1. KEY TERMINOLOGY / CONCEPTS ➢ Accuracy: How close the measurement is to the accepted value, your “correctness” ➢ Precision: How well the measurement can be repeated, your “repeatability” ● Precision of measurements: amount of agreement between identical trials and procedures ● Precision of equipment: value of markings on your tool ➢ Significant: actually measured

2. Science demands that you accurately report your measurements and your results The precision of equipment, markings on the tool, will impact your measuring and reporting ability EQUIPMENT LIMITATIONS Metric side measures to 1 decimal 15.5 cm English side measures to 4 decimals 6.0625 in

3. FLAVORS OF PRECISION We are always limited by the precision of our equipment, markings or scale on the tool. We can estimate 1 digit so 4.2 or 4.3 2 1 34 5

4. 21345 The smaller the measuring units are on the tool, the greater the precision of the equipment More people obtain identical measurements giving precision in measurements which is repeatability Everyone would agree the length is 4.3cm

5. REPORTING LIMITATIONS Your results are only accurate up to what you could measure with your least precise tool 25.451 3.2?? +15.04? 43.691 If we had a better tool we could measure the “?’s” We are uncertain of values for the 2 nd decimal and really uncertain of the value for the 3 rd decimal Reporting a value of 43.691 would be untruthful

6. REPORTING LIMITATIONS/ RULES ➢ You can only report out based on your “shoddiest piece of equipment” ➢ Significant digits help us provide accurate reporting based upon the limitations of our equipment ➢ This takes away the excuse that any error you have is because you had bad equipment

7. KEY TERMINOLOGY / CONCEPTS ● Accuracy: How close the measurement is to the accepted value, your “correctness” ● Precision: How well the measurement can be repeated, your “repeatability” ● Precision of measurements: amount of agreement between identical trials and procedures ● This relates to the quality of the tool used to make the measurement or precision of equipment

8. Inaccurate – didn’t hit the bulls-eye Imprecise – not grouped together very well Inaccurate – didn’t hit the bulls-eye Precision is good – grouped tightly together Accurate – hit the bulls-eye Precise – grouped tightly together ACCURACY VS. PRECISION

9. THE AMOUNT OF LIQUID IN THE GRADUATED CYLINDER SHOWN BELOW WAS MEASURED AND RECORDED FIVE TIMES. THESE MEASUREMENTS WOULD BE CONSIDERED TrialVolume Measurement 140.3mL 240.4mL 340.3mL 4 540.4mL A.Accurate & precise B.Accurate, but not precise C.Precise, but not accurate D.Neither accurate nor precise

10. WHICH SET OF MEASUREMENTS FOR THE LENGTH OF THE SCREW SHOWN BELOW WOULD BE CONSIDERED BOTH ACCURATE AND PRECISE? A.5.10 cm, 5.10 mm, 5.10 in, 5.10 cm B.5.00 cm, 5.20 cm, 5.50 cm, 5.05 cm C.510 cm, 5.01 cm, 5.90 cm, 4.90 cm D.5.10 cm, 5.12 cm, 5.10 cm, 5.09 cm

11. Significant: actually measured and are known to be true This becomes important when measurements made with equipment of varying precision get used in a calculation Science is picky about truthful reporting…your answer are only accurate to what you could measure with your worst piece of equipment DEALING WITH UNCERTAINTY Accurate reporting involves knowing which digits have some uncertainty vs. which digits are significant

12. SIGNIFICANT DIGITS Exact numbers - have an infinite number of significant figures. No limitation on counting! Example: 1 minute = 60 seconds 1 Dozen = 12 eggs COUNTED OUT, exactly No Measuring No Uncertainty Unlimited Significant Digits This is why sig figs are not important in math class

13. Nonzero numbers - Always count as being significant ► They are part of the measurement 3456 has 4 sig figs 17 has 2 sig figs Leading zeroes - Zeroes before the 1 st measured number DO NOT count as being significant ►They aren’t part of the measurement ►They just locate the decimal / hold place value 0.48673 has 5 sig figs 0.00021 has 2 sig figs

14. Captive zeroes - Zeroes between measured numbers ALWAYS count as being significant ►They are part of the measurement 50,069 has 5 sig figs 703.0409 has 7 sig figs Trailing zeroes - Zeroes at the end of a measurement SOMETIMES are significant ►A decimal is used, they were measured & significant ►No decimal appears, they weren’t measured and only keep place value so they are not significant NO DECIMAL = NO COUNT

15. 9.300 has a decimal, the zeroes were measured otherwise you would just write 9.3 8,600 has no decimal, the zeroes weren’t measured and are used to keep the 8 in the thousands place and the 6 in the hundreds place you cannot drop them because 8,600 ≠ 86 15.250has 5 sig figs 3,510has 3 sig figs

16. The Zero Question Zeroes have multiple purposes - they hold place value (do not count) - they locate the decimal point (do not count) - they are part of what you actually measured (do count)

17. Leading zeros never count (just locate the decimal) 0.0035g0.1mL0.07cm Captive zeros always count (part of the measurement) 102cm3.09g2,067.05L Trailing zeroes sometimes count (no decimal = no count) ☺Count – decimal point so is part of a measurement 10.00g3.20cm5.0L ☺Don’t count - no a decimal so zero is just holding place value 10g2,000mL30,900 ZERO RULE SUMMARY

18. WHAT DO YOU DO IF A ZERO IS SIGNIFICANT, NOT CAPTIVE AND YOU HAVE NO DECIMAL? The beaker can measure to the tens place 100 → only significant to hundreds place 100. → significant to the ones place Solution is to use a bar over the top to indicate that the zero is significant 100

19. REPORTING LIMITATIONS 25.451 3.2?? +15.04? 43.691 We are uncertain of the value for the 2 nd decimal and really uncertain of the value for the 3 rd decimal Reporting a value of 43.691 would be untruthful To be truthful we need to cut off what is uncertain round to report what we are certain of

20. MATH OPERATIONS ➢ The final answer you report CANNOT be any more significant then your least significant measurement o Carry out your math operations as you normally would o Round your calculator answer to reflect what was measured Adding and Subtracting: round to common places Multiply and Dividing: round to common significant digits IMPORTANT NOTICE DO NOT ALTER ANY MEASUREMENTS ONLY ROUND YOUR CALCULATOR ANSWER

21. ROUNDING o Take your answer o Starting at the highest place value (left → right) o Count out the number digits that are significant o Look at the number you are going to cut off o If it is a 4 or less you Round Down (leave as is) 67.348→67.3|48→ 67.3 o If it is a 5 with numbers after it or higher Round Up 165.99→16|5.99→ 170 o If exactly 5 (alone or just zeroes after it) Round Even 16.50→16.|50→16

22. 1.4 1.5 1.4 1.45 1.5 1.55 1.6 1.451.5 1.4509 Exactly half way Closer to higher number Round Even Down 1.4 Not Even Round Up 1.5 Round Even Up 1.6

23. ADDING & SUBTRACTING + & - : determined by precision which is the amount of measured PLACES your measurements have in common ▪ All units remain the same Example: 18.65mL + 22.3mL + 42mL = 82.92 mL All measurements can be made to the ones place 82|.92 mL →83 mL

24. MULTIPLY & DIVIDING x & ÷ : determined by your weakest measurements number of SIGNIFICANT DIGITS ▪The units in the change Example:40.70g ÷ 5.2mL = 7.826923077 g/mL Weakest measurement has 2 digits known for sure 7.8|26923077 g/mL →7.8 g/mL

25. WHAT HAPPENS IF YOU HAVE + WITH X OR / WITH - ? You must follow the rule for the math operation!! ➢ Follow your order of operations ➢ Do the first math step, follow the sig fig rule ➢ Do the next step, follow that sig fig rule DO NOT DO ALL THE MATH & THEN ROUND AT THE END

26. MIXED MATH EXAMPLE (3.65 g + 2.9 g + 58 g) ÷ (57.654 mL - 24.3 mL) = ? 1 ST Add 3.65 g + 2.9 g + 58 g = 64.55 → PLACES = 65 g 2 ND Subtract 57.654 mL = 24.3 mL = 33.354 → PLACES = 33.4 mL 3 rd Divide 65 g / 33.4mL = 1.9461 → DIGITS = 1.9 g/mL