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3.1 Measurements and their uncertainty

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 ×10 n How do we write it? 1. Take the number 2. Write it as #.### (you may have to move the decimal point over)

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3.1 Measurements and their uncertainty

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  1. 3.1 Measurements and their uncertainty

  2. 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.

  3. 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.

  4. Significant figures: Many are rules for zero vvvNot in the order the book has vvv 3 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 2Rules to not even start to think about significant figures, bro (67) • If you’re just counting stuff • Exactly defined ratios

  5. Significant figures: sandwiched, right-right 3Rules 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

  6. Significant figures: between the decimal and the number .0# / #0. 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 ⇒9.99x10-5 9990000. ⇒9.99x106

  7. Significant figures: count-ratio 2 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

  8. Scientific notation • Help on page R56

  9. Significant figures for calculations • In general, a calculated answer cannot be more precise than the least precise measurement

  10. 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 9.045 9.045 9.055 BEFORE I GO, I’LL TELL YOU WHAT TO DO!

  11. Addition (and subtraction) • Do the math like normal and get an answer. • Now, look back at the numbers you started with. • What number has the least amount of DECIMAL PLACES? • Round the answer YOU ALREADY got to that amount of decimal places. PLUS - PLACES

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

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