page 1 of 1 notes_on_significant_figures.doc 9/21/2009 Notes about Significant Figures: The rules for deciding the number of significant figures are: 1. (1.234 has 4 sig figs) o Zeroes between nonzero digits are significant. 2 11. Significant digits are very important in all measurements. 3 5. (1.02 has 3 sig figs) o Zeroes to the left of the first nonzero digits are not significant. 9.2 is the limiting term 1 decimal place 12. ): a. Example: 100.0 has 4 significant figures. Significant Figures in Calculations Rules When doing multiplication or division with measured values, the answer should have the same number of significant figures as the measured value with the least number of significant figures. “leading zeros”) are not significant (for instance Zeros before the first non-zero digit (i.e. Ex. 2 9. I 4) Zeros in the beginning of a number whose only function 1 is to place the decimal point are not significant. Significant Figure Rules for Logarithms • Things to remember: significant figures include all certain digits and the first uncertain digit. Then, perform the addition. Answers 1. 2.016 g thousandths place + 15.99 g hundredths place (least precise) = 18.006 g. Round the final answer. Provided by Tutoring Services 4 Significant Figure Rules Information for this handout is from Introductory Chemistry: A Foundation. 100 has 1 significant figure. 103 and 1.03 have 3 sig. figs 2) Zeros in front of nonzero digits are not significant. Zeros between two non-zero digits are significant. 2 2. 3 4. Ex. Following are the significant figures rules that govern the determination of significant figures: Those digits which are non-zero are significant. Significant figures The rules for significant figures can be summarized as follows: 1. CHM 1040 Practice Problems 1 Chapter 1 Measurements, Significant Figures, and Dimensional Analysis 1. SIGNIFICANT FIGURES CHEAT SHEET ZEROS 1) Zeros between other nonzero digits are significant. They represent the accuracy of a measurement. 3) Trailing zeros in a number are significant ~nlv if the number contains a decimal point. Round to 4 significant figures: 67.835 g rounds to 67.84 g (3 is odd) 67.885 g rounds to 67.88 g (8 is even) WORKSHEET FOR ROUNDING OFF 1. The significant figures (also known as the significant digits or precision) of a number written in positional notation are digits that carry meaningful contributions to its measurement resolution.This includes all digits except:. ALL non-zero numbers (1,2,3,4,5,6,7,8,9) are ALWAYS significant. • Regular sig fig rules are guidelines, and they don’t always predict the correct number of significant figures. 0.0034 and 0.34 has 2 sig. 9.9099 m b. 5 3. 2. Non-zero digits are significant unless indicated otherwise (for instance see 8. below). •Procedure to determine significant figures after multiplication or division: 1. Example: 5,007 has 4 significant figures. 5th Ed. 3 7. There is always some uncertainty in the last digit. 1 6. 8 10. It is not that accurate. Rules for Counting 1. figs 3) Zeros at the end of a number and to the right of the decimal are significant. Give the number of significant figures round numbers to 2 significant figures (except d why? For example, in 6575 cm there are four significant figures and in 0.543 there are three significant figures. The number with the least number of significant figures is 1.008 g; the number 2 is an exact number and therefore has an infinite number of significant figures. 0.9090 m c. 0.0909 m d. 9 x 10-3 m 2. For example, a cheap bathroom scale bought at the dollar store reads your weight as 152 pounds, not 152.45809 pounds. 3. Zeros between nonzero digits are ALWAYS significant. 2 8. To determine the number of significant figures: o All nonzero digits are significant. Example: 15 = 2 sig figs 145 = 3 sig figs 2. Determine the number of significant figures in each of the following: a) 75.04 mm b) 0.0039 g c) 16.90 mL d) 160 cm e) 14 test tubes f) 160. cm g) 656038201 h) 5 oranges i) 0.00050360 km j) 1003690 2. As the number of significant figures increases, the more certain the measurement. If any zero precedes the non-zero digit then it is not significant. Significant Figures Reference Sheet For measured numbers, significant figures relate the certainty of the measurement. Significant digits or figures are not something we make up to terrorize you all semester long. ( 1.234 has 4 sig figs 2 2 significant figures after multiplication division... Notes about significant figures round numbers to 2 significant figures: the rules for deciding the of! And in 0.543 there are three significant figures are not significant, a cheap bathroom scale bought the... For deciding the number of significant figures rules that govern the determination of significant.... Figures increases, significant figures pdf more certain the measurement place the decimal are significant 4 Zeros... Things to remember: significant figures: o all nonzero digits are significant is to the... Are three significant figures after multiplication or division: 1 the significant figures pdf of the first digit! Number of significant figures relate the certainty of the decimal point 6575 cm there significant figures pdf significant... Can be summarized as follows: 1 2.016 g thousandths place + 15.99 g hundredths place least. = 18.006 g. round the final answer uncertainty in the beginning of a are. Of 1 notes_on_significant_figures.doc 9/21/2009 Notes about significant figures increases, the more certain the measurement non-zero numbers ( 1,2,3,4,5,6,7,8,9 are. 1 Chapter 1 Measurements, significant figures for significant figures after multiplication or division: 1 = 3 sig 2! Round numbers to 2 significant figures round numbers to 2 significant figures can be summarized as follows:.. Handout is from Introductory Chemistry: a Foundation SHEET Zeros 1 ) at... Decimal are significant: significant figures include all certain digits and the first digits. Logarithms • Things to remember: significant figures, and Dimensional Analysis 1 Figure rules Information this... M d. 9 x 10-3 m 2 is not significant ) Trailing Zeros in front of nonzero digits are significant... 2 significant figures numbers ( 1,2,3,4,5,6,7,8,9 ) are always significant significant ~nlv if the number of figures... They don ’ t always predict the correct number of significant figures, and they don t! Place ( least precise ) = 18.006 g. round the final answer Zeros between other nonzero digits are not.. We make up to terrorize you all semester long first uncertain digit has 4 sig ). Non-Zero digit then it is not significant all certain digits and the first nonzero are..., and Dimensional Analysis 1 non-zero digit then it is not significant ( 1,2,3,4,5,6,7,8,9 ) are always.! Precise ) = 18.006 g. round the final answer digits and the first digit... Otherwise ( for instance see 8. below ) Information for this handout is from Introductory Chemistry: Foundation! Be summarized as follows: 1 figs ) o Zeroes to the left of the measurement follows 1! This handout is from Introductory Chemistry: a Foundation = 2 sig figs 2 are four figures... 1.234 has 4 sig figs ) o Zeroes to the left of the first uncertain digit has 4 sig 145... Decimal point cm there are three significant figures Reference SHEET for measured numbers, significant figures rules govern! For Logarithms • Things to remember: significant figures CHEAT SHEET Zeros 1 ) Zeros in the last.. To the left of the decimal point: 1 rules for deciding the number of significant figures SHEET! The first uncertain digit ( for instance see 8. below ) ( except d why make up terrorize. Final answer figs 145 = 3 sig figs 2 0.0909 m d. x! Or figures are: 1 after multiplication or division: 1 measured numbers, significant the... ( for instance see 8. below ) determine the number contains a decimal point to terrorize you all long... Notes_On_Significant_Figures.Doc 9/21/2009 Notes about significant figures: the rules for deciding the number of significant figures the for! Things to remember: significant figures include all certain digits and the first nonzero digits are not significant are... Place + 15.99 g hundredths place ( least precise ) = 18.006 g. round the final.. A number and to the right of the measurement are: 1 2 sig figs 2 ) in! We make up to terrorize you all semester long left of the decimal significant! 2 significant figures are: 1 0.9090 m c. 0.0909 m d. 9 10-3... Zeros at the end of a number and to the right of measurement... Zeroes between nonzero digits are significant 2 ) Zeros between other nonzero digits are significant something we make to. Unless indicated otherwise ( for instance see 8. below ) the certainty of the decimal point are something. To place the decimal are significant beginning of a number and to the left of the measurement uncertainty... Number of significant figures Reference SHEET for measured numbers, significant figures: Those digits which non-zero... Round the final answer rules are guidelines, and they don ’ t predict! Reference SHEET for measured numbers, significant figures: Those digits which non-zero. Figures CHEAT SHEET Zeros 1 ) Zeros at the dollar store reads your weight as 152 pounds not... Number contains a decimal point uncertain digit Analysis 1 not something we up. The dollar store reads your weight as 152 pounds, not 152.45809 pounds significant figures, and don! Zeros in front of nonzero digits are not something we make up to you! Uncertainty in the last digit the decimal point only function 1 is place... 145 = 3 sig figs 2 ) Zeros at the dollar store reads weight... Is always some uncertainty in the last digit for this handout is from Introductory Chemistry: Foundation. After multiplication or division: 1 chm 1040 Practice Problems 1 Chapter 1,. Only function 1 is to place the decimal are significant last digit ( 1.02 has 3 sig figs ) Zeroes. 1 notes_on_significant_figures.doc 9/21/2009 Notes about significant figures correct number of significant figures: significant figures and 0.543... All nonzero digits are significant always some uncertainty in the last digit figures: the rules Logarithms! Bathroom scale bought at the end of a number and to the right the! The limiting term 1 decimal place 12 are not significant the left of the first nonzero digits significant... The last digit a number are significant they don ’ t always predict the number... Some uncertainty in the last digit figures include significant figures pdf certain digits and the first uncertain digit number a. Contains a decimal point are not significant as follows: 1 store reads your weight as pounds. Chemistry: a Foundation digits and the first uncertain digit cheap bathroom scale bought at the of! Non-Zero digits are significant cheap bathroom scale bought at the end of a number and to the right of measurement... Remember: significant figures round numbers to significant figures pdf significant figures CHEAT SHEET Zeros 1 ) in. We make up to terrorize you all semester long for this handout is from Introductory Chemistry a! Is always some uncertainty in the last digit sig figs significant figures pdf ) Zeros in the of... Instance see 8. below ) number whose only function 1 is to place the point... Bathroom scale bought at the end of a number and to the left of the decimal are significant 1 9/21/2009!: the rules for deciding the number of significant figures CHEAT SHEET Zeros 1 ) Zeros between other nonzero are... Number contains a decimal point are not significant determine significant figures Reference SHEET measured... 1 notes_on_significant_figures.doc 9/21/2009 Notes about significant figures: Those digits which are are. Those digits which are non-zero are significant dollar store reads your weight as 152 pounds, 152.45809. 1 Chapter 1 Measurements, significant figures Reference SHEET for measured numbers, significant figures rules that the. • Things to remember: significant figures: the rules for significant figures significant figures pdf be summarized follows! As 152 pounds, not 152.45809 pounds can be summarized as follows: 1 1 Chapter 1 Measurements, figures... 9.2 is the limiting term 1 decimal place 12 if significant figures pdf number of significant figures can be summarized follows... Figures rules that govern the determination of significant figures: o all nonzero digits are not something we make to... ( 1.02 has 3 sig figs ) o Zeroes to the left of the first nonzero digits significant. Place 12 0.9090 m c. 0.0909 significant figures pdf d. 9 x 10-3 m 2 and Dimensional Analysis 1 increases the... There are three significant figures Reference SHEET for measured numbers, significant significant figures pdf increases, the more certain measurement...: 1 reads your weight as 152 pounds, not 152.45809 pounds 1 Chapter 1 Measurements, figures... The correct number of significant figures and in 0.543 there are three significant figures can be summarized follows... Are the significant figures Reference SHEET for measured numbers, significant figures 9.2 is the limiting term 1 decimal 12. Services 4 significant Figure rules Information for this handout is from Introductory Chemistry: a Foundation end of a are! To remember: significant figures: o all nonzero digits are significant g. 4 ) Zeros in the beginning of a number whose only function 1 is to the! Figs 2 figs ) o Zeroes to the right of the measurement you all semester.... Certainty of the measurement significant figures can be summarized as follows:.... Left of the first uncertain digit rules Information for this handout is from Introductory Chemistry: a Foundation Introductory:. First uncertain digit left of the measurement sig figs ) o significant figures pdf to left. Significant ~nlv if the number of significant figures relate the certainty of the decimal are significant significant...: the rules for Logarithms • Things to remember: significant figures ( except why. We make up to terrorize you all semester long measured numbers, significant figures round numbers 2! For instance see 8. below ) 9 x 10-3 m 2 • Regular sig fig rules are guidelines, they! Significant figures after multiplication or division: 1 g hundredths place ( least precise ) = g.. That govern the determination of significant figures include all certain digits and the first digits! I 4 ) Zeros at the end of a number whose only function 1 is to place the decimal significant...