Significant digits:

• A significant digit is one which is actually measured.
  
• The number of significant digits in a measurement depends on the ability of the measuring device.

When a calculation involves measurements with different numbers of significant digits, the answer should have the same number of significant digits as the least in the measurements.

 

 

 Rules for assigning significance to a digit:

1.      Digits other than zero are always significant.

2.      Rules about zeros:

    a.      Final zeros after a decimal point are always significant.

    b.      Zeros between two other significant digits are always significant.

    c.       Zeros used only to space the decimal are never significant. 

Addition and Subtraction with Scientific Notation:
 When adding or subtracting numbers in scientific notation, their powers of 10 must be equal. If the powers are not equal, then you must first convert the numbers so that they all have the same power of 10.

Example: (6.7 x 10⁹) + (4.2 x 10⁹) = (6.7 + 4.2) x 10⁹ = 10.9 x 10⁹ = 1.09 x 10¹⁰. (Note that the last step is necessary in order to put the answer in scientific notation.)

Example: (4 x 10⁸) - (3 x 10⁶) = (4 x 10⁸) - (0.03 x 10⁸) = (4 - 0.03) x 10⁸ = 3.97 x 10⁸.

 

Multiplication and Division with Scientific Notation:
 It is very easy to multiply or divide just by rearranging so that the powers of 10 are multiplied together.

Example: (6 x 10²) x (4 x 10^-5) = (6 x 4) x (102 x 10-5) = 24 x 10^2-5 = 24 x 10^-3 = 2.4 x 10^-2. (Note that the last step is necessary in order to put the answer in scientific notation.)

 

 

Exact Numbers

Exact numbers, such as the number of people in a room, have an infinite number of significant figures. Exact numbers are counting up how many of something are present, they are not measurements made with instruments. Another example of this are defined numbers, such as 1 foot = 12 inches. There are exactly 12 inches in one foot. Therefore, if a number is exact, it DOES NOT affect the accuracy of a calculation nor the precision of the

 

Practice Problems

Identify the number of significant figures:

A.     3.0800

B.     0.00418

C.     7.09 x 10¯⁵

D.     91,600

E.      0.003005

F.      3.200 x 10⁹

G.     250

H.     780,000,000

I.        0.0101

J.       0.00800

K.    6.751 g

L.      0.157 kg

M.   28.0 ml

N.    2500 m

O.    0.070 g

P.      30.07 g

Q.    0.0067 cm

R.     6.02 x 10²³ atoms

 

 

Key

1. 5

2. 3

3. 3

4. 3

5. 4

6. 4

7. 3

8. 2

9. 3

10. 3

 

 

11. 4

12. 3

13. 3

14. 2

15. 2

16. 4

17. 2

18. 3