Rules for Use of Significant Figures

Slides:



Advertisements
Similar presentations
CHEMISTRY 11 TODAY’s OBJECTIVE:
Advertisements

Significant Figures and Rounding
IB Chem I Uncertainty in Measurement Significant Figures.
Accuracy, Precision, Signficant Digits and Scientific Notation.
Aim: How can we perform mathematical calculations with significant digits? Do Now: State how many sig. figs. are in each of the following: x 10.
Chapter 1.5 Uncertainty in Measurement. Exact Numbers Values that are known exactly Numbers obtained from counting The number 1 in conversions Exactly.
Uncertainty in Measurements: Using Significant Figures & Scientific Notation Unit 1 Scientific Processes Steinbrink.
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.
2.4 Significant Figures in Measurement
A measured value Number and unit Example 6 ft.. Accuracy How close you measure or hit a true value or target.
The Importance of measurement Scientific Notation.
Significant Figures and Scientific Notation Significant Figures:Digits that are the result of careful measurement. 1.All non-zero digits are considered.
Week.  Student will: scientific notation  Write in scientific notation.
Chemistry 100 Significant Figures. Rules for Significant Figures  Zeros used to locate decimal points are NOT significant. e.g., 0.5 kg = 5. X 10 2 g.
Significant Figures. Accuracy vs. Precision Percentage Error.
Significant Figure Rules RulesExamples The following are always significant Non zero digits Zeros between non zero digits Zero to the right of a non zero.
Introduction to Physics Science 10. Measurement and Precision Measurements are always approximate Measurements are always approximate There is always.
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.
1.9 Significant Figures Writing Numbers to Reflect Precision.
Mastery of Significant Figures, Scientific Notation and Calculations Goal: Students will demonstrate success in identifying the number of significant figures.
Significant Figures Chemistry I. Significant Figures The numbers reported in a measurement are limited by the measuring tool Significant figures in a.
Significant Figures. Rule 1: Nonzero numbers are always significant. Ex.) 72.3 has 3 sig figs.
Significant Figures When we take measurements or make calculations, we do so with a certain precision. This precision is determined by the instrument we.
Adding, Subtracting, Multiplying and Dividing with Sig Figs.
Significant Figures ► ► Physical Science. What is a significant figure? ► There are 2 kinds of numbers: –Exact: the amount is known with certainty. 2.
Rules for Significant Figures
How big is the beetle? Measure between the head and the tail!
Significant Figures.
Part 2 Significant Figures with Calculations
Unit 1 Chapter 2 Pages
Using Scientific Measurements.
Significant Figures Sig Figs.
Significant Figures.
BELLWORK 9/13/16 1 Tm = 1012 m 1mm = 10-3 m 1Mm = 106 m
Significant Figures.
Aim: Why are Significant Figures Important?
Significant Figures.
Significant Figures.
Significant Digits or Significant Figures
(sig figs if you’re cool)
Our Friends, the Significant Figures
PHYSICS 11 TODAY’s OBJECTIVE:
Significant Figures
Text Section 2.3 Pages
Significant Figures General Chemistry.
Using Scientific Measurements.
Significant figures RULES TO MEMORIZE!.
DETERMINING SIGNIFICANT FIGURES
Intro to Agriculture AAEC – Paradise Valley Fall 2014
Chapter 2 Measurements and Calculations
Chapter 3 Scientific Measurement 3.1 Using and Expressing Measurements
Section 3-2 Uncertainty in Measurements
Review of Essential Skills:
Super important tool to use with measurements!
Significant Figures Be able to identify the number of significant figures that an number has.
Chapter 2 Measurements 2.4 Significant Figures in Calculations
Scientific Measurement
5. Significant Figures- = represent the valid digits of a measurement and tells us how good your instrument is.
Scientific Notation and Significant Figures
Accuracy vs. Precision & Significant Figures
Scientific Measurements
Using Scientific Measurements
How do you determine where to round off your answers?
Measurement and Calculations
Uncertainty in Measurement
Significant Figures.
Introduction to Significant Figures &
Our Friends, the Significant Figures
Presentation transcript:

Rules for Use of Significant Figures

If you calculate the area of a parcel of land 94 If you calculate the area of a parcel of land 94.53 m long and 63 m wide, your calculator tells you the area is 5,955.39 m2.

But, if you’re certain of one length only to the closest meter (63), how can you be certain of the area to the hundredth of a square meter (5,955.39)?

Likewise, if we add three measured values of length:. 24. 3 cm. 1 Likewise, if we add three measured values of length: 24.3 cm 1.245 cm + 103 cm we can’t know the total length, with certainty, to any precision greater than the whole cm.

Obviously, we have to use care in calculating with measured values.

Significant figures relate to measurements and include all certain digits plus one and only one uncertain digit (the estimated digit).

Defined numbers and counting numbers are not measurements and contain an unlimited number of significant figures(they are exact numbers).  Examples:  Number of pounds in a ton equals exactly 2000 Number of cards in a deck equals exactly 52

Counting Significant Figures

The digits 1, 2, 3, 4, 5, 6, 7, 8, and 9 are always significant.

27,356 (5 significant figures) 49. 2 (3 significant figures) 81 27,356 (5 significant figures) 49.2 (3 significant figures) 81.6762 (6 significant figures)

Zeros are not significant at the end of a whole number which does not have a decimal point (they are place-holders).   Examples:  3400 (2 significant  figures)     2000 (1 significant figure)

Zeros are not significant at the beginning of a deci-number which does not have a whole number (they are place-holders).    Examples:  0.0034 (2 sig fig)    0.0002 (1 sig fig)

All other zeros are significant. Examples:. 3400. (4 sig figs). 200 All other zeros are significant.    Examples:  3400.  (4 sig figs)    200.0 (4 sig figs)    1.0034 (5 sig figs)    2.00020 (6 sig figs)

Special case - when some zeros are significant and some are not, use a line to  show which ones are.    Examples:  3400 (3 sig fig)    2000 (2 sig fig)

Or, even better, use scientific notation to show which zeros are significant. The “M” part of the number is always written using significant figures. 3400 (to 3 sig figs) is 3.40 x 103

Significant Figures in Calculated Answers The precision of a calculated answer is limited by the least precise measurement used in the calculation.

Addition & Subtraction

Find the last precise value in each quantity to be added or subtracted (the colored numbers below). 7003 mm 21.2 mm   + 130.00 mm 7154.20 mm = 7154 mm

The ones place is the last digit in the least precise measurement 7003 21.2   + 130.00 7154.20 = 7154 Therefore, the ones place is the last digit in the answer.

In a subtraction problem such as:. 597. 0 m. - 56. 742 m. 540 In a subtraction problem such as: 597.0 m - 56.742 m 540.258 m = 240.3 m the tenths place is the last place to have a digit in the answer.

Multiplication & Division

Determine how many significant figures there are in each number to be multiplied or divided.

Determine which of these has the least number of significant figures.

This is the number of significant digits to keep in the final answer.

Multiplication 3020. 1 m (5 significant figures) x 2 Multiplication 3020.1 m  (5 significant figures)    x      2.0 m   (2 sig fig) 6040.2 m2  = 6000 m2 (= 6.0 x 103 m2) 2 is the least number of significant figures.  So, keep 2 sig figs in the final answer.  The line indicates that the first zero is significant, and the last two are place holders.

Division 50830 cm (4 significant figures) 201 (3 significant figures) = 253 cm (3 sig figs) 3 is the least number of significant figures.  So, keep 3 sig fig in the final answer.

Rules for Rounding:

If the digit immediately to the right of the last significant figure you want to retain is greater than 5, increase the last digit by 1.

497.356 (to 4 significant figures) is 497.4

If the digit immediately to the right of the last significant figure you want to retain is less than 5, do not change the last digit.

8442.63 (to 3 significant figures) is 8440 The 0 is a place holder and is not a significant digit.