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SIGNIFICANT DIGITS
SIGNIFICANT DIGITS
Rule #1:
All non-zero numbers are significant
Ex. 5489.213  7 significant digits
SIGNIFICANT DIGITS
Rule #2:
All zeros located between non-zero
numbers are significant
Ex. 0.08006  4 significant digits
SIGNIFICANT DIGITS
Rule #3:
Zeros located to the left of a value
are not significant
Ex. 0.00004  1 significant digit
SIGNIFICANT DIGITS
Rule #4:
Zeros that are located to the right of
a value may or may not be
significant
Ex. 1000.mL
4 significant digits
Ex. 1000mL
1 significant digit
SIGNIFICANT DIGITS
Ex. 1000mL  1 significant digit
Why?
1000mL could have been anything from
951mL to 1049mL
SIGNIFICANT DIGITS
Ex. 1000.0mL  5 significant digits
Why?
Rule #5
Any 0’s to the right of a decimal that
are not followed by any number are
significant
CALCULATIONS WITH
SIGNIFICANT DIGITS
Rule #1: Multiplying and Dividing
1.008 x 4.67
= 4.70736
= 4.71
This value has the
lowest number of
significant digits
The value with the lowest number of significant
digits determines how many significant digits
will appear in the answer
CALCULATIONS WITH
SIGNIFICANT DIGITS
Rule #2: Adding and Subtracting
1.008 + 4.67
= 5.678
= 5.68
This value has the
lowest number of
decimal places
The value with the lowest number of decimal
places determines how many decimal places
will appear in the answer
CALCULATIONS WITH
SIGNIFICANT DIGITS
Rule #3: Rounding
If greater than 5, round up
If less than 5, round down
CALCULATIONS WITH
SIGNIFICANT DIGITS
Rule #3: Rounding
If 5, then...
...Round up if the preceding number is
odd
Ex. 18.35
Odd
number
 18.4
CALCULATIONS WITH
SIGNIFICANT DIGITS
Rule #3: Rounding
If 5, then...
...Round down if the preceding number
is even
Ex. 18.25
Even
number
 18.2
CALCULATIONS WITH
SIGNIFICANT DIGITS
12cm
6.782cm
5.18cm
Calculate the volume of the
rectangular prism
CALCULATIONS WITH
SIGNIFICANT DIGITS
12cm
6.782cm
5.18cm
V= l x w x h
= (5.18cm) x (6.782cm) x (12cm)
= 421.56912cm3
= 4.2 x 102
cm3
“12” has the lowest number of significant
digits. So the answer must have 2
significant digits.
SIGNIFICANT DIGITS
Practice: How many
significant digits are in
the following values?
a) 5.703
b) 70
c) 100.
d) 395830
e) 0.0101
f) 21.0
Practice: Round the
following numbers to 2
significant digits
a) 1.01
b) 24.5
c) 17.5
d) 25.6
e) 48665
f) 11.5
SIGNIFICANT DIGITS
Practice: Calculate the
perimeter of the
following shape
Practice: Calculate the
volume of the following
rectangular prism
2.67cm
2.562cm
1cm
1.5cm
2.8753cm
1.43cm
11.54cm
8.7cm
10.56cm
SIGNIFICANT DIGITS
Practice: How many
significant digits are in
the following values?
a) 5.703 4
b) 70 1
c) 100. 3
d) 395830 5
e) 0.0101 3
f) 21.0 3
Practice: Round the
following numbers to 2
significant digits
a) 1.01 1.0
b) 24.5 24
c) 17.5 18
d) 25.6 26
e) 48665 4.9x104
f) 11.5 12
SIGNIFICANT DIGITS
Practice: Calculate the
perimeter of the
following shape
Practice: Calculate the
volume of the following
rectangular prism
2.67cm
2.562cm
1cm
1.5cm
2.8753cm
1.43cm
11.54cm
8.7cm
10.56cm
= 12.0373cm
= 12cm
= 1060.20288cm3
= 1.1x103
cm3
SIGNIFICANT DIGITS
Significant digits for logarithmic values:
If a solution had an H+
concentration of 2.5x10-4
mol/L,
then what is the pH to the correct number of significant
digits?
i.e. pH = - log [2.5x10-4
mol/L]
pH = 3.602059
These two digits are significant
This digit is derived from the power of 10, so it is not a significant digit
The two digits to the right of the decimal are significant
.: pH = 3.60
SIGNIFICANT DIGITS
What is the volume of the graduated cylinder?
What digits are you absolutely sure about?
6.6mL, 6.61mL, or
6.62mL?
6.6mL
So there are 2 significant digits in your measurement
SIGNIFICANT DIGITS
What is the volume of the graduated cylinder?
What digits are you absolutely sure about?
21.5mL or
21.50mL?
21.5mL
So there are 3 significant digits in your measurement
SIGNIFICANT DIGITS
If the scale says that your
sample is 30.69g, then
how many significant
digits are in this value?
4 significant digits
It is NOT 30.690g, because the scale is not accurate to 3 decimal places
You cannot be more accurate than what your
instrument allows.

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01 significant digits

  • 2. SIGNIFICANT DIGITS Rule #1: All non-zero numbers are significant Ex. 5489.213  7 significant digits
  • 3. SIGNIFICANT DIGITS Rule #2: All zeros located between non-zero numbers are significant Ex. 0.08006  4 significant digits
  • 4. SIGNIFICANT DIGITS Rule #3: Zeros located to the left of a value are not significant Ex. 0.00004  1 significant digit
  • 5. SIGNIFICANT DIGITS Rule #4: Zeros that are located to the right of a value may or may not be significant Ex. 1000.mL 4 significant digits Ex. 1000mL 1 significant digit
  • 6. SIGNIFICANT DIGITS Ex. 1000mL  1 significant digit Why? 1000mL could have been anything from 951mL to 1049mL
  • 7. SIGNIFICANT DIGITS Ex. 1000.0mL  5 significant digits Why? Rule #5 Any 0’s to the right of a decimal that are not followed by any number are significant
  • 8. CALCULATIONS WITH SIGNIFICANT DIGITS Rule #1: Multiplying and Dividing 1.008 x 4.67 = 4.70736 = 4.71 This value has the lowest number of significant digits The value with the lowest number of significant digits determines how many significant digits will appear in the answer
  • 9. CALCULATIONS WITH SIGNIFICANT DIGITS Rule #2: Adding and Subtracting 1.008 + 4.67 = 5.678 = 5.68 This value has the lowest number of decimal places The value with the lowest number of decimal places determines how many decimal places will appear in the answer
  • 10. CALCULATIONS WITH SIGNIFICANT DIGITS Rule #3: Rounding If greater than 5, round up If less than 5, round down
  • 11. CALCULATIONS WITH SIGNIFICANT DIGITS Rule #3: Rounding If 5, then... ...Round up if the preceding number is odd Ex. 18.35 Odd number  18.4
  • 12. CALCULATIONS WITH SIGNIFICANT DIGITS Rule #3: Rounding If 5, then... ...Round down if the preceding number is even Ex. 18.25 Even number  18.2
  • 14. CALCULATIONS WITH SIGNIFICANT DIGITS 12cm 6.782cm 5.18cm V= l x w x h = (5.18cm) x (6.782cm) x (12cm) = 421.56912cm3 = 4.2 x 102 cm3 “12” has the lowest number of significant digits. So the answer must have 2 significant digits.
  • 15. SIGNIFICANT DIGITS Practice: How many significant digits are in the following values? a) 5.703 b) 70 c) 100. d) 395830 e) 0.0101 f) 21.0 Practice: Round the following numbers to 2 significant digits a) 1.01 b) 24.5 c) 17.5 d) 25.6 e) 48665 f) 11.5
  • 16. SIGNIFICANT DIGITS Practice: Calculate the perimeter of the following shape Practice: Calculate the volume of the following rectangular prism 2.67cm 2.562cm 1cm 1.5cm 2.8753cm 1.43cm 11.54cm 8.7cm 10.56cm
  • 17. SIGNIFICANT DIGITS Practice: How many significant digits are in the following values? a) 5.703 4 b) 70 1 c) 100. 3 d) 395830 5 e) 0.0101 3 f) 21.0 3 Practice: Round the following numbers to 2 significant digits a) 1.01 1.0 b) 24.5 24 c) 17.5 18 d) 25.6 26 e) 48665 4.9x104 f) 11.5 12
  • 18. SIGNIFICANT DIGITS Practice: Calculate the perimeter of the following shape Practice: Calculate the volume of the following rectangular prism 2.67cm 2.562cm 1cm 1.5cm 2.8753cm 1.43cm 11.54cm 8.7cm 10.56cm = 12.0373cm = 12cm = 1060.20288cm3 = 1.1x103 cm3
  • 19. SIGNIFICANT DIGITS Significant digits for logarithmic values: If a solution had an H+ concentration of 2.5x10-4 mol/L, then what is the pH to the correct number of significant digits? i.e. pH = - log [2.5x10-4 mol/L] pH = 3.602059 These two digits are significant This digit is derived from the power of 10, so it is not a significant digit The two digits to the right of the decimal are significant .: pH = 3.60
  • 20. SIGNIFICANT DIGITS What is the volume of the graduated cylinder? What digits are you absolutely sure about? 6.6mL, 6.61mL, or 6.62mL? 6.6mL So there are 2 significant digits in your measurement
  • 21. SIGNIFICANT DIGITS What is the volume of the graduated cylinder? What digits are you absolutely sure about? 21.5mL or 21.50mL? 21.5mL So there are 3 significant digits in your measurement
  • 22. SIGNIFICANT DIGITS If the scale says that your sample is 30.69g, then how many significant digits are in this value? 4 significant digits It is NOT 30.690g, because the scale is not accurate to 3 decimal places You cannot be more accurate than what your instrument allows.