Significant Figures (S.F)

Definition: The most significant figure (s.f) in a number is the non-zero digit which has the highest place value of the number.

872.09 has five digits. The most or 1^st significant figure is 8. The 2^nd significant figure is 7, the 3rd is 2, the fourth is 0 and the fifth is 9.

However, the 1^st significant figure in a decimal fraction is the first non-zero figure after the decimal point. For example, the number 0.0008051 is given to 4 s.f. Note that the 0 between 8 and 5 is significant.

Example 3.3.1:

Give the following numbers

i. 546,740

ii. 65.0457 to 

(a) 1s.f
(b) 2 s.f
(c) 3 s.f

Solution (i):

a. 546,740 = 500,000 to 1 s.f (round down 4)

b. 546,740 = 550,000 to 2 s.f (round up 6)

c. 546,740 = 547,000 to 3 s.f (round up 7)

Solution (ii):

a. 65.0457 = 70 to 1 s.f (round up 5)

b. 65.0457 = 65 to 2 s.f 

c. 65.0457 = 65.0 to 3s.f (round down 4)

Example 3.3.2:

Round the following numbers

i. 0.0008729

ii. 0.003996

iii. 0.09952 to

(a) 1s.f (b) 2s.f (c) 3s.f

Solution (i):

a. 0.0008729 = 0.0009 to 1s.f (round up 7)

b. 0.0008729 = 0.00087 to 2s.f (round down 2)

c. 0.0008729 = 0.000873 to 3s.f (round up 9)

Solution (ii):

a. 0.003996 = 0.004 to 1s.f (round up 9)

b. 0.003996 = 0.0040 to 2s.f (round up the 2nd 9)

c. 0.003996 = 0.00400 to 3s.f (round up 6)

Solution (ii):

a. 0.09952 = 0.1 to 1s.f (round up 9)

b. 0.09952 = 0.10 to 2s.f (round up 5)

c. 0.09952 = 0.0995 to 3s.f (round down 2)