Significant Digits ….or “Sig Digs”, if you prefer. Sometimes called “Significant figures” That’s right: “Sig Figs” Anyway…..

Slides:

Advertisements

Similar presentations

  Non-zero digits are significant.  Ex: 453 kg  All non-zero digits are always significant  # of Sig Fig’s?  3! Rule 1:

Advertisements

Significant Figures Every measurement has a limit on its accuracy based on the properties of the instrument used. we must indicate the precision of the.

 Significant Figures. So Many Numbers  How many places do you carry out?  What do we round to?  These are no longer acceptable questions for the science.

Physics Rules for using Significant Figures. Rules for Averaging Trials Determine the average of the trials using a calculator Determine the uncertainty.

Chemistry Notes Significant Figures & Scientific Notation

Calculations with Significant Figures

POWERPOINT THE SECOND In which you will learn about: Scientific notation +/-/x/÷ with sig figs Rounding.

TOPIC: Significant Figures Do Now: Round 9, to the… 1.Tenths 2.Ones 3.Hundreds 4.Thousandths 5.Thousands.

Significant digits Nilufa Rahim Sept. 21, Identifying significant digits 1. All non-zero digits are significant. Example: '123.45' has five significant.

Rules For Significant Digits

Starter 1.How would you record the following measurements? How many sig figs? a.b. 2.Count the sig figs in the following measured values: a

A measured value Number and unit Example 6 ft.. Accuracy How close you measure or hit a true value or target.

Significant Numbers All numbers in a measurement that are reasonable and reliable.

Chapter 2 “Scientific Measurement” Significant Figures in Calculations.

Significant Figures & Rounding Chemistry A. Introduction Precision is sometimes limited to the tools we use to measure. For example, some digital clocks.

 Significant figures are the figures that are known with a degree of certainty.

Significant Figures How to count the number of significant figures in a decimal number. How to count the number of significant figures in a decimal number.

Significant Figures (HOW TO KNOW WHICH DIGITS OF A NUMBER ARE IMPORTANT)

Significant Figures 1.All non-zero digits are significant (2.45 has 3 SF) 2.Zeros between (sandwiched)non- zero digits are significant (303 has 3 SF)

SIGNIFICANT FIGURES AMOLE WHAT & WHY?  Refer to them as “Sig Figs” for short  Used to communicate the degree of precision measured  Example -

Percent Composition. Molar Mass Calculate the Molar Mass of H 2 O 1 mole of H 2 O contains 2 mols H and 1 mol O. The mass of 2 moles H = 2 mol(1.008 g/mol)=

Significant Figures A tutorial adapted from

Significant Figures Physical Science. What is a significant figure? There are 2 kinds of numbers: –Exact: counting objects, or definitions. –Approximate:

Significant Figures.

Significant Figures SPH3U. Precision: How well a group of measurements made of the same object, under the same conditions, actually agree with one another.

Mastery of Significant Figures, Scientific Notation and Calculations Goal: Students will demonstrate success in identifying the number of significant figures.

Significant Figures. Rule 1: Digits other than zero are significant 96 g = 2 Sig Figs 152 g = __________ Sig Figs 61.4 g = 3 Sig Figs g = __________.

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)

SCIENTIFIC NOTATION 5.67 x 10 5 –Coefficient –Base –Exponent 1. The coefficient must be greater than or equal to 1 and less than The base must be.

Mastery of Significant Figures, Scientific Notation and Calculations Goal: Students will demonstrate success in identifying the number of significant figures.

Mathematical Operations with Significant Figures Ms. McGrath Science 10.

Significant Figures. Rule 1: Nonzero numbers are always significant. Ex.) 72.3 has 3 sig figs.

1-2 Significant Figures: Rules and Calculations (Section 2.5, p )

Scientific Notation and Significant Figures. Scientific Notation Purpose: – To simplify writing of large or small numbers (faster) – To show significant.

SIG FIGURE’S RULE SUMMARY COUNTING #’S and Conversion factors – INFINITE NONZERO DIGIT’S: ALWAYS ZERO’S: LEADING : NEVER CAPTIVE: ALWAYS TRAILING :SOMETIMES.

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. What is a significant figure?  There are 2 kinds of numbers:  Exact: the amount of money in your account. Known with certainty.

Rules for Significant Figures

Part 2 Significant Figures with Calculations

Significant Figures Notes on PAGE _____. Significant Figures Notes on PAGE _____.

Rules for Significant Figures

“The lost and puzzling art of the ancient world”

Significant Figures Why significant figures are important

Significant Figures Sig Figs.

Significant Digits Coordinate Algebra.

Significant Figures.

Significant Figures Why significant figures are important

Scientific Notation and Significant Figures

Significant Figures.

Aim: Why are Significant Figures Important?

SIG FIGURE’S RULE SUMMARY

Significant Digits or Significant Figures

1.6 – Calculating with Significant Figures

Significant Figures

Rules for Significant Digits

Significant Figures General Chemistry.

Sig Fig Math and Measurement

Significant Figures.

Exact and Inexact Numbers

Significant digits.

Significant Figures or Digits

Significant Figures.

“The lost and puzzling art of the ancient world”

5. Significant Figures- = represent the valid digits of a measurement and tells us how good your instrument is.

Manipulating Sig Figs - Notes B

….or “Sig Digs”, if you prefer.

How do you determine where to round off your answers?

Is it OK to write down all digits on your calculator?

Significant Figures and Rounding

Presentation transcript:

Significant Digits ….or “Sig Digs”, if you prefer. Sometimes called “Significant figures” That’s right: “Sig Figs” Anyway…..

First, some rules: 1. All non-zero digits ARE significant. 1, 2, 3, 4, 5, 6, 7, 8, 9. Example: the number “5691” has… _____ sig digs. 4

Next Rule: Zeros between other sig digs ARE significant. Example: the number “204017” has ____ sig digs. 6

3 rd Rule: (hold on tight- this is where it gets a little complicated…) 3. Zeros to the right of the decimal placeand …to the right other sig digs ARE significant. Example: The number “1.000” has ____ sig digs. 4

Last Rule: 4. All other zeros are NOT significant. …they are just “place holders”. Confused? Lets do some examples….

Examples: has ____ sig dig(s) has ____ sig dig(s). (only) has ___ sig dig(s) has ____ sig dig(s). 3

Multiplying & Dividing: So what’s the big deal? Remember the old saying: “A chain is only a strong as it’s….. …weakest link”? Same kind of idea with sig digs:

A calculated number is only as accurate as …. …the least accurate measured number that went into that calculation. In other words: Your answer should have no more (and no less) sig digs than the least number that went into that calculation. OK- more examples…. Multiplying & Dividing:

12.6 divided by 5.1 Your calculator would say… But you should only report the answer as… 2.5 (5.1 has only 2 sig digs) Round up when appropriate. Multiplying & Dividing:

One more example: x x Your calculator would say… But you should only report since has only 4 sig digs. Multiplying & Dividing:

OK- last one, really…. …how ‘bout: 2.00 x The answer is just “3”, right…? Nope- you need to report your answer as 3.00 (remember- answers can have no more but no less sig digs than the least number that went into the calculation.) Multiplying & Dividing:

Adding & Subtracting This rule is a little different. This time, it’s limited to the least sensitive decimal place. So, with adding & subtracting, you don’t need to count sig digs, You look at decimal places!!!

Example: When added gives you HOWEVER: Since 3.9 in the above problem only goes to the tenths place…. You must only report your answer to the tenths place: 19.9 Notice: you can have as many sig digs as you need, as long as you keep to the least sensitive decimal place.

So to review: For multiplying & dividing: Count sig digs in the equation and limit the answer to the least number. For adding & subtracting: Look for the least number of decimal places and limit it that way.