1. Trouble free Significant Figures (Sig.Figs or s.f)
Presentation By
Sathanan, Duraippandian M.Sc, B.Ed
Physics Teacher,
Central Medical Magnet High School,
Beaumont ISD

2. Rules for Significant Figures
Significant figures (s.f) have real world application. For example, it tells us about the precision of a measurement or of a data Since, sig.figs are one of the ways we can quantify the precision of real world Measurements, Scientist use Significant figures (s.f) in measured quantities where it is not possible an exact number/value.

3. Examples for Measured quantities where it is not possible an exact value.
The number , ‘π’ is mathematical
constant, the ratio of a circle's
circumference to its diameter,
commonly approximated as
It has been represented by the Greek letter
"π"
since the mid-18th century,
though it is also sometimes
spelled out as "pi" (/paɪ)
π= …

4. Examples for Measured quantities where it is not possible an exact value.
The speed of light in vacuum, commonly denoted c, is a universal physical constant . It is important in many areas of physics. Its exact value is meters per second. (approximately 3.00×108 m/s, approximately 186,282 mi/s)
Sunlight takes about 8 minutes 17 seconds to travel the average distance from the surface of the Sun to the Earth

5. Examples for Measured quantities where it is not possible an exact value.
There are many simple ways of estimating this, i.e. taking the mean mass of a cell (1 nano- gram), and extrapolating out to 70 trillion cells for an adult of 70 kg. This is very approximate however, as it is extremely difficult to know the true mean mass of a persons cells. Also, certain regions of a persons mass has a lower cell density that other regions (e.g. comparing skin and blood).
Sunlight takes about 8 minutes 17 seconds to travel the average distance from the surface of the Sun to the Earth

6. Examples for Measured quantities where it is not possible an exact value.
Welcome to the Euros (EUR) to Dollars (USA) page, updated every minute between Sunday 22:00 and Friday 22:00 (UK) 1 EUR = USD The Euro to Dollar exchange rate (EUR USD) as of 17 Feb 2017 at 8:21 PM.
Sunlight takes about 8 minutes 17 seconds to travel the average distance from the surface of the Sun to the Earth

7. a.613 c. 4377 has three sig.figs has _____ sig.figs b. 123456
Rule (1) : All non zero numbers are significant (meaning they count as sig figs)
a.613
has three sig.figs b
has six sig.figs
c. 4377
has _____ sig.figs d
has ____ sig.figs

8. -----------------------------------
Rule (2): Zeros located between non-zero digits are significant (they count)
a.4003
has four sig.figs b
has six sig.figs
c has _____ sig.figs d. 205 has ______ sig.figs

9. ----------------------------------- b. 4006000. has seven sig.figs
Law (3): Trailing zeros (those at the end) are significant only if the number contains a decimal Point. a
has five sig.figs b
has seven sig.figs c
has _____ sig.figs d
has ______ sig.figs

10. ----------------------------------- b. 400600 has four sig.figs
Law (4): Trailing zeros (those at the end) are insignificant , (they don’t count) if the number does not contains a decimal Point. a
has three sig.figs b
has four sig.figs c
has _____ sig.figs d
has ______ sig.figs

11. ----------------------------------- b. 0.000000000034 has two sig.figs
Rule (5): placeholders (Zeros to left of the first non-zero digit) are insignificant (they don’t count). a
has three sig.figs b
has two sig.figs c
has _____ sig.figs d
has ______ sig.figs

12. Answer the followings: c. 4.300 x 107 has _____ sig.figs d. 7.00 x 105
Special Rule (6): When a number is written in the Scientific Notation, all numbers including zero are significant (meaning all count), except the exponent part/power part of 10.
Examples:
a x 107
has three sig.figs
b x 105
has four sig.figs
Answer the followings:
c x 107
has _____ sig.figs
d x 105
has ______sig.figs

13. Rules for addition/subtraction problems
Your calculated value cannot be more precise than the least precise quantity used in the calculation.
The least precise quantity has the fewest digits to the right of the decimal point.
Your calculated value will have the same number of digits to the right of the decimal point as that of the least precise quantity.
In practice, find the quantity with the fewest digits to the right of the decimal point.
In the example below, 11.1 the least precise quantity
When you use your calculator, it will spit out as =
In this case, your final answer is limited to one sig.fig to the right of the decimal or 25.3
(rounded up).

14. Answer the followings:
b = = _____
c = 8.31 = ______
d = 6.45 = ______

15. Check your Answers
a = = 7.7 ✔
b = = 5.0✔
c = 8.31 = 8 ✔
d = 6.45 = 6.5✔

16. Rules for multiplication/division problems
The number of sig figs in the final calculated value will be the same as that of the quantity with the fewest number of sig figs used in the calculation.
In practice, find the quantity with the fewest number of sig figs.
In the example below, the quantity with the fewest number of sig figs is 27.2 (three sig figs).
Your final answer is therefore limited to three sig figs.
(27.2 x 15.63) ÷ =
(this is what you calculator spits out)
In this case, since your final answer is limited to three sig figs only, the answer is 230.
(rounded down)
So, (27.2 x 15.63) ÷ = 230. ✔
is the correct answer.

17. Rules for multiplication/division problems
The number of sig figs in the final calculated value will be the same as that of the quantity with the fewest number of sig figs used in the calculation.
In practice, find the quantity with the fewest number of sig figs.
Answer the following Correctly:
2.33 x x 2.1 = ___
How many significant figures must be there in the answer? Answer - _____
Which number decides this?
Answer - the _____
Why? It has the least number of significant figures in the problem. It is, therefore, the least precise measurement.
So, 2.33 x x 2.1 = = _______is the correct answer

18. Rules for multiplication/division problems
The number of sig figs in the final calculated value will be the same as that of the quantity with the fewest number of sig figs used in the calculation.
In practice, find the quantity with the fewest number of sig figs.
Check your answer:
2.33 x x 2.1 = ___
How many significant figures must be there in the answer? Answer - 2.
Which number decides this?
Answer - the 2.1.
Why? It has the least number of significant figures in the problem. It is, therefore, the least precise measurement.
So, 2.33 x x 2.1 = = 30. ✔ is the correct answer

19. So, the above step becomes as below
Rules for combined addition/subtraction and multiplication/division problems
Let us consider the example below.
(23 + 7) ÷ 10.0
(For the above operation, if we use a calculator, it will spit out as 3.)
So, (23 + 7) ÷ 10.0 = 3,
But, the above answer is wrong here.
Why because; first we need to add 23 and 7. That is , = 30. )
So, the above step becomes as below
30 ÷ 10.0
Here, 30 is considered to have 2 s.f ; since, it is a special class of combined operations.
And hence, the final answer is limited to 2 sig.figs.
Therefore, 30 ÷ 10.0 = ✔
is the correct answer.
Use the order of mathematical operations to determine which order to apply the rules for addition/subtraction (determine the number of sig figs for that step) or the rules for multiplication/division.
Special Rules for THIS CLASS!
For this class only we will consider all numbers less than 1000 as significant. That means 900 has 3 significant digits and 1000 has 1 significant digit.

20. (____) + ( ____) = _____ (8.0 x 2.50) + ( 3.132– 2.13) = __
Rules for combined addition/subtraction and multiplication/division problems
Answer the following Correctly:
(8.0 x 2.50) + ( 3.132– 2.13) = __
If we use a calculator, it will spit out as below
(20) + ( 1.002) = ___
Write down the above values as per the
rules of sig.figs in the space given below.
(____) + ( ____) = _____
Therefore,
is the correct answer
Use the order of mathematical operations to determine which order to apply the rules for addition/subtraction (determine the number of sig figs for that step) or the rules for multiplication/division.
Special Rules for THIS CLASS!
For this class only we will consider all numbers less than 1000 as significant. That means 900 has 3 significant digits and 1000 has 1 significant digit.

21. (_20_) + ( _1.00_) = _21.00_ (8.0 x 2.50) + ( 3.132– 2.13) = __
Rules for combined addition/subtraction and multiplication/division problems
Check Your Answer :
(8.0 x 2.50) + ( 3.132– 2.13) = __
If we use a calculator, it will spit out as below
(20) + ( 1.002) = ___
Write down the above values as per the
rules of sig.figs in the space given below.
(_20_) + ( _1.00_) = _21.00_
Therefore,
(8.0 x 2.50) + ( 3.132– 2.13) = 21
is the correct answer
Use the order of mathematical operations to determine which order to apply the rules for addition/subtraction (determine the number of sig figs for that step) or the rules for multiplication/division.
Special Rules for THIS CLASS!
For this class only we will consider all numbers less than 1000 as significant. That means 900 has 3 significant digits and 1000 has 1 significant digit.

22. Thank you for your esteemed presence!
Sathanan,
Duraippandian M.Sc, B.Ed
Physics Teacher
Central Medical Magnet High School
Beaumont ISD