3.1 MEASUREMENTS AND THEIR UNCERTAINTY

USING AND EXPRESSING MEASUREMENTS Scientific notation

AKA: “we’re to lazy to write the whole #” AAKA: “we want save paper” Look for ×10n

How do we write it? 1. Take the number 2. Write it as #.### (you may have to move the decimal point over) 3. Then make n = {the number of places you moved the decimal}

If you moved it to the right, n is (-) negative. If you moved it to the left, n is (+) positive.

ACCURACY, PRECISION, AND ERROR Accuracy

How close did we get to the correct number? Precision

How well could we measure it? Error

How far were we off from what we should expect?

Error = experimental value – accepted value

% Error = [] × 100

Experimental value: the data you got from doing an experiement Accepted value: the data you’d find in a book, or by calculating it theoretically without actually

doing an experiment.

SIGNIFICANT FIGURES: MANY ARE RULES FOR ZEROvvv Not in the order the book has vvv3 Rules for being SIGNIFICANT (66-67)

Nonzeros (1s through 9s) Sandwiched between nonzeros Right of the decimal point (.) AND to the right of ANY number (0-9)

1 Rules for NOT being SIGNIFICANT (67) Between a decimal point AND the number

2 Rules to NOT EVEN START TO THINK ABOUT SIGNIFICANT FIGURES, bro (67)

If you’re just counting stuff Exactly defined ratios

SIGNIFICANT FIGURES: SANDWICHED, RIGHT-RIGHT

3 Rules for being SIGNIFICANT (66-67) 1. Nonzeros (1s through 9s)

If you look like this: 1, 2, 3, 4, 5, 6, 7, 8, 9 Listed as #1 on page 66

The rest of the rules are for ZERO

2. Sandwiched between nonzeros If you’re a zero and you snuck in between your nonzero friends 909, for example Listed as #2 on page 66

3. Right of the decimal point (.) AND to the right of ANY number (0-9) 9.00000000000000000000000000000000000 Yup, they’re all good to go This even more so represents the PRECISION of your instruments Listed as #4 on page 66

SIGNIFICANT FIGURES: BETWEEN THE DECIMAL AND THE NUMBER

1 Rule for being INSIGNIFICANT (66-67)

4. Between the decimal point (.) AND the ENTIRE number Think about if you can just write that number in scientific notation If you can without ditching any significant figures, then it AIN’T significant. Combined rule from #3 & #5

.0000999 ⇒ 9.99x10-59990000. ⇒ 9.99x106

.0# / #0.

SIGNIFICANT FIGURES: COUNT-RATIO2 Rules to not even start to think about significant figures (67) 1. If you’re just counting stuff

Count how many people are in class That number has NOTHING TO DO with significant figures!

Count how many fingers you have That number has NOTHING TO DO with significant figures!

Count how many BLANK That number has NOTHING TO DO with significant figures!

2. Exactly defined ratios How many seconds per minute?

That number has NOTHING TO DO with significant figures! How many pints per gallon?

That number has NOTHING TO DO with significant figures! How many licks to get to the center of a tootsie pop?

That number has NOTHING TO DO with significant figures! Sort of like counting stuff, isn’t it…?

COUNT RATIO

SCIENTIFIC NOTATIONHelp on page R56

SIGNIFICANT FIGURES FOR CALCULATIONS In general, a calculated answer cannot be more precise than the least

precise measurement

ROUND UP OR NOT First figure out how many significant figures you’re rounding to.

Usually, you’ll be asked to round to something specific, like in practice problems 3 and 4 on page 69. Remember

You’re rounding the 2nd-to-LAST number Look at the LAST number

If it’s 5 or more, round up the 2nd-to-LAST number Otherwise, just take off the LAST number

9.0459.0459.055

BEFORE I GO,I’LL TELL YOU WHAT TO DO!

ADDITION (AND SUBTRACTION)1. Do the math like normal and get an answer.2. Now, look back at the numbers you started with.3. What number has the least amount of DECIMAL PLACES?4. Round the answer YOU ALREADY got to that amount of decimal places.

PLUS - PLACES

MULTIPLICATION (AND DIVISION)1. Do the math like normal and get an answer.2. Now, look back at the numbers you started with.3. What number has the least amount of SIGNIFICANT FIGURES?4. Round the answer YOU ALREADY got to that amount of sig figs.

MULTIPLICATION & DIVISION

SIGNIFICANT FIGURES