Scientific Measurement

Measurements are fundamental to the experimental sciences.

Measurement: A quantity that has both a number and a unit.

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 PracticeWrite the following numbers in scientific notation1) 3200000000000000000

3.2 X 1018 2)0.000000000054

5.4 X 10-11

3) 3600003.6 X 105

4) 0.0000000666.6 X 10-8

Significant Figures in Measurements

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

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 numbersExactly 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 & SubtractionRounded to the same number of decimal places as the measurement with the least number of decimal placesMultiplication & DivisionRound 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.

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%