significant digits

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


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


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


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



point shownpoint shown Rule 4 – 0 beginning zerosRule 4 – 0 beginning zeros




10 Significant Digits10 Significant Digits

Example 2Example 2

0.0070500.007050


0.000.0077005500 Rule 1 – 2 sig digs non-zero numbersRule 1 – 2 sig digs non-zero numbers


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


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


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



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)



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.


770000.. Rule 1 – 1 sig dig non-zero numberRule 1 – 1 sig dig non-zero number


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


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


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


85850000 Rule 1 – 2 sig digs non-zero numbersRule 1 – 2 sig digs non-zero numbers


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


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


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)



point is NOT shown)point is NOT shown) Rule 4 – 0 beginning zerosRule 4 – 0 beginning zeros

Example 5Example 5

8500.8500.


85850000.. Rule 1 – 2 sig digs non-zero digitsRule 1 – 2 sig digs non-zero digits


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


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


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


Example 6Example 6

0.00000010.0000001


0.0000000.00000011 Rule 1 – 1 sig dig non-zero numberRule 1 – 1 sig dig non-zero number


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


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


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)


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)


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


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


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)


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


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


Example 8Example 8

1010


1100 Rule 1 – 1 sig dig non-zero numberRule 1 – 1 sig dig non-zero number


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


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


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)



decimal point is NOT shown)decimal point is NOT shown) Rule 4 – 0 leading zerosRule 4 – 0 leading zeros



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


11000.000000.000 Rule 1 – 1 sig dig non-zero numberRule 1 – 1 sig dig non-zero number


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


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


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


Example 10Example 10

11361136


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


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)


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

Extra PracticeExtra Practice

Extra Practice AnswersExtra Practice Answers

significant digits

Documents

sig digs

trapped zerosrule

trapped zerosexample

ending zeros

trapped zerorule

trapped zeroexample

decimal point shownrule

decimal point shownexample