Significant Digits

What are significant digits? So that we don’t have endless numbers behind a decimal point, scientists have agreed on some rules to determine which numbers in a measurement are really important Significant digits are the digits of a number that really mean something

Rules for significant digits: Non-zero digits in a measurement are always significant. For example: if a car odometer measures 7.2 miles, then there are TWO significant digits (the “7” and the “2”)

Rules for significant digits (contd.) Zeros between two significant digits in a measurement are significant. For example: The number 1.609 has 4 significant digits.

Rules for significant digits (contd.) All final zeros to the right of a decimal point are significant. If there is no decimal point, final zeros are NOT significant. So, “1.000” would have 4 sig. digits, but “10” would only have 1 sig. digit.

Rules for significant digits (contd.) Zeros that exist only to put the decimal point in the right place are NOT significant. So if we had “0.0008 kilometers”, it would only have 1 sig. digit.

How many sig. digits are there in . . . 36.33 minutes? Answer: 4 significant digits

How many significant figures are there in . . . 0.0074? Answer: 2 0.010 kilograms?

“Math for Science”

Accuracy How close a measurement comes to the actual or true value “Correctness”

Precision A measure of how close a series of measurements are to one another “Repeatable”

Error Error: The difference between the accepted value and the value you measured in the lab

% Error Calculation (Accepted – Experimental)

Types of Observations Quantitative = number Qualitative = like (description) Examples: 171cm or tall 2.35kg or heavy 122OC or hot

Scientific Notation (x 10) means “time 10 to the __ power) Move Decimal Point (by # of spaces) If positive, makes number bigger (right) If negative, makes number smaller (left) Ex: 1 x 102 or 1.35 x 10-2 Ex: 385000000 or 0.000790