1. SIGNIFICANT figures Two types of numbers: exact and inexact. Exact numbers are obtained by counting or by definitions – a dozen of wine, hundred cents in a dollar All measured numbers are inexact.

2. All analog measurements involve a scale and a pointer Errors arise from: – Quality of scale – Quality of pointer – Calibration – Ability of reader

3. ACCURACY and PRECISION ACCURACY: how closely a number agrees with the correct value PRECISION: how closely individual measurements agree with one another – repeatability – Can a number have high precision and low accuracy?

4. Significant figures are the number of figures believed to be correct In reading the number the last digit quoted is a best estimate. Conventionally, the last figure is estimated to a tenth of the smallest division 2.02.12.22.32.42.5 2.36

5. The last figure written is always an estimate In this example we recorded the measurement to be 2.36 The last figure “6” is our best estimate It is really saying 2.36 ±.01 2.02.12.22.32.42.5

6. Precision of measurement (No. of Significant figures) depends on scale – last digit always estimated Smallest Division = 1 Estimate to 0.1 – tenth of smallest division 3 S.F. 99.6 979899100

7. Lower precision scale Smallest Division = 10 Estimate to 1 – tenth of smallest division 2 S.F. 96 708090100

8. Precision in measurement follows the scale Smallest Division = 100 Estimate to 10 – tenth of smallest division 1 S.F. 90 0100

9. Measuring length What is value of large division? – Ans: 1 cm What is value of small division? – Ans: 1 mm To what decimal place is measurement estimated? – Ans: 0.1 mm (3.48 cm)

10. Scale dictates precision What is length in top figure? – Ans: 4.6 cm What is length in middle figure? – Ans: 4.56 cm What is length in lower figure? – Ans: 3.0 cm

11. Scientific notation simplifies large and small numbers 1,000,000 = 1 x 10 6 0.000 001 = 1 x 10 -6 234,000 = 2.34 x 10 5 0.00234 = 2.34 x 10 -3

12. Multiplying and dividing numbers in scientific notation (A x 10 n )x(B x 10 m ) = (A x B) x 10 n + m (A x 10 n )/(B x 10 m ) = (A/B) x 10 n - m

13. Adding and subtracting (A x 10 n ) + (B x 10 n ) = (A + B) x 10 n (A x 10 n ) - (B x 10 n ) = (A - B) x 10 n