Significant Digits 0123456789 Mr Gabrielse How Long is
Significant Digits 0123456789. . . Mr. Gabrielse
How Long is the Pencil? Mr. Gabrielse
Use a Ruler Mr. Gabrielse
Can’t See? Mr. Gabrielse
How Long is the Pencil? Look Closer. Mr. Gabrielse
How Long is the Pencil? 5. 8 cm or 5. 9 cm 5. 8 cm 5. 9 cm ? Mr. Gabrielse
How Long is the Pencil? Between 5. 8 cm & 5. 9 cm 5. 8 cm Mr. Gabrielse
How Long is the Pencil? At least: 5. 8 cm 5. 9 cm 5. 8 cm Not Quite: 5. 9 cm Mr. Gabrielse
Solution: Add a Doubtful Digit • Guess an extra doubtful digit between 5. 80 cm and 5. 90 cm. 5. 9 cm 5. 8 cm • Doubtful digits are always uncertain, never precise. • The last digit in a measurement is always doubtful. Mr. Gabrielse
Pick a Number: 5. 80 cm, 5. 81 cm, 5. 82 cm, 5. 83 cm, 5. 84 cm, 5. 85 cm, 5. 86 cm, 5. 87 cm, 5. 88 cm, 5. 89 cm, 5. 90 cm 5. 9 cm 5. 8 cm Mr. Gabrielse
Pick a Number: 5. 80 cm, 5. 81 cm, 5. 82 cm, 5. 83 cm, 5. 84 cm, 5. 85 cm, 5. 86 cm, 5. 87 cm, 5. 88 cm, 5. 89 cm, 5. 90 cm 5. 9 cm I pick 5. 83 cm because I think the pencil is closer to 5. 80 cm than 5. 90 cm. 5. 8 cm Mr. Gabrielse
Extra Digits 5. 837 cm I guessed at the 3 so the 7 is meaningless. 5. 9 cm 5. 8 cm Mr. Gabrielse
Extra Digits 5. 837 cm I guessed at the 3 so the 7 is meaningless. 5. 9 cm 5. 8 cm Digits after the doubtful digit are insignificant (meaningless). Mr. Gabrielse
Example Problem – Example Problem: What is the average velocity of a student that walks 4. 4 m in 3. 3 s? • • d = 4. 4 m t = 3. 3 s v=d/t v = 4. 4 m / 3. 3 s = 1. 3 m/s not 1. 3333333333 m/s Mr. Gabrielse
Identifying Significant Digits Rule 1: Nonzero digits are always significant. Examples: 45 19, 583. 894. 32 136. 7 [2] [8] [2] [4] Mr. Gabrielse
Identifying Significant Digits Zeros make this interesting! FYI: 0. 000, 340, 056, 100, 0 Beginning Zeros Middle Zeros Ending Zeros Mr. Gabrielse Beginning, middle, and ending zeros are separated by nonzero digits.
Identifying Significant Digits Rule 2: Beginning zeros are never significant. Examples: 0. 005, 6 0. 078, 9 0. 000, 001 0. 537, 89 [2] [3] [1] [5] Mr. Gabrielse
Identifying Significant Digits Rule 3: Middle zeros are always significant. Examples: 7. 003 59, 012 101. 02 604 [4] [5] [3] Mr. Gabrielse
Identifying Significant Digits Rule 4: Ending zeros are only significant if there is a decimal point. Examples: 430 43. 0 0. 00200 0. 040050 [2] [3] [5] Mr. Gabrielse
Your Turn Counting Significant Digits Classwork: start it, Homework: finish it Mr. Gabrielse
Using Significant Digits Measure how fast the car travels. Mr. Gabrielse
Example Measure the distance: 10. 21 m Mr. Gabrielse
Example Measure the distance: 10. 21 m Mr. Gabrielse
Example Measure the distance: 10. 21 m Measure the time: 1. 07 s 1. 07 0. 00 s start stop Mr. Gabrielse
speed = distance time Physicists take data (measurements) and use equations to make predictions. Measure the distance: 10. 21 m Measure the time: 1. 07 s Mr. Gabrielse
speed = distance = 10. 21 m time 1. 07 s Physicists take data (measurements) and use equations to make predictions. Measure the distance: 10. 21 m Measure the time: 1. 07 s Use a calculator to make a prediction. Mr. Gabrielse
speed = 10. 21 m = 9. 542056075 m 1. 07 s s Physicists take data (measurements) and use equations to make predictions. Too many significant digits! We need rules for doing math with significant digits. Mr. Gabrielse
speed = 10. 21 m = 9. 542056075 m 1. 07 s s Physicists take data (measurements) and use equations to make predictions. Too many significant digits! We need rules for doing math with significant digits. Mr. Gabrielse
Math with Significant Digits The result can never be more precise than the least precise measurement. Mr. Gabrielse
speed = 10. 21 m = 9. 54 m 1. 07 s s we go over how to round next 1. 07 s was the least precise measurement since it had the least number of significant digits The answer had to be rounded to 9. 54 so it wouldn’t have more significant digits than 1. 07 s. Mr. Gabrielse
Rounding Off to X X: the new last significant digit Y: the digit after the new last significant digit Example: Round 345. 0 to 2 significant digits. If Y ≥ 5, increase X by 1 If Y < 5, leave X the same Mr. Gabrielse
Rounding Off to X X: the new last significant digit Y: the digit after the new last significant digit Example: Round 345. 0 to 2 significant digits. X Y If Y ≥ 5, increase X by 1 If Y < 5, leave X the same Mr. Gabrielse
Rounding Off to X X: the new last significant digit Y: the digit after the new last significant digit If Y ≥ 5, increase X by 1 If Y < 5, leave X the same Example: Round 345. 0 to 2 significant digits. X Y 345. 0 350 Fill in till the decimal place with zeroes. Mr. Gabrielse
Multiplication & Division You can never have more significant digits than any of your measurements. Mr. Gabrielse
Multiplication & Division (3. 45 cm)(4. 8 cm)(0. 5421 cm) = 8. 977176 cm 3 (3) (2) (4) = (? ) Round the answer so it has the same number of significant digits as the least precise measurement. Mr. Gabrielse
Multiplication & Division (3. 45 cm)(4. 8 cm)(0. 5421 cm) = 8. 977176 cm 3 (3) (2) (4) = (2) Round the answer so it has the same number of significant digits as the least precise measurement. Mr. Gabrielse
Multiplication & Division (3. 45 cm)(4. 8 cm)(0. 5421 cm) = 9. 000000 cm 3 (3) (2) (4) = (2) Round the answer so it has the same number of significant digits as the least precise measurement. Mr. Gabrielse
Multiplication & Division (3) (? ) (2) Round the answer so it has the same number of significant digits as the least precise measurement. Mr. Gabrielse
Multiplication & Division (3) (2) Round the answer so it has the same number of significant digits as the least precise measurement. Mr. Gabrielse
Multiplication & Division (3) (2) Round the answer so it has the same number of significant digits as the least precise measurement. Mr. Gabrielse
Addition & Subtraction Rule: Example: You can never have more decimal places than any of your measurements. 13. 05 309. 2 + 3. 785 326. 035 Mr. Gabrielse
Addition & Subtraction Example: Rule: The answer’s doubtful digit is in the same decimal place as the measurement with the leftmost doubtful digit. 13. 05 309. 2 + 3. 785 326. 035 Hint: Line up your decimal places. leftmost doubtful digit in the problem Mr. Gabrielse
Addition & Subtraction Rule: Example: The answer’s doubtful digit is in the same decimal place as the measurement with the leftmost doubtful digit. 13. 05 309. 2 + 3. 785 326. 035 Hint: Line up your decimal places. Mr. Gabrielse
Your Turn Classwork: Using Significant Digits Mr. Gabrielse
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