Scientific Measurement

Measurements are fundamental to the experimental sciences. Measurement: A quantity that has both a number and a unit.

Significant Figures in Measurements Significant figures: include all the digits that are known, plus a last digit that is estimated.

Precision in Measuring All measurements are found by using an instrument (ruler, thermometers, clocks, volt meters, bathroom scales) Measurement depends upon the quality of the instrument used to make the measurement Depending on how sensitive the instrument is, there is a level of uncertainty

Proper Measuring In measuring, we can only measure as close as the device will allow us. Scale A is only divided into 5’s so our first number that is read is estimated. Scale B is split into 1’s so the second measurement we read is estimated. Scale C is divided in 0.1 so we can read two digits and estimate the third.

Proper Measuring In the picture, we can measure something as small as 0.1 units. Is that the best we can do?

VERY IMPORTANT: You should always guess the last number. Proper Measuring First, look at how your measuring tool is divided up. What is the smallest you can measure with it? Our ruler only gave us down to 0.1units Second, guess a bit past what your measuring tool can do. VERY IMPORTANT: You should always guess the last number.

Proper Measuring Third: Write down your measurement, including the guess You have now measured something properly 81 82 83

(Measurement should be taken to 1 digit past the exact known mark) Uncertainty Rule When measuring read all digits that are represented by marked lines PLUS one digit past to represent the estimated digit (Measurement should be taken to 1 digit past the exact known mark)

Scientific Notation Scientific notation: a given number is written as the product of two numbers: a coefficient and 10 raised to a power. Scientific notation is useful for very large or very small numbers. Example: 602000000000000000000000 hydrogen atoms written 6.02 X 1023 The coefficient is 6.02 the exponent is 23. When moving the decimal place to the left the coefficient is positive. When moving the decimal to the right the exponent is negative.

Let’s Practice Write the following numbers in scientific notation 1) 3200000000000000000 3.2 X 1018 2)0.000000000054 5.4 X 10-11 3) 360000 3.6 X 105 4) 0.000000066 6.6 X 10-8

Rules for Determining Whether a Digit in a Measured Value is Significant Every nonzero in a reported measurement is assumed to be significant Zeros appearing between nonzero digits are significant Leftmost zeros appearing in front of nonzero digits are not significant Zeros at the end of a number and to the right of a decimal point are always significant. Zeros at the rightmost end of a measurement that lie to the left of an understood decimal point are not significant if they serve as placeholders to show the magnitude of the number. There are two situations in which numbers have an unlimited significant firgures: Counting numbers Exactly defined quantities

Examples: How many significant figures do each of the following have? a)24.8 b)0.0005412 c)6000 d)700. e)60min

Significant Figures in Calculations A calculated answer cannot be more precise than the least precise measurement form which it was calculated. Addition & Subtraction Rounded to the same number of decimal places as the measurement with the least number of decimal places Multiplication & Division Round the number to the same number of significant figures as the measurement with the least number of significant figures

Examples: Examples: 12.52m+349.0m+8.24m= 369.8m 7.55m X 0.34m= 2.6m2 2.4526m/8.4= 0.29m

Accuracy, Precision, and Error Accuracy: A measure of how close a measurement comes to the actual or true value or whatever is measured. Precision: A measure of how close a series of measurements are to one another.

Error = experimental value – accepted value Determining Error Accepted Value: value based on reliable references Experimental Value: The value measured in lab Error: The difference between the experimental value and the accepted value. Error = experimental value – accepted value Percent error is the absolute value of the error divided by the accepted value, multiplied by 100%