Introduction to PhysicsIntroduction to Physics

Science 10Science 10

Measurement and PrecisionMeasurement and Precision

Measurements are always approximateMeasurements are always approximate There is always some error involvedThere is always some error involved

Precision = the amount of information a Precision = the amount of information a measurement involvesmeasurement involves

Deals with the smallest division on the Deals with the smallest division on the scalescale

Ex. Meter stick Ex. Meter stick readable to nearest readable to nearest mmmm

EstimatingEstimating

However you can estimate the However you can estimate the readings between the lines if you readings between the lines if you look carefullylook carefully

Scientists agree to only add one Scientists agree to only add one additional figure to their additional figure to their measurements in this waymeasurements in this way

Significant FiguresSignificant Figures

Because the precision of all measuring Because the precision of all measuring devices is limited, the number of digits devices is limited, the number of digits for measurement is also limited. for measurement is also limited.

The valid digits are called significant The valid digits are called significant figures (or digits)figures (or digits)

Ex. A ruler has 2 certain digits and we Ex. A ruler has 2 certain digits and we can estimate 1 (9.40cm)can estimate 1 (9.40cm)

Digital MeasurementsDigital Measurements

The last digit is assumed to be The last digit is assumed to be estimatedestimated

Ex. Digital balance reads 4.75gEx. Digital balance reads 4.75g The 5 is estimatedThe 5 is estimated

Significant FiguresSignificant Figures

It is a shorthand notation of showing It is a shorthand notation of showing error in measurement in calculations error in measurement in calculations and experimentsand experiments

When are digits significant?When are digits significant?

A Non-Zero is always significantA Non-Zero is always significant EX. 22 EX. 22 2 sig fig’s 2 sig fig’s EX. 22.3 EX. 22.3 3 sig fig’s 3 sig fig’s

With Zeros:With Zeros:

1)1) Zeros placed before digits are NOT Zeros placed before digits are NOT significantsignificant

- Ex. 0.046L - Ex. 0.046L 2 sig fig’s 2 sig fig’s

2) Zeros placed between digits are 2) Zeros placed between digits are ALWAYS significantALWAYS significant

- Ex. 204 - Ex. 204 3 sig fig’s 3 sig fig’s

With ZerosWith Zeros

3) Zeros placed after digits and after a 3) Zeros placed after digits and after a decimal are ALWAYS significantdecimal are ALWAYS significant

Ex. 7.90 Ex. 7.90 3 sig fig’s 3 sig fig’s

4) Zeros at the end of a number are only 4) Zeros at the end of a number are only significant if there is a decimal aftersignificant if there is a decimal after

Ex. 390 Ex. 390 2 sig fig’s 2 sig fig’s

390. 390. 3 sig fig’s 3 sig fig’s

How many sig figs?How many sig figs?

100000056100000056 1.02565201.0256520 100100 0.0000060.000006 0.015402500.01540250 3600.3600. 36003600

Rounding NumbersRounding Numbers

Often when doing arithmetic on a Often when doing arithmetic on a calculator, the answer is displayed calculator, the answer is displayed with more significant figures than with more significant figures than are really justified.are really justified.

How do you decide how many digits How do you decide how many digits to keep?to keep?

Once you decide how many digits to Once you decide how many digits to keep, the rules for rounding off keep, the rules for rounding off numbers are straightforward:numbers are straightforward:

RULE 1. RULE 1. If the first digit you remove If the first digit you remove is 4 or less, drop it and all following is 4 or less, drop it and all following digits. 2.6271 becomes 2.6 when digits. 2.6271 becomes 2.6 when rounded off to two significant figures rounded off to two significant figures because the first dropped digit (a 2) because the first dropped digit (a 2) is 4 or less.is 4 or less.

RULE 2. RULE 2. If the first digit removed is greater If the first digit removed is greater than 5, round up by adding 1 to the last digit than 5, round up by adding 1 to the last digit kept. 4.5832 is 4.6 when rounded off to 2 kept. 4.5832 is 4.6 when rounded off to 2 significant figures since the first dropped significant figures since the first dropped digit (an 8) is 5 or greater.digit (an 8) is 5 or greater.

RULE 3RULE 3. If the first digit removed is . If the first digit removed is equalequal to to 5 and the digit before it is an even number, 5 and the digit before it is an even number, drop it and all following digits. If the digit drop it and all following digits. If the digit before it is an odd number, round up by before it is an odd number, round up by adding 1 to the last digit kept. adding 1 to the last digit kept.

Note about 5Note about 5

* If there are any numbers written * If there are any numbers written after the five, then you must round after the five, then you must round up.up.

Example: 1.245 is 1.24 when Example: 1.245 is 1.24 when rounding to 3 sig figsrounding to 3 sig figs

Example: 1.245000001 is 1.25 Example: 1.245000001 is 1.25 because there is a number after the because there is a number after the 5.5.

Adding And Subtracting Adding And Subtracting

When adding or subtracting, the When adding or subtracting, the number of decimal places (not sig number of decimal places (not sig fig’s) in the answer should be the fig’s) in the answer should be the same as the least number of decimal same as the least number of decimal places in either numberplaces in either number Ex. 5.67 J (2 DP)Ex. 5.67 J (2 DP)

1.1 J (1 DP)1.1 J (1 DP)

+0.9378J (4 DP)+0.9378J (4 DP)

7.7 J7.7 J (1 DP) (1 DP)

Multiplying and DividingMultiplying and Dividing

Keep the least number of significant Keep the least number of significant figures in your answer that you have figures in your answer that you have in the numbersin the numbers

Ex. 1.2 m (2 SF)Ex. 1.2 m (2 SF)

x 2 mx 2 m (1 SF) (1 SF)

2.4 m (2 SF)2.4 m (2 SF)

=2 m=2 m (can only keep 1 SF) (can only keep 1 SF)