SIGNIFICANT FIGURES OR DIGITS
Significant Digits/FiguresSept. 2, 2014
SIGNIFICANT FIGURES OR DIGITS THE NUMBER OF SIGNIFICANT FIGURESINCLUDED IN A CALCULATION ORMEASUREMENT IS DEPENDENT ON THEACCURACY OF THE MEASURING DEVICEOR INSTRUMENT USED TO MAKE THEORIGINAL MEASUREMENTS
Exact v. Inexact Numbers Exact numbers – those numbers knownexactly (by definition or by counting)– One dozen 12, one inch 2.54 cm, 33students in the room Inexact numbers – values with someuncertainty; anything measured using a pieceof equipment (balance, graduated cylinder)– Mass of penny 3.03 grams
Precision v. Accuracy Precision – a measure of how closelyindividual measurements agree withone another (repeatability)– A balance is precise if it gives you the samevalue for every trial Accuracy – how closely individualmeasurements agree with the correct or“true” value (bullseye)– a balance is considered more accurate withincreasing decimal places ( /- 0.0001 g ismore accurate than /- 0.01 g)– Greater accuracy of an instrument meansmore significant figures.
SIGNIFICANT FIGURES RULE 1: Digits other than zero are alwayssignificant.Examples:96g61.4g0.52g2 significant digits3 significant digits2 significant digits
SIGNIFICANT FIGURES RULE 2: One or more final zeros used after thedecimal point are always significant (determined bythe accuracy of the measuring device: i.e. - balanceor electronic balance, etc.)Example:4.72 km4.7200 km82.0 m3 significant digits5 significant digits3 significant digits
SIGNIFICANT FIGURES RULE 3: Zeros between two othersignificant digits are always significant.Example:5.029 m306 km6.02 x 10²³ particles4 significant digits3 significant digits3 significant digits
SIGNIFICANT FIGURES RULE 4: Zeros used solely for spacing thedecimal point are not significant. The zerosare place holders only.– You can tell a number is a placeholder if when youremove the zeros, the number CHANGES its valueExample:7000 g0.00783 kg1 significant digit3 significant digits
SIGNIFICANT FIGURES RULE 5: Counting numbers and definedconstants have and infinite number ofsignificant digits
Summary SIGNIFICANT DIGITS: digits that representactual measurements.1. Digits other than zero.2. Zeros after the decimal.3. Zeros in the middle of significantdigits.
You Try! How many sig figs in the following:Number of Significant Figures:Examples:a) 4a) 1001 kmb) 4b) 34.00 mc) 5c) 129,870 md) 1d) .003 kme) 4e) 1.003f) 5f) .0072561 gg) 1g) 20,000 cmh) 2h) .0023 g
CALCULATIONS WITH SIG FIGS RULE: When multiplying or dividingmeasurements, round off the final answer to thenumber of significant digits in yourmeasurement having the least number ofsignificant digitsExamples:1. 2.03 cm x 36.00 cm 73.08 cm² 73.1 cm²2. (1.13 m)(5.126122m) 5.7925178 m² 5.79 m²3. 49.6000 cm² / 47.40 cm 1.0464135 cm 1.046 cm
CALCULATIONS WITH SIG FIGS RULE: For addition and subtraction, the answermay contain only as many decimal places as themeasurement with the least number of decimalplaces.Examples:1) 677.1 cm39.24 cm 6.232 cm722.572 cm 722.6 cm2) 34.231 g3) 16.45 cm6.709 g- 8.329 cm 18.20 g8.121 cm59.140 g 8.12 cm 59.14 g
You Try! Addition165.5 cm 8 cm 4.37 cm Multiplication2.6 cm x 3.78 cm
You Try! Addition165.5 cm 8 cm 4.37 cm 177.87 cm 178 cm Multiplication2.6 cm x 3.78 cm 9.828 cm2 9.8 cm2
Sep 02, 2014 · SIGNIFICANT FIGURES RULE 4: Zeros used solely for spacing the decimal point are not significant. The zeros are place holders only. –You can tell a number is a placeholder if when you remove the zeros, the number CHANGES its value Example: 7000 g 1 significant
Significant Figures are the digits in your number that were actually measured plus one estimated digit. Significant Figures Rules: 1) All nonzero digits are significant. 2) Zeros between significant digits are significant. 3) Zeros to the left of nonzero digits are not significant. 4) Zeroes at the end of a
This can be determined by the number of “significant digits”, also called “significant figures”, in the measurement. 6.8 meters has 2 significant digits. 7 meters has 1 significant digit. 6.76 meters has 3 significant digits. The measurement of 6.76 meters is more precise than 6.8 meters or 7 meters because it has more significant digits.
Significant Digits and Numbers When writing numbers, zeros used ONLY to help in locating the decimal point are NOT significant—others are. See examples. 0.0062 cm 2 significant figures 4.0500 cm 5 significant figures 0.1061 cm 4 significant figures 50.0 cm 3 significant figures
2. Zero digits that occur between nonzero digits are significant. 202 contains three significant figures In these examples, the zeros 450.5 contains four significant figures are part of a measurement. 390.002 contains six significant figures 3. Zeros at the beginning of a number (i.e., on the left-hand side) are considered to be placeholders and
(2) Significant figures. The digits used to express a number are called significant digits (figures). Thus each of the numbers 7845, 3.589, 0.4758 contains four significant figures while the numbers 0.00386, 0.000587 and 0.0000296 contain only three significant figures since zeros only help to fix the position of the decimal point.
Significant Figure Rules There are three rules on determining how many significant figures are in a number: 1. Non-zero digits are always significant. 2. Any zeros between two significant digits are significant. 3. A final zero or trailing zeros in the decimal portion ONLY are significant. F
Significant Digits: The number of significant figures in a result is simply the number of figures that are known with some degree of reliability. The number 13.2 is said to have 3 significant figures. The number 13.20 is said to have 4 signif
numbers of significant figures: three in 1.67 10-18 and four in 453.6. The number of significant figures, which is equal to the number of meaningful digits in a value, reflects the degree of uncertainty in the value (this is discussed more specifically in Study Sheet 2.1). A larger number of significant figures indicates a smaller uncertainty.
