Introduction to Physics Science 10

Measurement and Precision Measurements are always approximate Measurements are always approximate There is always some error involved There is always some error involved Precision = the amount of information a measurement involves Precision = the amount of information a measurement involves Deals with the smallest division on the scale Deals with the smallest division on the scale Ex. Meter stick  readable to nearest mm Ex. Meter stick  readable to nearest mm

Estimating However you can estimate the readings between the lines if you look carefully However you can estimate the readings between the lines if you look carefully Scientists agree to only add one additional figure to their measurements in this way Scientists agree to only add one additional figure to their measurements in this way

Significant Figures Because the precision of all measuring devices is limited, the number of digits for measurement is also limited. Because the precision of all measuring devices is limited, the number of digits for measurement is also limited. The valid digits are called significant figures (or digits) The valid digits are called significant figures (or digits) Ex. A ruler has 2 certain digits and we can estimate 1 (9.40cm) Ex. A ruler has 2 certain digits and we can estimate 1 (9.40cm)

Digital Measurements The last digit is assumed to be estimated The last digit is assumed to be estimated Ex. Digital balance reads 4.75g Ex. Digital balance reads 4.75g The 5 is estimated The 5 is estimated

Significant Figures It is a shorthand notation of showing error in measurement in calculations and experiments It is a shorthand notation of showing error in measurement in calculations and experiments

When are digits significant? A Non-Zero is always significant A Non-Zero is always significant EX. 22  2 sig fig’s EX. 22  2 sig fig’s EX  3 sig fig’s EX  3 sig fig’s

With Zeros: 1) Zeros placed before digits are NOT significant - Ex L  2 sig fig’s 2) Zeros placed between digits are ALWAYS significant - Ex. 204  3 sig fig’s

With Zeros 3) Zeros placed after digits and after a decimal are ALWAYS significant Ex  3 sig fig’s 4) Zeros at the end of a number are only significant if there is a decimal after Ex. 390  2 sig fig’s 390.  3 sig fig’s 390.  3 sig fig’s

How many sig figs?

Rounding Numbers Often when doing arithmetic on a calculator, the answer is displayed with more significant figures than are really justified. Often when doing arithmetic on a calculator, the answer is displayed with more significant figures than are really justified. How do you decide how many digits to keep? How do you decide how many digits to keep?

Once you decide how many digits to keep, the rules for rounding off numbers are straightforward: Once you decide how many digits to keep, the rules for rounding off numbers are straightforward: RULE 1. If the first digit you remove is 4 or less, drop it and all following digits becomes 2.6 when rounded off to two significant figures because the first dropped digit (a 2) is 4 or less. RULE 1. If the first digit you remove is 4 or less, drop it and all following digits becomes 2.6 when rounded off to two significant figures because the first dropped digit (a 2) is 4 or less.

RULE 2. If the first digit removed is greater than 5, round up by adding 1 to the last digit kept is 4.6 when rounded off to 2 significant figures since the first dropped digit (an 8) is 5 or greater. RULE 2. If the first digit removed is greater than 5, round up by adding 1 to the last digit kept is 4.6 when rounded off to 2 significant figures since the first dropped digit (an 8) is 5 or greater. RULE 3. If the first digit removed is equal to 5 and the digit before it is an even number, drop it and all following digits. If the digit before it is an odd number, round up by adding 1 to the last digit kept. RULE 3. If the first digit removed is equal to 5 and the digit before it is an even number, drop it and all following digits. If the digit before it is an odd number, round up by adding 1 to the last digit kept.

Note about 5 * If there are any numbers written after the five, then you must round up. * If there are any numbers written after the five, then you must round up. Example: is 1.24 when rounding to 3 sig figs Example: is 1.24 when rounding to 3 sig figs Example: is 1.25 because there is a number after the 5. Example: is 1.25 because there is a number after the 5.

Adding And Subtracting When adding or subtracting, the number of decimal places (not sig fig’s) in the answer should be the same as the least number of decimal places in either number When adding or subtracting, the number of decimal places (not sig fig’s) in the answer should be the same as the least number of decimal places in either number Ex J (2 DP) Ex J (2 DP) 1.1 J (1 DP) 1.1 J (1 DP) J (4 DP) J (4 DP) 7.7 J (1 DP)

Multiplying and Dividing Keep the least number of significant figures in your answer that you have in the numbers Keep the least number of significant figures in your answer that you have in the numbers Ex. 1.2 m (2 SF) Ex. 1.2 m (2 SF) x 2 m (1 SF) x 2 m (1 SF) 2.4 m (2 SF) =2 m (can only keep 1 SF) =2 m (can only keep 1 SF)