102.5 MHz 4 s.d.4 s.d. 2500 J2500 J 2 s.d.2 s.d. 100.0 V100.0 V 4 s.d.4 s.d. 40.20 A40.20 A 0.09030 km0.09030 km


following?following? 1.40 1.40 s.d.s.d. 0.075 h0.075 h 2 s.d.2 s.d. 102.5 MHz102.5 MHz 4 s.d.4 s.d. 2500 J2500 J 2 s.d.2 s.d. 100.0 V100.0 V 4 s.d.4 s.d. 40.20 A40.20 A 4 s.d.4 s.d. 0.09030 km0.09030 km


following?following? 1.40 1.40 s.d.s.d. 0.075 h0.075 h 2 s.d.2 s.d. 102.5 MHz102.5 MHz 4 s.d.4 s.d. 2500 J2500 J 2 s.d.2 s.d. 100.0 V100.0 V 4 s.d.4 s.d. 40.20 A40.20 A 4 s.d.4 s.d. 0.09030 km0.09030 km 4 s.d.4 s.d.

Round each measurement Round each measurement to the required significant to the required significant

digits:digits: 4080 J to 1 s.d.4080 J to 1 s.d. 4080 J to 2 s.d.4080 J to 2 s.d. 2.715 kg to 1 s.d.2.715 kg to 1 s.d. 2.715 kg to 2 s.d.2.715 kg to 2 s.d. 0.987 V to 1 s.d.0.987 V to 1 s.d. 0.987 V to 2 s.d.0.987 V to 2 s.d.


digits:digits: 4080 J to 1 s.d.4080 J to 1 s.d. 4000 J4000 J 4080 J to 2 s.d.4080 J to 2 s.d. 2.715 kg to 1 s.d.2.715 kg to 1 s.d. 2.715 kg to 2 s.d.2.715 kg to 2 s.d. 0.987 V to 1 s.d.0.987 V to 1 s.d. 0.987 V to 2 s.d.0.987 V to 2 s.d.


digits:digits: 4080 J to 1 s.d.4080 J to 1 s.d. 4000 J4000 J 4080 J to 2 s.d.4080 J to 2 s.d. 4100 J4100 J 2.715 kg to 1 s.d.2.715 kg to 1 s.d. 2.715 kg to 2 s.d.2.715 kg to 2 s.d. 0.987 V to 1 s.d.0.987 V to 1 s.d. 0.987 V to 2 s.d.0.987 V to 2 s.d.


digits:digits: 4080 J to 1 s.d.4080 J to 1 s.d. 4000 J4000 J 4080 J to 2 s.d.4080 J to 2 s.d. 4100 J4100 J 2.715 kg to 1 s.d.2.715 kg to 1 s.d. 3 kg3 kg 2.715 kg to 2 s.d.2.715 kg to 2 s.d. 0.987 V to 1 s.d.0.987 V to 1 s.d. 0.987 V to 2 s.d.0.987 V to 2 s.d.


digits:digits: 4080 J to 1 s.d.4080 J to 1 s.d. 4000 J4000 J 4080 J to 2 s.d.4080 J to 2 s.d. 4100 J4100 J 2.715 kg to 1 s.d.2.715 kg to 1 s.d. 3 kg3 kg 2.715 kg to 2 s.d.2.715 kg to 2 s.d. 2.7 kg2.7 kg 0.987 V to 1 s.d.0.987 V to 1 s.d. 0.987 V to 2 s.d.0.987 V to 2 s.d.


digits:digits: 4080 J to 1 s.d.4080 J to 1 s.d. 4000 J4000 J 4080 J to 2 s.d.4080 J to 2 s.d. 4100 J4100 J 2.715 kg to 1 s.d.2.715 kg to 1 s.d. 3 kg3 kg 2.715 kg to 2 s.d.2.715 kg to 2 s.d. 2.7 kg2.7 kg 0.987 V to 1 s.d.0.987 V to 1 s.d. 1 V1 V 0.987 V to 2 s.d.0.987 V to 2 s.d.


digits:digits: 4080 J to 1 s.d.4080 J to 1 s.d. 4000 J4000 J 4080 J to 2 s.d.4080 J to 2 s.d. 4100 J4100 J 2.715 kg to 1 s.d.2.715 kg to 1 s.d. 3 kg3 kg 2.715 kg to 2 s.d.2.715 kg to 2 s.d. 2.7 kg2.7 kg 0.987 V to 1 s.d.0.987 V to 1 s.d. 1 V1 V 0.987 V to 2 s.d.0.987 V to 2 s.d. 0.99 V0.99 V


digits:digits: 13.5 N to 2 s.d.13.5 N to 2 s.d. 12.5 N to 2 s.d.12.5 N to 2 s.d. 12.51 N to 2 s.d.12.51 N to 2 s.d.

100.5 km to 3 s.d.100.5 km to 3 s.d.


digits:digits: 13.5 N to 2 s.d.13.5 N to 2 s.d. 14 N14 N 12.5 N to 2 s.d.12.5 N to 2 s.d. 12.51 N to 2 s.d.12.51 N to 2 s.d.

100.5 km to 3 s.d.100.5 km to 3 s.d.


digits:digits: 13.5 N to 2 s.d.13.5 N to 2 s.d. 14 N14 N 12.5 N to 2 s.d.12.5 N to 2 s.d. 12 N12 N 12.51 N to 2 s.d.12.51 N to 2 s.d.

100.5 km to 3 s.d.100.5 km to 3 s.d.


digits:digits: 13.5 N to 2 s.d.13.5 N to 2 s.d. 14 N14 N 12.5 N to 2 s.d.12.5 N to 2 s.d. 12 N12 N

The “Rule of 5”:The “Rule of 5”:

If the first digit to be dropped is a lone If the first digit to be dropped is a lone 5 (or a 5 followed by zeroes), round 5 (or a 5 followed by zeroes), round down if the preceding digit is even down if the preceding digit is even and up if the preceding digit is odd.and up if the preceding digit is odd.


digits:digits: 13.5 N to 2 s.d.13.5 N to 2 s.d. 14 N14 N 12.5 N to 2 s.d.12.5 N to 2 s.d. 12 N12 N 12.51 N to 2 s.d.12.51 N to 2 s.d.

100.5 km to 3 s.d.100.5 km to 3 s.d.


digits:digits: 13.5 N to 2 s.d.13.5 N to 2 s.d. 14 N14 N 12.5 N to 2 s.d.12.5 N to 2 s.d. 12 N12 N 12.51 N to 2 s.d.12.51 N to 2 s.d. 13 N13 N

100.5 km to 3 s.d.100.5 km to 3 s.d.


digits:digits: 13.5 N to 2 s.d.13.5 N to 2 s.d. 14 N14 N 12.5 N to 2 s.d.12.5 N to 2 s.d. 12 N12 N 12.51 N to 2 s.d.12.51 N to 2 s.d. 13 N13 N

100.5 km to 3 s.d.100.5 km to 3 s.d. 1.00 1.00 ×× 10 1022 km km

Write each of the following Write each of the following in scientific notationin scientific notation

20450 cal20450 cal 1200 N1200 N 0.235 J0.235 J 0.09030 km0.09030 km 0.0000007 s0.0000007 s 20.5 kHz20.5 kHz


20450 cal20450 cal 2.045 2.045 ×× 10 1044 calcal

1200 N1200 N 0.235 J0.235 J 0.09030 km0.09030 km 0.0000007 s0.0000007 s 20.5 kHz20.5 kHz


20450 cal20450 cal 2.045 2.045 ×× 10 1044 calcal

1200 N1200 N 1.2 1.2 ×× 10 1033 N N 0.235 J0.235 J 0.09030 km0.09030 km 0.0000007 s0.0000007 s 20.5 kHz20.5 kHz


20450 cal20450 cal 2.045 2.045 ×× 10 1044 calcal

1200 N1200 N 1.2 1.2 ×× 10 1033 N N 0.235 J0.235 J 2.35 2.35 ×× 10 10-1-1 J J 0.09030 km0.09030 km 0.0000007 s0.0000007 s 20.5 kHz20.5 kHz


20450 cal20450 cal 2.045 2.045 ×× 10 1044 calcal

1200 N1200 N 1.2 1.2 ×× 10 1033 N N 0.235 J0.235 J 2.35 2.35 ×× 10 10-1-1 J J 0.09030 km0.09030 km 9.030 9.030 ×× 10 10-2-2 km km 0.0000007 s0.0000007 s 20.5 kHz20.5 kHz


20450 cal20450 cal 2.045 2.045 ×× 10 1044 calcal

1200 N1200 N 1.2 1.2 ×× 10 1033 N N 0.235 J0.235 J 2.35 2.35 ×× 10 10-1-1 J J 0.09030 km0.09030 km 9.030 9.030 ×× 10 10-2-2 km km 0.0000007 s0.0000007 s 7 7 ×× 10 10-7-7 s s 20.5 kHz20.5 kHz


20450 cal20450 cal 2.045 2.045 ×× 10 1044 calcal

1200 N1200 N 1.2 1.2 ×× 10 1033 N N 0.235 J0.235 J 2.35 2.35 ×× 10 10-1-1 J J 0.09030 km0.09030 km 9.030 9.030 ×× 10 10-2-2 km km 0.0000007 s0.0000007 s 7 7 ×× 10 10-7-7 s s 20.5 kHz20.5 kHz 2.05 2.05 ×× 10 1011

kHzkHz

The Final AnswerThe Final Answer

When a measurement is used in a When a measurement is used in a calculation, the final answer must calculation, the final answer must take into consideration the take into consideration the uncertainty in the original uncertainty in the original measurements.measurements.


When a measurement is used in a When a measurement is used in a calculation, the final answer must take into calculation, the final answer must take into consideration the uncertainty in the consideration the uncertainty in the original measurements.original measurements.

Why? You don’t want to suggest that you Why? You don’t want to suggest that you know something to a greater precision than know something to a greater precision than you actually measured. For example,you actually measured. For example,

4 m/3 s = 1.3333333333333333333333 4 m/3 s = 1.3333333333333333333333 m/s???m/s???


When a measurement is used in a When a measurement is used in a calculation, the final answer must take calculation, the final answer must take into consideration the uncertainty in the into consideration the uncertainty in the original measurements.original measurements.

Why? You don’t want to suggest that you Why? You don’t want to suggest that you know something to a greater precision know something to a greater precision than you actually measured. For than you actually measured. For example,example,

4 m/3 s = 1 m/s.4 m/3 s = 1 m/s.


When a measurement is used in a When a measurement is used in a calculation, the final answer must take calculation, the final answer must take into consideration the uncertainty in into consideration the uncertainty in the original measurements.the original measurements.

NoteNote: Exact numbers used in calculations : Exact numbers used in calculations (e.g. a factor such as ½ in the equation (e.g. a factor such as ½ in the equation KK=½=½mvmv22) are not measurements and ) are not measurements and do not have any uncertainty.do not have any uncertainty.

Addition and SubtractionAddition and Subtraction

When adding or subtracting When adding or subtracting measurements, the final answer should measurements, the final answer should be rounded off to the least number of be rounded off to the least number of decimals in the original measurements.decimals in the original measurements.

e.g.e.g. 5.124 cm 5.124 cm (3 decimal places)(3 decimal places)

++ 0.01 cm0.01 cm (2 decimal places)(2 decimal places)

5.13 cm 5.13 cm (2 decimal places)(2 decimal places)

PracticePractice

7 m + 7 m =7 m + 7 m =

7 m + 7.0 m =7 m + 7.0 m =

7.0 m + 7.0 m =7.0 m + 7.0 m =

PracticePractice

7 m + 7 m = 14 m7 m + 7 m = 14 m

7 m + 7.0 m =7 m + 7.0 m =

7.0 m + 7.0 m =7.0 m + 7.0 m =

PracticePractice

7 m + 7 m = 14 m7 m + 7 m = 14 m

7 m + 7.0 m = 14 m7 m + 7.0 m = 14 m

7.0 m + 7.0 m =7.0 m + 7.0 m =

PracticePractice

7 m + 7 m = 14 m7 m + 7 m = 14 m

7 m + 7.0 m = 14 m7 m + 7.0 m = 14 m

7.0 m + 7.0 m = 14.0 m7.0 m + 7.0 m = 14.0 m

Multiplication and Multiplication and DivisionDivision

When multiplying or dividing When multiplying or dividing measurements, the final answer should measurements, the final answer should be rounded off to the same number of be rounded off to the same number of sig digs as are in the measurement with sig digs as are in the measurement with the least number of sig digs.the least number of sig digs.

e.g.e.g. 5.124 cm 5.124 cm (4 sig digs)(4 sig digs)

xx 0.01 cm0.01 cm (1 sig dig)(1 sig dig)

0.05 cm0.05 cm22 (1 sig dig)(1 sig dig)

PracticePractice

7 m x 7 m =7 m x 7 m =

7 m x 7.0 m =7 m x 7.0 m =

7.0 m x 7.0 m =7.0 m x 7.0 m =

PracticePractice

7 m x 7 m = 50 m7 m x 7 m = 50 m22

(Yes, your math teacher would not (Yes, your math teacher would not approve.)approve.)

7 m x 7.0 m =7 m x 7.0 m =

7.0 m x 7.0 m =7.0 m x 7.0 m =

PracticePractice

7 m x 7 m = 50 m7 m x 7 m = 50 m22

7 m x 7.0 m = 50 m7 m x 7.0 m = 50 m22

7.0 m x 7.0 m =7.0 m x 7.0 m =

PracticePractice

7 m x 7 m = 50 m7 m x 7 m = 50 m22

7 m x 7.0 m = 50 m7 m x 7.0 m = 50 m22

7.0 m x 7.0 m = 49 m7.0 m x 7.0 m = 49 m22

A WarningA Warning

When solving multi-step problems, When solving multi-step problems, round-off error can occur if a round-off error can occur if a rounded-off answer from one step is rounded-off answer from one step is used in a later step. used in a later step.

Record or store in your calculator all Record or store in your calculator all calculated digits for use in later calculated digits for use in later steps.steps.

A WarningA Warning

When solving multi-step problems, When solving multi-step problems, round-off error can occur if a rounded-round-off error can occur if a rounded-off answer from one step is used in a off answer from one step is used in a later step. later step.

Record or store in your calculator all Record or store in your calculator all calculated digits for use in later steps.calculated digits for use in later steps.

SERIOUSLY!!!!SERIOUSLY!!!!

DON’T ROUND TOO SOONDON’T ROUND TOO SOON

This is GUSSThis is GUSS

This is GUSSThis is GUSS

GUSS has a procedure for solving GUSS has a procedure for solving problems.problems.

First, he identifies his First, he identifies his GivensGivens..

Then he identifies his Then he identifies his UnknownUnknown..

Next, he Next, he SelectsSelects an equation that relates an equation that relates his Givens and his Unknown, his Givens and his Unknown, rearranging it for the Unknown if rearranging it for the Unknown if necessary.necessary.

Finally, he substitutes his Givens into the Finally, he substitutes his Givens into the equation and equation and SolvesSolves for his Unknown. for his Unknown.

An ExampleAn Example

How long does it take an object How long does it take an object travelling at a speed of 3.0 m/s to travelling at a speed of 3.0 m/s to travel a distance of 1.5 km?travel a distance of 1.5 km?



Givens: Givens: vv = 3.0 m/s = 3.0 m/s

dd = 1.5 km = 1.5 km




dd = 1.5 km = 1500 m = 1.5 km = 1500 m




dd = 1.5 km = 1500 m = 1.5 km = 1500 m

Unknown:Unknown: tt = ? = ?


Select an Equation:Select an Equation:

v = d/tv = d/t



v = d/tv = d/t t = d/vt = d/v




Substitute and Solve:Substitute and Solve:

tt = (1500 m/3.0 m/s) = = (1500 m/3.0 m/s) =





tt = (1500 m/3.0 m/s) = 500 s = (1500 m/3.0 m/s) = 500 s





tt = (1500 m/3.0 m/s) = 500 s = (1500 m/3.0 m/s) = 500 s

i.e. 5.0 x 10i.e. 5.0 x 1022 s s



v = v = d/d/tt t = t = d/vd/v


tt = (1500 m/3.0 m/s) = 500 s = (1500 m/3.0 m/s) = 500 s

i.e. 5.0 x 10i.e. 5.0 x 1022 s s

or 8.3 minor 8.3 min



v = v = d/d/tt t = t = d/vd/v


tt = (1500 m/3.0 m/s) = 500 s = (1500 m/3.0 m/s) = 500 s

i.e. 5.0 x 10i.e. 5.0 x 1022 s s

or 8.3 minor 8.3 min

PLEASE NOTE THAT ALL OUR MEASUREMENTS ALWAYS HAVE UNITS!

More PracticeMore Practice

Homework:Homework:

Significant Digits and GUSS Significant Digits and GUSS HandoutHandout

The Return of GUSS

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