Chapter Two Significant Figures

Accuracy vs. Precision ► Most people think they mean the same thing ► In science, however, they have two very distinct meanings

Accuracy ► Refers to the closeness of measurements to the correct or accepted value of the quantity measured. ► Let’s say your lab group wants to measure the mass of a block of aluminum.  You get out a balance.  You tare the balance.  You mass the block of aluminum…it weighs 6.00 grams.

Your teacher comes along… ► And wants to verify your measurement.  She tares the balance  She places the block of aluminum on it  She gets 6.02 g.  Not bad. VERY close. ► Guess you’re both pretty ACCURATE.  Assuming your balance is working correctly.

Now another group wants to repeat your measurements… ► But it’s that other lab group, you know, the ones who are always breaking things. ► They get out a balance, but since they never pay attention to details, they forget to tare the balance. ► They each take turns massing the aluminum.

Their results: ► Desmond got 5.40 g ► Mathilda got 5.41 g ► Jim-Bob got 5.38 g ► Cindylou got 5.41 g ► Wow. All four got almost the exact same measurement. How accurate are they?

NOT VERY. ► Remember, they forgot to tare the balance.  Their measurements were all close to each other, but they’re all off a bit compared to what you and your teacher got. (and your teacher is NEVER wrong). So they break a lot of glassware, and they’re not very accurate. But they are PRECISE.

Precision ► Refers to the closeness of a set of measurements of the same quantity made in the same way. ► These measurements are close to one another, but not close to the accepted value.

So what happens if ► Your measurements are neither accurate nor precise? ► Well, you’ll probably fail the lab (JK) ► There is SOME margin of error when you’re doing an experiment.  Of course you want the best results possible.  When you write your lab report, consider what could have gone wrong.

Percentage Error ► We can calculate how accurate your experimental values are compared to the correct or accepted value ► Percentage error is calculated by subtracting the accepted value from the experimental value, dividing the difference by the accepted value, then multiplying by 100

The Formula ► Percentage error = Value experimental – Value accepted x 100 Value accepted Value accepted Or, what you got – what you shoulda got x 100 what you shoulda got what you shoulda got

Why are there errors in measurements? ► It could be the skill of the person doing the measuring ► It could the conditions under which you are measuring ► It could even be the measuring instruments you are using ► All measuring devices have varying degrees of precision.

Balances

Beakers

Graduated Cylinders

Significant Figures ► In science, we report measurements in terms of significant figures ► Significant Figures consist of all digits known with certainty, plus one more that is estimated. ► When you look at a measured quantity, you must determine which digits are significant.

Sig Fig Rules

All non zero digits are significant ► m 4444 ► g 5555 ► 43,221.2 ft 6666 ► 2.1 L 2222

Trapped zeros are significant ► m 5555 ► 1,001 ft 4444 ► s 4444

Leading zeros are NEVER significant ► Leading zeros are zeros at the beginning of a number. It doesn’t matter where the decimal is….they are never significant. ► m 2222 ► ft 4444 ► g 1111

Zeros a the end of a number ► With a decimal are always significant ► g 4444 ► m 5555 ► L 7777

Zeros at the end of a number ► Without a decimal are never significant ► 23,000 ft 2222 ► 2,002,000 mi 4444 ► 1,000,000 km 1111

Adding Measurements ► When adding and subtracting measurements, your answer should be rounded to the same decimal place as the least precise number ► g g g =  g  For our answer to be in correct sig figs, we round to the decimal place of the least precise measurement (1.1 g). Our answer would round to  9.4 g

Subtracting Measurements ► When adding and subtracting measurements, your answer should be rounded to the same decimal place as the least precise number ► g – g = g ► The least precise number here is g, so our answer rounds to 2 decimal places ► g

Multiplying Measurements ► When multiplying or dividing, your answer will round to the same number of significant figures as the least precise measurement (least number of sig figs). ► m x m x m =  m  The least precise measurement is m, so our answer will round to 3 sig figs ► 4.53 m

Get used to ‘em, they’ll be following you all year Get used to ‘em, they’ll be following you all year