40 b sigfigrules excercises

7/28/2019 40 B SigfigRules Excercises

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Introduction to Gen. Chem. Prof. K. Golestaneh, Copyright 2010

Supplement B. Significant Figures in Math Operations and Uncertainty Page 1 of 4

Significant Figures Rules / Exercises

Write the number of significant figures (SF) above each number asyou read and understand the rules.

1.All non-zero digits (1-9) are to be counted as significantincluding zero(s) between numbers (captive zeros).

178 905 10078 345 1.375 5.075

2. Zeros that make a number larger or smaller are not significant(in precision). They are usually omitted from the number throughscientific notation. Write the scientific notation below eachnumber:

1750000 160800 0.000723 0.000000008107

Note: Zero to the left of a decimal (a number less than 1) is

never significant and often omitted. You do not have to enter it inyour calculator.

0.85 = .85 0.00375 = .00375

3. Zeros to the right of a decimal are always significant. Why?These zeros do not have any impact on the value of the numberbut make the number more or less precise. For example,

1.6 1.60 1.600 or 0.95 .950 0.9500

Note: You do not have to enter these zeros in your calculator.

How many SF are in: 4200 ??

If this number is exact? (i.e. exact number of people),

You would write it as: 4200 (exact) it now has indefinite SF

What if it is an approximate vale (only good to 3 SF)?

You have no choice but to use scientific notation: 4.20 x 103

What if it is should be expressed to 4 SF?

You can use scientific notation _____________ or simply 4200.


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Note : Placing a decimal after these zeros will not change the value ofthe number (you do not have to enter it in your calculator) but makesthe zeros captive and they count toward SF.

Example: Write 5000 to 2 SF ___________, 3 SF __________

4 SF ___________ or _____________ .

Rule For Expressing Proper Number Of Significant Digits InMultiplication or Division

For multiplication and Division:

THE PRODUCT OR QUOTIENT WILL BE REPORTED AS HAVING AS MANY

SIGNIFICANT DIGITS AS THE NUMBER INVOLVED IN THE OPERATIONWITH THE LEAST NUMBER OF SIGNIFICANT DIGITS.

For example:

0.06001 x 230.80 = ___________

According to the indicated rule, the product should be expressed withno more than _______ SF since 0.06001 has only _____ SF, while230.80 has ____ SF.

1.87 x 105/ 7.500 x 10-37 = ___________

The answer should be expressed with no more than _____ SF since thelowest number of SF is ____ .

Example:

(2.0)(600.0) = ___________

Example: (1.809)(14.0) (5.0 X 102) = ____________


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Rule For Expressing The Correct Number of Significant Figures inAddition or Subtraction

This rule is considerably different than the one for multiplication ordivision.

FOR ADDITION AND SUBTRACTION THE ANSWER MUST BE EXPRESSEDTO THE GREATER OF UNCERTAINTITIES.

What is uncertainty?

The lowest place significant digit of every number is always uncertainby 1 unit. This means that the TRUE value of the number is somewherebetween the upper limit and lower limit expressed as :

Number ! uncertainty

For example :

1.07 ! 0.01 (since the least SF 7 is in the hundredths place)

650 _______

3000 ______

0.0820 _______

Now add and follow the indicated rule. Place the uncertainty aboveeach number before adding.

123.13 + 8.7 =

190.92 12.678 =

34000 + 1280 =

6700 + 12 =

17.123 + 9.0014 + 27.13


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Rules For Rounding Off Digits

How do we round off insignificant digits ?

1. If the least significant figure (LSF) is to the right of the decimaland the digit that follows it is less than 5, simply eliminate alldigits to the right of the LSF.

2. If the LSF is to the right of the decimal and the digit that followsit is greater than 5, add 1 to the LSF and then eliminate all digitsto the right of the LSF.

3. If the LSF is to the LEFT of the decimal and the digit that followsit is less than 5, place zero(s) in place of all digits to the right ofthe LSF.

For example if we wish to round off the following number to 3significant digits:

17.382 ________

Round off 6.805 to three significant digits: __________

Another problem:

(6.75 x 7.5) + (2.79 x .017) =

40 b sigfigrules excercises

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