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## Significant Digits

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**Other ways of saying it…**• Significant Digits • Significant Figures • Sigfigs • Sigdigs**The problem…**• Numbers are perfect and exact • Measurements are neither perfect nor exact • Accuracy = closeness to correct value • Accuracy itself is not a number, but a description • Precision = how close multiple measurements came to one another • Precision can also describe the number of sigfigs • The precision of an answer is not the same as the accuracy of an answer.**Precision vs. Accuracy**Accurate, but not precise Precise, but not accurate**Precision vs. Accuracy**Accurate and precise Neither accurate nor precise**Numerical example:**• Let’s say a table has a correct height of 0.68215 m • 4 groups measure the table several times… • 0.7 m, 0.6 m, 0.7 m • 0.91521 m, 0.91525 m, 0.91528 m • 0.6822 m, 0.6821 m, 0.6822 m • 2 m, 3 m, 1 m**How ALL measurements are to be made**• Read your measurements to all known values plus one estimated value • Check your understanding**A**P resent bsent**Counting Significant Digits in somebody else’s measurement**• If decimal point is Present • Count all digits from left to right starting with first nonzero number • If decimal point is Absent • Count all digits from right to left starting with first nonzero number**A**P resent bsent**Count the significant digits**• 0.000275 • 3 digits • 1.0052 • 5 digits • 270 • 2 digit • 25300 • 3 digits A P**Typical Example of using and following significant digits**through a calculation • Read the measurement from the BOTTOM of the meniscus • lazy answer: 21 mL • better answer: 20.6 mL • best answer: 20.65 mL**Density is mass divided by volume. The mass of 20.65 mL of**acetone is measured to be 16.3 g. Calculate the density of acetone. • But our calculation cannot be more precise than our measurements. (Round to ___ digits) • D = 0.789 g/mL**Adding with significant digits**• Add these masses: 0.265 g, 0.1820 g, 12.05 g • 00.265 g • 00.1820 g • 12.05 g • ============ • 12.497 g • (but the least precise measurement forces us to round to the hundredths place) • 12.50 g**Calculating error and percent error**• Density of lead is measured to be 10.9 g/cm3. • Actual, accept, or correct value of the density of lead is 11.34 g/cm3. • Error = experimental value – accepted value**Summary**• When making a measurement, report all known numbers, plus one estimated digit. • Counting significant digits with a decimal point left to right • Counting significant digits without a decimal point right to left • Multiplying or dividing with sigfigs, your result has no more sigfigs than the number with the least sigfigs in the problem. • Adding or subtracting with sigfigs, your answer has no more decimal places than the number with the fewest decimal places in the problem. • Error = exp. value – measured value • % error = absolute value of error divided by accepted value * 100.