How do I determine what the significant figures of a number are?

Question

What are the rules for significant figures?

Answer 1

There are few rules to it.U don't need to BY-HEART them just remember.

1.)All non-zero digits are significant.eg.) In number 124,there are 3 significant digits.

2.)All zeroes between the non-zero digits are also significant.eg.) In number 102,there are 3 significant digits.

3.)In a number less than 1,all zeroes from the left of the decimal point to the first non-zero digit on the right are non-significant.eg.) 0.009 has only 1 significant digit.

4.)In a number having no decimal point,all trailing zeroes are non-significant.eg.) 1200000 has 2 significant digits.

5.)In a number having decimal point,,all trailing zeroes are significant.eg.) 12.000 has 5 significant digits.

That's all to it I guess.

Answer 2

Significant Figures Explained

Answer 3

I have cut and pasted something I wrote about this, but it is very long. But you may find it useful as it includes plenty of examples.

_____________________________________________________



How to work out how many significant figures a number has.



Note1. + or – signs can be ignored when working out significant figures. E.g. –2.10 has the same number of significant figures as 2.10 (both have 3 significant figures, as explained below).



Note 2. For numbers given in standard form (scientific notation), e.g. 2.10 x 10⁶,

just use the mantissa (the ‘2.10’ part). So 2.10 x 10⁶ has 3 significant figures.



Working out significant figures can be a confusing at first because there are different rules depending on the number. There are 3 situations:



A: numbers without a decimal point. (e.g. 1230)



B: numbers with a decimal point, when the number is equal to or greater than 1 (e.g. 3.12)



C: numbers with a decimal point, when the number is less than 1. (e.g. 0.04310)



How to work out the significant figures in each situation is explained below.

________________________

A: Numbers without a decimal point.



Ignore any leading zeroes – e.g. treat 0028030 as 28030

Work left to right.

The most significant figure (msf) is the 1st digit on the left (‘2’ in the example).

The least significant figure (lsf) is the LAST NON-ZERO digit on the right (‘3’ in the example).

Count from msf to lsf:

1st (most) significant figure = 2

2nd significant figure = 8

3rd significant figure = 0

4th (least) significant figure = 3

There are 4 significant figures in 28030

.

Other examples:

‘70001’ has 5 significant figures

‘71000’ has 2 significant figures

‘70010’ has 4 significant figures

‘9’ has 1 significant figure

‘900’ has 1 significant figure

001000230000 has 6 significant figures

________________________

B: numbers with a decimal point, when the number is equal to or greater than 1



Ignore any leading zeroes – e.g. treat 005670.980 as 5670.980

Work left to right.

The most significant figure (msf) is the digit on the left (‘5’ in the example).

The least significant figure (lsf) is the LAST DIGIT on the right (‘0’ in the example).

Count from msf to lsf:

1st (most) significant figure = 5

2nd significant figure = 6

3rd significant figure = 7

4th significant figure = 0

5th significant figure = 9

6th significant figure = 8

7th significant figure = 0

There are 7 significant figures in 5670.980



Other examples:

‘2830.98’ has 6 significant figures

‘2830.980’ has 7 significant figures

‘7.1’ has 2 significant figures

‘7.100’ has 4 significant figures

700.00700 has 8 significant figures

1.000 has 4 significant figures

1.0 has 2 significant figures

____________________

C: Numbers with a decimal point when the number is less than 1



This is probably the easiest.

Work left to right and ignore ALL zeroes till you get to the 1st non-zero.

E.g. 0.08450

The most significant figure (msf) is the FIRST NON-ZERO digit, which is 8 in the example.

The least significant figure (lsf) is the LAST DIGIT, which is 0 in the example.

1st (most) significant figure = 8

2nd significant figure = 4

3rd significant figure = 5

4th (least) significant figure = 0

There are 4 significant figures in 0.08450



Other examples:

‘0.098’ has 2 significant figures

‘0.0980’ has 3 significant figures

‘0.0001002’ has 4 significant figures‘

‘0.1002’ has 4 significant figures

Answer 4

all the numbers in a scientific notation are significant (i.e. 1.000 x 10^4 has 4 sig figs)

the zeros before the first non zero number are not significant (however the zeros after are)



the maximum amount of sig figs is determined by the least precise of your calculations