Significant Figures © R. A. Hill

significant figures (def) – All those digits in a measurement known to be accurate plus one more which is an estimate.

significant figures (def) – All those digits in a measurement known to be accurate plus one more which is an estimate. 5.4 m m 1 2 3 4 5 6 7

significant figures (def) – All those digits in a measurement known to be accurate plus one more which is an estimate. 5.4 m m 1 2 3 4 5 6 7

significant figures (def) – All those digits in a measurement known to be accurate plus one more which is an estimate. 5.4 m m 1 2 3 4 5 6 7

significant figures (def) – All those digits in a measurement known to be accurate plus one more which is an estimate. 5.37 m m 5 7 6

significant figures (def) – All those digits in a measurement known to be accurate plus one more which is an estimate. 5.37 m m 5 7 6

significant figures (def) – All those digits in a measurement known to be accurate plus one more which is an estimate. 5.37 m m 5 7 6

significant figures (def) – All those digits in a measurement known to be accurate plus one more which is an estimate. 5.368 m 0.4 0.1 0.2 0.3 5 m

significant figures (def) – All those digits in a measurement known to be accurate plus one more which is an estimate. 5.368 m 0.4 0.1 0.2 0.3 5 m

significant figures (def) – All those digits in a measurement known to be accurate plus one more which is an estimate. 5.368 m 0.4 0.1 0.2 0.3 5 m In every measurement there are accurately known, estimated and unknown digits.

The problem… 5 . 0 4 3 + 1 . 2

5 . 0 4 3 + 1 . 2 0 0 The problem… Assume there are zeros … + 1 . 2 0 0 Assume there are zeros … But that is a guess, if measured with a device of greater accuracy it could be anything…

5 . 0 4 3 + 1 . 2 0 0 The problem… There are then 3 types of digits: guesses 5 . 0 4 3 + 1 . 2 0 0

5 . 0 4 3 + 1 . 2 0 0 The problem… There are then 3 types of digits: guesses estimates accurately known 5 . 0 4 3 + 1 . 2 0 0

5 . 0 4 3 + 1 . 2 0 0 6 . 2 4 3 The problem… There are then 3 types of digits: guesses estimates accurately known 5 . 0 4 3 + 1 . 2 0 0 6 . 2 4 3 Classify the digits in the answer.

5 . 0 4 3 + 1 . 2 0 0 6 . 2 4 3 The problem… There are then 3 types of digits: guesses estimates accurately known 5 . 0 4 3 + 1 . 2 0 0 6 . 2 4 3 Classify the digits in the answer.

5 . 0 4 3 + 1 . 2 0 0 6 . 2 4 3 The problem… There are then 3 types of digits: guesses estimates accurately known 5 . 0 4 3 + 1 . 2 0 0 6 . 2 4 3 Classify the digits in the answer.

5 . 0 4 3 + 1 . 2 0 0 6 . 2 4 3 The problem… There are then 3 types of digits: guesses estimates accurately known 5 . 0 4 3 + 1 . 2 0 0 6 . 2 4 3 Classify the digits in the answer. Guesses are not significant figures. So the answer is…

5 . 0 4 3 + 1 . 2 0 0 6 . 2 The problem… There are then 3 types of digits: guesses estimates accurately known 5 . 0 4 3 + 1 . 2 0 0 6 . 2 Classify the digits in the answer. Guesses are not significant figures. So the answer is… Classify the digits in the answer. Guesses are not significant figures.

5 . 0 4 3 + 1 . 2 0 0 6 . 2 The problem… There are then 3 types of digits: guesses estimates accurately known 5 . 0 4 3 + 1 . 2 0 0 6 . 2 To get rid of guesses in answers more quickly & simply: 1st we must be able to identify significant digits (accurate and estimated digits in measurements) 2nd we learn how to round away guesses in the answers from all operations.

Rules for Identifying the # of S.F. in a Measurement   If a measurement is made correctly, all the nonzero digits are significant figures. Zeros are significant or not depending on their position within the measurement.

Markings every: 1000 ml 100 ml 10 ml 1 ml 400 ml 380 ml 380 ml Same liquid sample in 4 different graduated cylinders. 400 ml 380 ml 380 ml 380.4 ml Zeros may be significant (measured accurately or estimated) or may not be significant (not measured).

Zeros in the front portion of a # are never significant. 0.32 2 S.F.   Zeros in the front portion of a # are never significant.   0.32 2 S.F. 0.0293 3 S.F.

Zeros between significant digits in a # are always significant.   Zeros between significant digits in a # are always significant. 203 3 S.F. 20.03 4 S.F.

Zeros at the end of a # and to the right of the decimal are   Zeros at the end of a # and to the right of the decimal are always significant. 1.10 3 S.F. 16.00 4 S.F.

Zeros at the end of a # and to the left of the decimal may   Zeros at the end of a # and to the left of the decimal may or may not be significant. 1 700 2 to 4 S.F. ?

Zeros at the end of a # and to the left of the decimal may   Zeros at the end of a # and to the left of the decimal may or may not be significant. 1 700 2 to 4 S.F. ?

Zeros at the end of a # and to the left of the decimal may   Zeros at the end of a # and to the left of the decimal may or may not be significant. 1 700 2 to 4 S.F. ?

Zeros at the end of a # and to the left of the decimal may   Zeros at the end of a # and to the left of the decimal may or may not be significant. 1 700 2 to 4 S.F. ?

Zeros at the end of a # and to the left of the decimal may   Zeros at the end of a # and to the left of the decimal may or may not be significant. 1 700 3 120 000 2 to 4 S.F. ? 3 to 7 S.F. ?

Zeros at the end of a # and to the left of the decimal may   Zeros at the end of a # and to the left of the decimal may or may not be significant. 1 700 3 120 000 2 to 4 S.F. ? 3 to 7 S.F. ?

Zeros at the end of a # and to the left of the decimal may   Zeros at the end of a # and to the left of the decimal may or may not be significant. 1 700 3 120 000 2 to 4 S.F. ? 3 to 7 S.F. ?

Zeros at the end of a # and to the left of the decimal may   Zeros at the end of a # and to the left of the decimal may or may not be significant. 1 700 3 120 000 2 to 4 S.F. ? 3 to 7 S.F. ?

Zeros at the end of a # and to the left of the decimal may   Zeros at the end of a # and to the left of the decimal may or may not be significant. 1 700 3 120 000 2 to 4 S.F. ? 3 to 7 S.F. ?

Zeros at the end of a # and to the left of the decimal may   Zeros at the end of a # and to the left of the decimal may or may not be significant. 1 700 3 120 000 2 to 4 S.F. ? 3 to 7 S.F. ?

How many significant figures are in the following measurements? (1) 10.0 (2) 32 000 (3) 302 (4) 0.031 (5) 1020 (6) 0.0310 (7) 202.0 (8) 30 801 (9) 52.40 (10) 17.010 (11) 300.0 (12) 300 (13) 1700 (14) 0.000 008 (15) 0.080 (16) 15