significant digits
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Significant Digits. By Michelle Lamary and Caitlin Ostrowski. Counting Significant Digit Rules. All non-zero digits are significant (725 , 2, 12) Trapped zeros are significant (101, 2003) Ending zeros are significant only if the decimal point can be seen ( 100. , 1.10, 100, 20 ) - PowerPoint PPT PresentationTRANSCRIPT
Significant Significant DigitsDigits
By Michelle LamaryBy Michelle Lamary
and and
Caitlin OstrowskiCaitlin Ostrowski
Counting Significant Digit Counting Significant Digit RulesRules
1.1. All non-zero digits are significantAll non-zero digits are significant(725 , 2, 12)(725 , 2, 12)
2.2. Trapped zeros are significantTrapped zeros are significant(101, 2003)(101, 2003)
3.3. Ending zeros are significant only if the Ending zeros are significant only if the decimal point can be seendecimal point can be seen
((100. , 1.10, 100. , 1.10, 100, 20100, 20))
4.4. Leading (beginning) zeros are never Leading (beginning) zeros are never significantsignificant
(0.001, 0.9)(0.001, 0.9)
Example 1Example 1
401700.0900401700.0900
Example 1 - AnswerExample 1 - Answer
440017170000..00990000 Rule 1 – 4 sig digs non-zero digitsRule 1 – 4 sig digs non-zero digits
Example 1 - AnswerExample 1 - Answer
401700.09401700.090000 Rule 1 – 4 sig digs non-zero digitsRule 1 – 4 sig digs non-zero digits Rule 2 – 4 sig digs trapped zerosRule 2 – 4 sig digs trapped zeros
Example 1 - AnswerExample 1 - Answer
401700.09401700.090000 Rule 1 – 4 sig digs non-zero digitsRule 1 – 4 sig digs non-zero digits Rule 2 – 4 sig digs trapped zerosRule 2 – 4 sig digs trapped zeros Rule 3 – 2 ending zerosRule 3 – 2 ending zeros
Example 1 - AnswerExample 1 - Answer
401700.0900401700.0900 Rule 1 – 4 sig digs non-zero digitsRule 1 – 4 sig digs non-zero digits Rule 2 – 4 sig digs trapped zerosRule 2 – 4 sig digs trapped zeros Rule 3 – 2 sig digs ending zeros with decimal Rule 3 – 2 sig digs ending zeros with decimal
point shownpoint shown
Example 1 - AnswerExample 1 - Answer
401700.0900401700.0900 Rule 1 – 4 sig digs non-zero digitsRule 1 – 4 sig digs non-zero digits Rule 2 – 4 sig digs trapped zerosRule 2 – 4 sig digs trapped zeros Rule 3 – 2 sig digs ending zeros with decimal Rule 3 – 2 sig digs ending zeros with decimal
point shownpoint shown Rule 4 – 0 beginning zerosRule 4 – 0 beginning zeros
Example 1 - AnswerExample 1 - Answer
401700.0900401700.0900 Rule 1 – 4 sig digs non-zero digitsRule 1 – 4 sig digs non-zero digits Rule 2 – 4 sig digs trapped zerosRule 2 – 4 sig digs trapped zeros Rule 3 – 2 sig digs ending zeros with decimal Rule 3 – 2 sig digs ending zeros with decimal
point shownpoint shown Rule 4 – 0 beginning zerosRule 4 – 0 beginning zeros
10 Significant Digits10 Significant Digits
Example 2Example 2
0.0070500.007050
Example 2 - AnswerExample 2 - Answer
0.000.0077005500 Rule 1 – 2 sig digs non-zero numbersRule 1 – 2 sig digs non-zero numbers
Example 2 - AnswerExample 2 - Answer
0.000.0070570500 Rule 1 – 2 sig digs non-zero numbersRule 1 – 2 sig digs non-zero numbers Rule 2 – 1 sig dig trapped zeroRule 2 – 1 sig dig trapped zero
Example 2 - AnswerExample 2 - Answer
0.000.0070570500 Rule 1 – 2 sig digs non-zero numbersRule 1 – 2 sig digs non-zero numbers Rule 2 – 1 sig dig trapped zeroRule 2 – 1 sig dig trapped zero Rule 3 – 1 ending zeroRule 3 – 1 ending zero
Example 2 - AnswerExample 2 - Answer
0.000.0070507050 Rule 1 – 2 sig digs non-zero numbersRule 1 – 2 sig digs non-zero numbers Rule 2 – 1 sig dig trapped zeroRule 2 – 1 sig dig trapped zero Rule 3 – 1 sig dig ending zero with decimal Rule 3 – 1 sig dig ending zero with decimal
point is shownpoint is shown
Example 2 - AnswerExample 2 - Answer
0.000.0070507050 Rule 1 – 2 sig digs non-zero numbersRule 1 – 2 sig digs non-zero numbers Rule 2 – 1 sig dig trapped zeroRule 2 – 1 sig dig trapped zero Rule 3 – 1 sig dig ending zero with decimal Rule 3 – 1 sig dig ending zero with decimal
point is shownpoint is shown Rule 4 – beginning zeros are not significant (3 Rule 4 – beginning zeros are not significant (3
beginning zeros)beginning zeros)
Example 2 - AnswerExample 2 - Answer
0.000.0070507050 Rule 1 – 2 sig digs non-zero numbersRule 1 – 2 sig digs non-zero numbers Rule 2 – 1 sig dig trapped zeroRule 2 – 1 sig dig trapped zero Rule 3 – 1 sig dig ending zero with decimal Rule 3 – 1 sig dig ending zero with decimal
point is shownpoint is shown Rule 4 – beginning zeros are not significant (3 Rule 4 – beginning zeros are not significant (3
beginning zeros)beginning zeros)
4 significant digits 4 significant digits
Example 3Example 3
700.700.
Example 3 - AnswerExample 3 - Answer
770000.. Rule 1 – 1 sig dig non-zero numberRule 1 – 1 sig dig non-zero number
Example 3 - AnswerExample 3 - Answer
770000.. Rule 1 – 1 sig dig non-zero numberRule 1 – 1 sig dig non-zero number Rule 2 – 0 sig dig trapped zerosRule 2 – 0 sig dig trapped zeros
Example 3 - AnswerExample 3 - Answer
770000.. Rule 1 – 1 sig dig non-zero numberRule 1 – 1 sig dig non-zero number Rule 2 – 0 sig dig trapped zerosRule 2 – 0 sig dig trapped zeros Rule 3 – 2 ending zerosRule 3 – 2 ending zeros
Example 3 - AnswerExample 3 - Answer
700.700. Rule 1 – 1 sig dig non-zero numberRule 1 – 1 sig dig non-zero number Rule 2 – 0 sig dig trapped zerosRule 2 – 0 sig dig trapped zeros Rule 3 – 2 sig digs ending zeros with decimal Rule 3 – 2 sig digs ending zeros with decimal
point shownpoint shown
Example 3 - AnswerExample 3 - Answer
700.700. Rule 1 – 1 sig dig non-zero numberRule 1 – 1 sig dig non-zero number Rule 2 – 0 sig dig trapped zerosRule 2 – 0 sig dig trapped zeros Rule 3 – 2 sig digs ending zeros with decimal Rule 3 – 2 sig digs ending zeros with decimal
point shownpoint shown Rule 4 – 0 leading zerosRule 4 – 0 leading zeros
Example 3 - AnswerExample 3 - Answer
700.700. Rule 1 – 1 sig dig non-zero numberRule 1 – 1 sig dig non-zero number Rule 2 – 0 sig dig trapped zerosRule 2 – 0 sig dig trapped zeros Rule 3 – 2 sig digs ending zeros with decimal Rule 3 – 2 sig digs ending zeros with decimal
point shownpoint shown Rule 4 – 0 leading zerosRule 4 – 0 leading zeros
3 significant digits3 significant digits
Example 4Example 4
85008500
Example 4 - AnswerExample 4 - Answer
85850000 Rule 1 – 2 sig digs non-zero numbersRule 1 – 2 sig digs non-zero numbers
Example 4 - AnswerExample 4 - Answer
85850000 Rule 1 – 2 sig digs non-zero numbersRule 1 – 2 sig digs non-zero numbers Rule 2 – 0 sig digs trapped zerosRule 2 – 0 sig digs trapped zeros
Example 4 - AnswerExample 4 - Answer
85850000 Rule 1 – 2 sig digs non-zero numbersRule 1 – 2 sig digs non-zero numbers Rule 2 – 0 sig digs trapped zerosRule 2 – 0 sig digs trapped zeros Rule 3 – 2 ending zerosRule 3 – 2 ending zeros
Example 4 - AnswerExample 4 - Answer
85850000 Rule 1 – 2 sig digs non-zero numbersRule 1 – 2 sig digs non-zero numbers Rule 2 – 0 sig digs trapped zerosRule 2 – 0 sig digs trapped zeros Rule 3 – 0 sig digs (2 ending zeros but decimal Rule 3 – 0 sig digs (2 ending zeros but decimal
point is NOT shown)point is NOT shown)
Example 4 - AnswerExample 4 - Answer
85850000 Rule 1 – 2 sig digs non-zero numbersRule 1 – 2 sig digs non-zero numbers Rule 2 – 0 sig digs trapped zerosRule 2 – 0 sig digs trapped zeros Rule 3 – 0 sig digs (2 ending zeros but decimal Rule 3 – 0 sig digs (2 ending zeros but decimal
point is NOT shown)point is NOT shown) Rule 4 – 0 beginning zerosRule 4 – 0 beginning zeros
Example 4 - AnswerExample 4 - Answer
85850000 Rule 1 – 2 sig digs non-zero numbersRule 1 – 2 sig digs non-zero numbers Rule 2 – 0 sig digs trapped zerosRule 2 – 0 sig digs trapped zeros Rule 3 – 0 sig digs (2 ending zeros but decimal Rule 3 – 0 sig digs (2 ending zeros but decimal
point is NOT shown)point is NOT shown) Rule 4 – 0 beginning zerosRule 4 – 0 beginning zeros
2 significant digits2 significant digits
Example 5Example 5
8500.8500.
Example 5 - AnswerExample 5 - Answer
85850000.. Rule 1 – 2 sig digs non-zero digitsRule 1 – 2 sig digs non-zero digits
Example 5 - AnswerExample 5 - Answer
85850000.. Rule 1 – 2 sig digs non-zero digitsRule 1 – 2 sig digs non-zero digits Rule 2 – 0 sig dig trapped zerosRule 2 – 0 sig dig trapped zeros
Example 5 - AnswerExample 5 - Answer
85850000.. Rule 1 – 2 sig digs non-zero digitsRule 1 – 2 sig digs non-zero digits Rule 2 – 0 sig dig trapped zerosRule 2 – 0 sig dig trapped zeros Rule 3 – 2 ending zerosRule 3 – 2 ending zeros
Example 5 - AnswerExample 5 - Answer
8500.8500. Rule 1 – 2 sig digs non-zero digitsRule 1 – 2 sig digs non-zero digits Rule 2 – 0 sig dig trapped zerosRule 2 – 0 sig dig trapped zeros Rule 3 – 2 sig digs ending zeros with decimal Rule 3 – 2 sig digs ending zeros with decimal
point shownpoint shown
Example 5 - AnswerExample 5 - Answer
8500.8500. Rule 1 – 2 sig digs non-zero digitsRule 1 – 2 sig digs non-zero digits Rule 2 – 0 sig dig trapped zerosRule 2 – 0 sig dig trapped zeros Rule 3 – 2 sig digs ending zeros with decimal Rule 3 – 2 sig digs ending zeros with decimal
point shownpoint shown Rule 4 – 0 beginning zerosRule 4 – 0 beginning zeros
Example 5 - AnswerExample 5 - Answer
8500.8500. Rule 1 – 2 sig digs non-zero digitsRule 1 – 2 sig digs non-zero digits Rule 2 – 0 sig dig trapped zerosRule 2 – 0 sig dig trapped zeros Rule 3 – 2 sig digs ending zeros with decimal Rule 3 – 2 sig digs ending zeros with decimal
point shownpoint shown Rule 4 – 0 beginning zerosRule 4 – 0 beginning zeros
4 significant digits4 significant digits
Example 6Example 6
0.00000010.0000001
Example 6 - AnswerExample 6 - Answer
0.0000000.00000011 Rule 1 – 1 sig dig non-zero numberRule 1 – 1 sig dig non-zero number
Example 6 - AnswerExample 6 - Answer
0.0000000.00000011 Rule 1 – 1 sig dig non-zero numberRule 1 – 1 sig dig non-zero number Rule 2 - 0 sig digs trapped zerosRule 2 - 0 sig digs trapped zeros
Example 6 - AnswerExample 6 - Answer
0.0000000.00000011 Rule 1 – 1 sig dig non-zero numberRule 1 – 1 sig dig non-zero number Rule 2 - 0 sig digs trapped zerosRule 2 - 0 sig digs trapped zeros Rule 3 – 0 sig digs ending zerosRule 3 – 0 sig digs ending zeros
Example 6 - AnswerExample 6 - Answer
0.0000000.00000011 Rule 1 – 1 sig dig non-zero numberRule 1 – 1 sig dig non-zero number Rule 2 - 0 sig digs trapped zerosRule 2 - 0 sig digs trapped zeros Rule 3 – 0 sig digs ending zeros (decimal point Rule 3 – 0 sig digs ending zeros (decimal point
is shown)is shown)
Example 6 - AnswerExample 6 - Answer
0.0000000.00000011 Rule 1 – 1 sig dig non-zero numberRule 1 – 1 sig dig non-zero number Rule 2 - 0 sig digs trapped zerosRule 2 - 0 sig digs trapped zeros Rule 3 – 0 sig digs ending zerosRule 3 – 0 sig digs ending zeros Rule 4 – beginning zeros are not significant (7 Rule 4 – beginning zeros are not significant (7
non significant beginning zeros)non significant beginning zeros)
Example 6 - AnswerExample 6 - Answer
0.0000000.00000011 Rule 1 – 1 sig dig non-zero numberRule 1 – 1 sig dig non-zero number Rule 2 - 0 sig digs trapped zerosRule 2 - 0 sig digs trapped zeros Rule 3 – 0 sig digs ending zerosRule 3 – 0 sig digs ending zeros Rule 4 – beginning zeros are not significant (7 Rule 4 – beginning zeros are not significant (7
non significant beginning zeros)non significant beginning zeros)
1 significant digit1 significant digit
Example 7 Example 7
200009200009
Example 7 - AnswerExample 7 - Answer
220000000099 Rule 1 – 2 sig digs non-zero numbersRule 1 – 2 sig digs non-zero numbers
Example 7 - AnswerExample 7 - Answer
200009200009 Rule 1 – 2 sig digs non-zero numbersRule 1 – 2 sig digs non-zero numbers Rule 2 – 4 sig digs trapped zerosRule 2 – 4 sig digs trapped zeros
Example 7 - AnswerExample 7 - Answer
200009200009 Rule 1 – 2 sig digs non-zero numbersRule 1 – 2 sig digs non-zero numbers Rule 2 – 4 sig digs trapped zerosRule 2 – 4 sig digs trapped zeros Rule 3 – 0 sig digs ending zeros Rule 3 – 0 sig digs ending zeros
Example 7 - AnswerExample 7 - Answer
200009200009 Rule 1 – 2 sig digs non-zero numbersRule 1 – 2 sig digs non-zero numbers Rule 2 – 4 sig digs trapped zerosRule 2 – 4 sig digs trapped zeros Rule 3 – 0 sig digs ending zeros (decimal point Rule 3 – 0 sig digs ending zeros (decimal point
NOT shown)NOT shown)
Example 7 - AnswerExample 7 - Answer
200009200009 Rule 1 – 2 sig digs non-zero numbersRule 1 – 2 sig digs non-zero numbers Rule 2 – 4 sig digs trapped zerosRule 2 – 4 sig digs trapped zeros Rule 3 – 0 sig digs ending zeros (decimal point Rule 3 – 0 sig digs ending zeros (decimal point
is NOT shown)is NOT shown) Rule 4 – 0 beginning zerosRule 4 – 0 beginning zeros
Example 7 - AnswerExample 7 - Answer
200009200009 Rule 1 – 2 sig digs non-zero numbersRule 1 – 2 sig digs non-zero numbers Rule 2 – 4 sig digs trapped zerosRule 2 – 4 sig digs trapped zeros Rule 3 – 0 sig digs ending zerosRule 3 – 0 sig digs ending zeros Rule 4 – 0 beginning zerosRule 4 – 0 beginning zeros
6 significant digits6 significant digits
Example 8Example 8
1010
Example 8 - AnswerExample 8 - Answer
1100 Rule 1 – 1 sig dig non-zero numberRule 1 – 1 sig dig non-zero number
Example 8 - AnswerExample 8 - Answer
1100 Rule 1 – 1 sig dig non-zero numberRule 1 – 1 sig dig non-zero number Rule 2 – 0 sig digs trapped zerosRule 2 – 0 sig digs trapped zeros
Example 8 - AnswerExample 8 - Answer
1100 Rule 1 – 1 sig dig non-zero numberRule 1 – 1 sig dig non-zero number Rule 2 – 0 sig digs trapped zerosRule 2 – 0 sig digs trapped zeros Rule 3 – 1 ending zeroRule 3 – 1 ending zero
Example 8 - AnswerExample 8 - Answer
1100 Rule 1 – 1 sig dig non-zero numberRule 1 – 1 sig dig non-zero number Rule 2 – 0 sig digs trapped zerosRule 2 – 0 sig digs trapped zeros Rule 3 – 0 sig digs ( 1 ending zero, but Rule 3 – 0 sig digs ( 1 ending zero, but
decimal point is NOT shown)decimal point is NOT shown)
Example 8 - AnswerExample 8 - Answer
1100 Rule 1 – 1 sig dig non-zero numberRule 1 – 1 sig dig non-zero number Rule 2 – 0 sig digs trapped zerosRule 2 – 0 sig digs trapped zeros Rule 3 – 0 sig digs ( 1 ending zero, but Rule 3 – 0 sig digs ( 1 ending zero, but
decimal point is NOT shown)decimal point is NOT shown) Rule 4 – 0 leading zerosRule 4 – 0 leading zeros
Example 8 - AnswerExample 8 - Answer
1100 Rule 1 – 1 sig dig non-zero numberRule 1 – 1 sig dig non-zero number Rule 2 – 0 sig digs trapped zerosRule 2 – 0 sig digs trapped zeros Rule 3 – 0 sig digs ( 1 ending zero, but Rule 3 – 0 sig digs ( 1 ending zero, but
decimal point is NOT shown)decimal point is NOT shown) Rule 4 – 0 leading zerosRule 4 – 0 leading zeros
1 significant digit1 significant digit
Example 9 Example 9
1000.0001000.000
Example 9 - AnswerExample 9 - Answer
11000.000000.000 Rule 1 – 1 sig dig non-zero numberRule 1 – 1 sig dig non-zero number
Example 9 - AnswerExample 9 - Answer
11000.000000.000 Rule 1 – 1 sig dig non-zero numberRule 1 – 1 sig dig non-zero number Rule 2 – 0 sig digs trapped zerosRule 2 – 0 sig digs trapped zeros
Example 9 - AnswerExample 9 - Answer
11000.000000.000 Rule 1 – 1 sig dig non-zero numberRule 1 – 1 sig dig non-zero number Rule 2 – 0 sig digs trapped zerosRule 2 – 0 sig digs trapped zeros Rule 3 – 6 ending zerosRule 3 – 6 ending zeros
Example 9 - AnswerExample 9 - Answer
1000.0001000.000 Rule 1 – 1 sig dig non-zero numberRule 1 – 1 sig dig non-zero number Rule 2 – 0 sig digs trapped zerosRule 2 – 0 sig digs trapped zeros Rule 3 – 6 sig digs ending zeros with decimal Rule 3 – 6 sig digs ending zeros with decimal
point shownpoint shown
Example 9 - AnswerExample 9 - Answer
1000.0001000.000 Rule 1 – 1 sig dig non-zero numberRule 1 – 1 sig dig non-zero number Rule 2 – 0 sig digs trapped zerosRule 2 – 0 sig digs trapped zeros Rule 3 – 6 sig digs ending zeros with decimal Rule 3 – 6 sig digs ending zeros with decimal
point shownpoint shown Rule 4 – 0 leading zerosRule 4 – 0 leading zeros
Example 9 - AnswerExample 9 - Answer
1000.0001000.000 Rule 1 – 1 sig dig non-zero numberRule 1 – 1 sig dig non-zero number Rule 2 – 0 sig digs trapped zerosRule 2 – 0 sig digs trapped zeros Rule 3 – 6 sig digs ending zeros with decimal Rule 3 – 6 sig digs ending zeros with decimal
point shownpoint shown Rule 4 – 0 leading zerosRule 4 – 0 leading zeros
7 significant digits7 significant digits
Example 10Example 10
11361136
Example 10 - AnswerExample 10 - Answer
11361136 Rule 1 – 4 sig digs non-zero numbersRule 1 – 4 sig digs non-zero numbers
Example 10 - AnswerExample 10 - Answer
11361136 Rule 1 – 4 sig digs non-zero numbersRule 1 – 4 sig digs non-zero numbers Rule 2 – 0 sig digs trapped zerosRule 2 – 0 sig digs trapped zeros
Example 10 - AnswerExample 10 - Answer
11361136 Rule 1 – 4 sig digs non-zero numbersRule 1 – 4 sig digs non-zero numbers Rule 2 – 0 sig digs trapped zerosRule 2 – 0 sig digs trapped zeros Rule 3 – 0 ending zeros Rule 3 – 0 ending zeros
Example 10 - AnswerExample 10 - Answer
11361136 Rule 1 – 4 sig digs non-zero numbersRule 1 – 4 sig digs non-zero numbers Rule 2 – 0 sig digs trapped zerosRule 2 – 0 sig digs trapped zeros Rule 3 – 0 ending zeros (Decimal point is NOT Rule 3 – 0 ending zeros (Decimal point is NOT
shown)shown)
Example 10 - AnswerExample 10 - Answer
11361136 Rule 1 – 4 sig digs non-zero numbersRule 1 – 4 sig digs non-zero numbers Rule 2 – 0 sig digs trapped zerosRule 2 – 0 sig digs trapped zeros Rule 3 – 0 ending zerosRule 3 – 0 ending zeros Rule 4 – 0 leading zerosRule 4 – 0 leading zeros
Example 10 - AnswerExample 10 - Answer
11361136 Rule 1 – 4 sig digs non-zero numbersRule 1 – 4 sig digs non-zero numbers Rule 2 – 0 sig digs trapped zerosRule 2 – 0 sig digs trapped zeros Rule 3 – 0 ending zerosRule 3 – 0 ending zeros Rule 4 – 0 leading zerosRule 4 – 0 leading zeros
4 significant digits4 significant digits
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