Everything you wanted to know about Significant Digits…

Everything you wanted to know about Significant Digits…

… but were afraid to ask… but were afraid to ask

What is a good way to express calculated numbers?

What is a good way to express calculated numbers?

Are these? 2 x 3.00 = 6.00 14.00000 2.1 = 6.66666

How about these? 2 x 3.00 = 6 14.00000 2.1 = 6.7

Are these? 2 x 3.00 = 6.00 14.00000 2.1 = 6.66666

How about these? 2 x 3.00 = 6 14.00000 2.1 = 6.7

Calculated answers need to have a balance between accuracy and precision to account for

the QUALITY of measure

Calculated answers need to have a balance between accuracy and precision to account for

the QUALITY of measure Accuracy: In science, engineering, industry and statistics,

accuracy is the degree of conformity of a measured or calculated quantity to its actual, nominal, absolute, or some other reference, value…It’s “correctness”

Precision: The precision of a measurement or value describes the number of digits that are used to express that value. This might be the total number of digits (sometimes called the significant digits)…How well was it measured

Accuracy: In science, engineering, industry and statistics, accuracy is the degree of conformity of a measured or calculated quantity to its actual, nominal, absolute, or some other reference, value…It’s “correctness”

Precision: The precision of a measurement or value describes the number of digits that are used to express that value. This might be the total number of digits (sometimes called the significant digits)…How well was it measured

SOME clarificationSOME clarification

Significant Figure (sig-fig): How well a measurement was taken

Significant Digit (sig-dig): How well we can express a calculated answer to account for sig-figs

Scientific notation: A base 10 method of expressing large answers

Significant Figure (sig-fig): How well a measurement was taken

Significant Digit (sig-dig): How well we can express a calculated answer to account for sig-figs

Scientific notation: A base 10 method of expressing large answers

Significant FigureSignificant Figure

A way to express the quality of a measured value

Rule of thumb: Estimate one and only one number beyond what you can read from the instrument

A way to express the quality of a measured value

Rule of thumb: Estimate one and only one number beyond what you can read from the instrument

Significant digitSignificant digit

A way to express the quality of measured value in a calculated answer using a balance of precision and accuracy

A way to express the quality of measured value in a calculated answer using a balance of precision and accuracy

Scientific NotationScientific Notation

1) One and only one integer left of the decimal

2) When converting from a number larger than one-move decimal left and express exponent positively

3) When converting from a number less than one-move decimal right and express exponent negatively

1) One and only one integer left of the decimal

2) When converting from a number larger than one-move decimal left and express exponent positively

3) When converting from a number less than one-move decimal right and express exponent negatively

Rules for determining how many significant digits exist in a

number

Rules for determining how many significant digits exist in a

number1) All Integers count2) Zeros contained between integers count3) All trailing zeros count as along as a decimal point is

expressed in the number. If there is no decimal, then the trailing zeros are only significant if it is a measurement.

4) Preceding zeros do not count as they are simply placeholders

1) All Integers count2) Zeros contained between integers count3) All trailing zeros count as along as a decimal point is

expressed in the number. If there is no decimal, then the trailing zeros are only significant if it is a measurement.

4) Preceding zeros do not count as they are simply placeholders

Rules for determining which value dictates the expressed

number

Rules for determining which value dictates the expressed

number Multiplication and division: The number with the least sig-figs

determine how many numbers you will use to express your answer

Example: 4.44 4 1.11 but expressed as 1

Addition and subtraction: The number with the least number of decimal places determines which number of sig figs, you will use to express your answer in. If there is a tie, refer to multiplication/division rule.

Example: 3.11-1.3-.055-1= .755 but expressed as 8 X 10-1

Multiplication and division: The number with the least sig-figs determine how many numbers you will use to express your answer

Example: 4.44 4 1.11 but expressed as 1

Addition and subtraction: The number with the least number of decimal places determines which number of sig figs, you will use to express your answer in. If there is a tie, refer to multiplication/division rule.

Example: 3.11-1.3-.055-1= .755 but expressed as 8 X 10-1

Rules for rounding valuesRules for rounding values

All rounding rules apply as usual UNLESS the number ends in 5 When you have an answer which ends with a 5 and you need to

express it with one less integer, use these rules: 1) If the number preceding the 5 is odd then round up 2) If the number preceding the 5 is even then leave it alone.

1.0975 is expressed as 1.098. 1.0985 expressed 1.098

THIS ONLY APPLIES IF THE NUMBER ENDS IN 5 AND YOU HAVE TO EXPRESS IN ONE NUMBER LESS

All rounding rules apply as usual UNLESS the number ends in 5 When you have an answer which ends with a 5 and you need to

express it with one less integer, use these rules: 1) If the number preceding the 5 is odd then round up 2) If the number preceding the 5 is even then leave it alone.

1.0975 is expressed as 1.098. 1.0985 expressed 1.098

THIS ONLY APPLIES IF THE NUMBER ENDS IN 5 AND YOU HAVE TO EXPRESS IN ONE NUMBER LESS

Practice TimePractice Time

How many sig-figs are in the following measured values? 2.555 .0000056 1.000055 45.9000000000

How many sig-figs are in the following measured values? 2.555 .0000056 1.000055 45.9000000000

AnswersAnswers

2.555-4 .0000056-2 1.000055-7 45.9000000000-12

2.555-4 .0000056-2 1.000055-7 45.9000000000-12

Expression practice problemExpression practice problem

Based on the rules, what is the proper expression of the answer in the problem below?

3.00 X 6 =

Based on the rules, what is the proper expression of the answer in the problem below?

3.00 X 6 =

AnswerAnswer

The sig-digs are determined by the least number of sig-figs when multiplying or dividing

3.00 X 6 = 18.000 but expressed in sig-digs as 2 X 101 because you can’t express 18 as 1 sig-dig

The sig-digs are determined by the least number of sig-figs when multiplying or dividing

3.00 X 6 = 18.000 but expressed in sig-digs as 2 X 101 because you can’t express 18 as 1 sig-dig

One MoreOne More

Use the sig-figs in the problem below to determine how many sig-digs to express the answer.

1.00 + 2.111 + 2,254 =

Use the sig-figs in the problem below to determine how many sig-digs to express the answer.

1.00 + 2.111 + 2,254 =

AnswerAnswer

The sig-fig with the least decimal places determines the number of sig-digs to express the answer

1.00 + 2.111 + 2,254 = 2257.111 but expressed as 2,257 or 2.257 x 103 because 2254 has the least decimal places and has sig-fig equal to 4

The sig-fig with the least decimal places determines the number of sig-digs to express the answer

1.00 + 2.111 + 2,254 = 2257.111 but expressed as 2,257 or 2.257 x 103 because 2254 has the least decimal places and has sig-fig equal to 4

DisclaimerDisclaimer

Sig-digs are NOT the most important concept in chemistry…they do help you express yourself more intelligently and thus can add to your popularity

Sig-digs are NOT the most important concept in chemistry…they do help you express yourself more intelligently and thus can add to your popularity