Significant Figures. Engineers often are doing calculations with numbers based on measurements. Depending on the technique used, the precision of the.

Slides:



Advertisements
Similar presentations
1.2 Measurements in Experiments
Advertisements

Ch. 3.1 – Measurements and Their Uncertainty
Significant Figures and Rounding
1 Significant Digits Reflect the accuracy of the measurement and the precision of the measuring device. All the figures known with certainty plus one extra.
Significant Figures PP 6a Honors Chemistry.
Objectives The student will be able to: ● Distinguish between accuracy and precision ● Use significant figures in measurements and calculations.
Significant Figures.  All measurements are inaccurate  Precision of measuring device  Human error  Faulty technique.
Measurement Notes From pages in the text Honors Intro Physics Friday, Sept. 4 th.
Precision vs. Accuracy There really is a difference.
NOTES – SIGNIFICANT FIGURES (SIG FIGS) ANY DIGIT OF MEASUREMENT KNOWN WITH CERTAINTY PLUS ONE FINAL DIGIT WHICH IS ESTIMATED.
Chapter 1.5 Uncertainty in Measurement. Exact Numbers Values that are known exactly Numbers obtained from counting The number 1 in conversions Exactly.
Section 2.3 Measurement Reliability. Accuracy Term used with uncertainties Measure of how closely individual measurements agree with the correct or true.
The Scientific Method 1. Using and Expressing Measurements Scientific notation is written as a number between 1 and 10 multiplied by 10 raised to a power.
Significant Figures.
MEASUREMENTS. What is the difference between these two measurement rulers? Should we record the same number for each scale reading?
Working with Significant Figures. Exact Numbers Some numbers are exact, either because: We count them (there are 14 elephants) By definition (1 inch =
Uncertainty in Measurements and Significant Figures Group 4 Period 1.
A measured value Number and unit Example 6 ft.. Accuracy How close you measure or hit a true value or target.
SIG FIGS Section 2-3 Significant Figures Often, precision is limited by the tools available. Significant figures include all known digits plus one estimated.
Significant Figures. Exact Numbers Some numbers are exact because they are known with complete certainty. Most exact numbers are integers: exactly 12.
Super important tool to use with measurements!. Significant Figures (sig. figs.) All digits in a measurement that are known for certain, plus the first.
Significant Numbers All numbers in a measurement that are reasonable and reliable.
The Importance of measurement Scientific Notation.
Scientific Method, Calculations, and Values. Accuracy Vs. Precision Measuring and obtaining data experimentally always comes with some degree of error.
Honors Chemistry I. Uncertainty in Measurement A digit that must be estimated is called uncertain. A measurement always has some degree of uncertainty.
Significant Figures. What is a significant figure? There are 2 kinds of numbers: 1. Exact : Known with certainty. Example: the number of students in this.
Significant Figures What do you write?
Rules For Significant Figures. 1. You can estimate one significant figure past the smallest division on an analog measuring device.
Unit 1 Chapter 2. Common SI Units SI System is set-up so it is easy to move from one unit to another.
Problem of the Day x m x m x 10 8 km – 3.4 x 10 7 m 3. (9.21 x cm)(1.83 x 10 8 cm) 4. (2.63 x m) / (4.08 x.
Significant Figures Physical Science. What is a significant figure? There are 2 kinds of numbers: –Exact: counting objects, or definitions. –Approximate:
Accuracy vs. Precision What’s the Diff?. Accuracy Accuracy refers to how closely a measurement matches true or actual values.
Scientific Measurement Measurements and their Uncertainty Dr. Yager Chapter 3.1.
Introduction to Physics Science 10. Measurement and Precision Measurements are always approximate Measurements are always approximate There is always.
Mastery of Significant Figures, Scientific Notation and Calculations Goal: Students will demonstrate success in identifying the number of significant figures.
1 INTRODUCTION IV. Significant Figures. A. Purpose of Sig Figs Units of Measurement: Measurements indicate the magnitude of something Must include: –A.
Section 2.3. Accuracy: the closeness of measurements to the correct or accepted value of the quantity measured Precision: the closeness of a set of measurements.
Accuracy vs. Precision. Calculations Involving Measured Quantities The accuracy of a measured quantity is based on the measurement tool. The last digit.
Using Scientific Measurements. Accuracy and Precision Accuracy –How close a measurement is to the true or accepted value Determined by calculating % Error.
Significant Digits or Significant Figures. WHY??? The number of significant figures in a measurement is equal to the number of digits that are known with.
Significant Figures. Significant Figure Rules 1) ALL non-zero numbers (1,2,3,4,5,6,7,8,9) are ALWAYS significant. 1) ALL non-zero numbers (1,2,3,4,5,6,7,8,9)
Mastery of Significant Figures, Scientific Notation and Calculations Goal: Students will demonstrate success in identifying the number of significant figures.
First-Year Engineering Program Significant Figures This module for out-of-class study only. This is not intended for classroom discussion.
Significant Figures.
SIGNIFICANT FIGURES Fun With Numbers!!. SIGNIFICANT FIGURES Significant figures are all numbers in a measurement that show the level of accuracy to which.
1-2 Significant Figures: Rules and Calculations (Section 2.5, p )
 How many steps are in the scientific method?  Why are sig figs important?  When are zeros significant?  How should we write our answers when using.
Calculating and using significant figures What’s the point why do scientist need to know them?
Significant Figures When we take measurements or make calculations, we do so with a certain precision. This precision is determined by the instrument we.
Significant Figures SIGNIFICANT FIGURES You weigh something and the dial falls between 2.4 lb and 2.5 lb, so you estimate it to be 2.46 lb. The first.
How big is the beetle? Measure between the head and the tail!
Part 2 Significant Figures with Calculations
How big is the beetle? Measure between the head and the tail!
Significant Figures Sig Figs.
BELLWORK 9/13/16 1 Tm = 1012 m 1mm = 10-3 m 1Mm = 106 m
Aim: Why are Significant Figures Important?
IV. Significant figures
BELLWORK 9/01/17 Complete #’s 1, 12, 22, and 34 in the new Virginia Bellwork Packet.
Significant Figures General Chemistry.
Significant figures RULES TO MEMORIZE!.
Significant Figures The numbers that count.
DETERMINING SIGNIFICANT FIGURES
Significant Digits and Scientific Notation
Exact and Inexact Numbers
BELLWORK 9/2/15 How does a scientist reduce the frequency of human error and minimize a lack of accuracy? A. Take repeated measurements B. Use the same.
Rules for Use of Significant Figures
Significant Digits and Scientific Notation
Accuracy vs. Precision & Significant Figures
Measurements and Calculations.
Accuracy and Precision
Presentation transcript:

Significant Figures

Engineers often are doing calculations with numbers based on measurements. Depending on the technique used, the precision of the measurements can vary greatly. It is very important that engineers properly signify the precision of the numbers being used and calculated. Significant figures is the method used for this purpose.

Accuracy vs. Precision Accuracy refers to how closely a measured value agrees with the true value Example A scale to increments of 10 lbs is not very precise, but, if it is well calibrated, it is accurate. Courtesy:

Precision vs. Accuracy Precision refers to the level of resolution of the number. Example A scale to increments of tenths of a gram has good precision, however, if it is not well calibrated, it would not be accurate. A scale measures to 0.1 lbs is more precise than one that measures to 1 lbs. Courtesy: College Physics by A. Giambattista, B. Richardson and R. Richardson

Significant Figures and Precision In engineering and science, a number representing a measurement must indicate the precision to which the measured value is known. The precision of a device is limited by the finest division on the scale. Example A meterstick, with millimeter divisions as the smallest divisions, can measure a length to a precise number of millimeters and estimate a fraction of a millimeter between two divisions. Courtesy: College Physics by A. Giambattista, B. Richardson and R. Richardson

Significant Figures

RuleExampleSignificant digits # Significant Figures Nonzero digits are always significant.585 and 82 Final or ending zeroes written to the right of the decimal point are significant , 8, and zeroes 4 Zeroes written on either side of the decimal point for the purpose of spacing the decimal point are not significant and 8 (zeroes are insignificant) 2 Zeroes written between significant figures are significant , 5, 8 and zeroes 5 Rules for Identifying Significant Figures

Exact Numbers Exact numbers: Numbers known with complete certainty. Exact numbers are often found as conversion factors or as counts of objects. Exact numbers have an infinite number of significant figures. Example Conversion factors : 1 foot = 12 inches Counts of objects: 23 students in a class Courtesy:

Addition and Subtraction of Significant Figures When quantities are added or subtracted, the number of decimal places (not significant figures) in the answer should be the same as the least number of decimal places in any of the numbers being added or subtracted. Example J (2 decimal places - 4 significant fig.) 0.1 J (1 decimal place - 1 significant fig.) J (4 decimal places - 4 significant fig.) J (4 decimal places - 6 significant fig.) Result: 51.7 J ROUNDING !!! (1 decimal place - 3 sig. fig.) Courtesy:

Multiplication, Division, etc., of Significant Figures In a calculation involving multiplication, division, trigonometric functions, etc., the number of significant digits in the answer should be equal to the least number of significant digits in any one of the numbers being multiplied, divided etc. Example m -1 (3 decimal places - 2 significant fig.) X 4.73 m (2 decimal places - 3 significant fig. ) (5 decimal places - 5 significant fig.) Result: 0.46 ROUNDING !!! (2 decimal place - 2 sig. fig.) Courtesy:

Combination of Operations In a long calculation involving combination of operations, carry as many digits as possible through the entire set of calculations and then round the final result appropriately. DO NOT ROUND THE INTERMEDIATE RESULTS. Example (5.01 / 1.235) (6.35 / 4.0)= = The first division should result in 3 significant figures. The last division should result in 2 significant figures. In addition of three numbers, the answer should result in 1 decimal place. Result: 8.6 ROUNDING !!! (1 decimal place - 2 sig. fig.) Courtesy:

Combination of Operations IF YOU ROUND THE INTERMEDIATE RESULTS: Example (5.01 / 1.235) (6.35 / 4.0)= =8.66 If first and last division are rounded individually before obtaining the final answer, the result becomes 8.7 which is incorrect. Courtesy:

Sample Problems PLEASE CHECK THE FOLLOWING WEBSITES TO PRACTISE: /sigfigs8.html