Chapter 3 - Measurements UNIT 1 Foundations Chapter 3 - Measurements

Chapter 3B Accuracy and Precision in Measuring

The Limits of Measuring Measuring can never be exact, why? Markings may not be in small enough increments to align exactly with the measurement Environment conditions; temperature, pressure humidity may alter the scale Observer may use or read the instrument wrong Instrument may have defects Instrument may be damaged Conditions of measuring may interfere with getting a good measurement.

The Limits of Measuring Every scientific measurement contains error! The difference between a measurement and the dimension’s actual value Try to minimize error by accuracy and precision

Accuracy Accuracy Evaluates how close a measurement is to the actual value An assessment of the measurement error Depends on how well the instrument is constructed and maintained Must not change due to environmental conditions Human error Try to eliminate it by averaging multiple readings

Precision Precision Evaluates how exactly a measurement is made An assessment of the exactness of a measurement More precise means more digits, more digits mean better scale calibrations Precision is limited to the size of the smallest subdivision on the instrument If a quantity is defined or counted it is not measured and has infinite precision Some measurements are read exactly, some are estimated The estimated digit is the last digit

Significant Digits Scientists have developed a system to communicate the precision of their measurements Significant digits (or figures) All the digits known from the instrument plus one estimated digit Purpose is to establish the precision of the measurement, not its accuracy

Identifying Significant Digits Rules – From now one all problems should have two answers: one normal, and one with significant figures Only apply to measure data Not counted or pure numbers Not fractions that are considered to be 1 by definition All nonzero digits 112.54m 34oC 3. All zeros between nonzero digits 10.6mL 15.06m 103K

Identifying Significant Digits Decimals points define significant digits All zeros to the right of the last nonzero digit are significant 45.0s 8.500L If a decimal point is not present, no trailing zeros are significant 10cm 120oC 1800g If a decimal point is present, none of the zeros to the left of the first nonzero digit are significant, leading zeros 0.050m

Identifying Significant Digits Significant zeros in the one’s place are followed by a decimal point 110.m or 110m 1000.K or 1000K

Scientific Notation Measurements in science often deal with very large or small numbers Difficult to write, read and use Numbers are more convenient if expressed in scientific notation Format is M x 10n M is a number greaten than or equal to 1 and less than 10 n is an integer (positive or negative) All digits in M are significant How can you make 3800 have three significant digits? Can’t unless you use scientific notation!

Appendix E Calculations with Measurements

Adding and Subtracting Data Rules – Deals with PRECISION The data must have the same units The precision of a sum or difference cannot be greater than that of the least precise data given Example Add 3.1m and 45 cm

Multiplying and Dividing Data Rules – uses SIGNIFICANT DIGITS & PRECISION A product or quotient cannot have more SDs than the measurement with the fewest SDs The product or quotient of a measurement and a pure number has the same number of decimal places, or same precision as the original measurement Examples 7 x 2.35cm = 16.45cm not 16.5cm 2.63 cm/5 = 0.53 cm not 0.526cm

Rounding Review Identify the place value you are going to round to If the digit to the right is 0-4 then it is unchanged, 5-9 the number goes up If the rounded place value is to the right of the decimal point, all digits to the right of the rounded number will be dropped; if it is to the left than the numbers turn into zeros. Examples in brown box on page 72