Exact vs approximate There are 2 kinds of numbers: 1.Exact: the amount of money in your account. Known with certainty. 2.Approximate: weight, height— anything MEASURED. No measurement is perfect.
Estimate of Uncertainty When a measurement is recorded the digits that are dependable are written down PLUS the estimate of uncertainty. You estimate to one place beyond the smallest scale division.
Math versus Science If you measured the width of a paper with your ruler you might record it as 21.7cm. To a mathematician 21.70, or 21.700 is the same as 21.7. But to a scientist means the measurement of 21.700 means it is accurate to within one thousandth of a cm.
But, to a scientist 21.7cm and 21.70cm is NOT the same If you used an ordinary ruler, the smallest marking is the mm, so your measurement has to be recorded as 21.7cm. If your measurement is exactly 21.7 cm, your estimate of uncertainty is one place past the mm scale. Your new measurement is 21.70 cm. If the measurement was halfway between the 7 mm and the 8 mm marks, your measurement would be 21.75 cm.
Significant Figures (sig figs) Rules 1.All non-zero digits are significant. 2.In whole numbers that end in zero, the zeros at the end are not significant.
How many sig figs? 7 40 0.5 0.00003 7 x 10 5 7,000,000 1 1 1 1 1 1
Significant Figures (sig figs) Rules (cont.) 3.If zeros are sandwiched between non- zero digits, the zeros become significant. 4.If zeros are at the end of a number that has a decimal, the zeros are significant. These zeros are showing how accurate the measurement or calculation are.
How many sig figs here? 1.2 2100 56.76 4.00 0.0792 7,083,000,000 2 2 4 3 3 4
How many sig figs here? 3401 2100 2100.0 5.00 0.00412 8,000,050,000 4 2 5 3 3 6
Adding and Subtracting with Sig Figs When adding or subtracting measured numbers, the answer can have no more places after the decimal than the LEAST of the measured numbers. Examples : 1. 2.45cm + 1.2cm = 3.65cm Round off to = 3.7cm 2. 7.432cm + 2cm = 9.432 round to 9cm
Multiplying and Dividing with Sig Figs When multiplying or dividing, the result can have no more significant figures than the least reliable measurement. Examples: 1. 56.78 cm x 2.45cm = 139.111 cm 2 Round to 139cm 2 2. 75.8cm x 9.6cm = ?