Significant figures (s.f) is the positioning of digits from 0 to 9 in a numeral with the exclusion of zero in some cases, this is applicable to both Whole and Decimal numbers.
Characteristics of significant Figures
Any non Zero digit is significant, eg. Digits from 1 to 9. That is 1 2 3 4 5 6 7 8 9. They are all significants
Leading zeros are not significant, eg. 00678, 0.0689 and so on. Those two zeros written before 6 are not significant.
Zeros written in-between non Zero digits are significant, eg 2600057, 50306, 63026 etc.
Trailing zeros are not significant, eg. 673000, 1.673000 and so on. Trailing zeros can be significant if the number has a decimal point. It can also be significant if there is an over line on one of those trailing zeros, it is thus significant and the rest still remains non significant.
Range to be called one(1)
From the group range 0 to 9, we still have two sub-groups which are from “0 to 4” and from “5 to 9”. Digits from 0 to 4 are not up to ONE(1), while digits from 5 to 9 can be called 1 and be taken to any number of required significant figure.
Expressing numbers to any given significant figures:
When expressing a number to any required significant figure, if any digits from 5 to 9 is found after the required significant figure, it will be rounded off by calling it 1 and added to the required figure to make it significant.
Example 1:
Express 0.007386 to
(a). 3 s.f
(b). 2 s.f
(c). 1 s.f
(a) 0.00739 3 s.f
The answer gotten above is because 6 is found at the range from 5 to 9, so the “6” will be called 1(one) and be added to the closest number when going from right to left, which is 8 + 1 = 9.
(b) 0.0074 2 s.f
(c) 0. 007 1 s.f
Example 2: (Significant Figures)
Express 73652 to 3 s.f
= 73700 3 s.f
Example 3: (Significant Figures)
Express 586.28 to 1 s.f
= 600 1 s.f
QUESTIONS AND SOLUTIONS
Q1. Correct the following to 2 significant figures.
(a) 0.86439
= 0.86
(b) 0.75128
= 0.75
(c) 0.00051873
= 0.00052
(d) 35864
= 36000
(e) 26423
= 26000
(f) 0.426009
= 0.43
Q2. Write each of the following, correct to the number of significant figure shown in front of each of them.
(a) 0.0973 (2 s.f)
= 0.097
(b) 14.0675 (3 s.f)
= 14.1
(c) 2.00584 (4 s.f)
= 2.006
(d) 0.008406 (2 s.f)
= 0.0084
(e) 1.05084 (3 s.f)
= 1.05
(f) 0.5543 (1 s.f)
= 0.6
Q3. Round off the following to 3 significant figures.
(a) 65869
= 65900
(b) 0.4931
= 0.493
(c) 0.6094
= 0.609
(d) 260.743
= 261
(e) 621.69
= 622
(f) 63.564
= 63.6
Q4. Round off the following to 2 s.f, 3 s.f and 4 s.f respectively.
(ai) 0.24519 (2 s.f)
= 0.25
(aii) 0.24519 (3 s.f)
= 0.245
(aiii) 0.24519 (4 s.f)
= 0.2452
(bi) 2943671 (2 s.f)
= 2900000
(bii) 2943671 (3 s.f)
= 2940000
(biii) 2943671 (4 s.f)
= 2944000
(ci) 284.00675 (2 s.f)
= 280
(cii) 284.00675 (3 s.f)
= 284
(ciii) 284.00675 (4 s.f)
= 284.0
(di) 63.04286 (2 s.f)
= 63
(dii) 63.04286 (3 s.f)
= 63.0
(diii) 63.04286 (4 s.f)
= 63.04
(ei) 0.0068426 (2 s.f)
= 0.0068
(eii) 0.0068426 (3 s.f)
= 0.00684
(ei) 0.0068426 (4 s.f)
= 0.006843
Q5. Correct the following into the number of significant figure shown in front of them.
(a) 4384467 (3 s.f)
= 4380000
(b) 28.0059 (4 s.f)
= 28.01
(c) 0.035481 ( 2 s.f)
= 0.035
(d) 0.002635 (1 s.f)
= 0.003
(e) 0.062178 (2 s.f, 3 s.f, 1 s.f)
(ei) 0.062178 (2 s.f)
= 0.062
(eii) 0.062178 (3 s.f)
= 0.0622
0.062178 (1 s.f)
= 0.06