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This pdf covers all the basics of significant figures and the conventions that must be followed for expressing numbers. Significant figures of a number in positional notation are digits in the number that are reliable and necessary to indicate the quantity of something.

1.
Student

Learningentre Significant Figures

C

Significant figures are the digits in a value that are known with some degree of confidence. As the number

of significant figures increases, the more certain the measurement. As precision of a measurement

increases, so does the number of significant figures.

There are conventions that must be followed for expressing numbers so that their significant figures are

properly indicated. These conventions are:

∼ 549 has three significant figures

All non zero digits are significant.

∼ 1.892 has four significant figures

∼ 4023 has four significant figures

Zeros between non zero digits are significant.

∼ 50014 has five significant figures

∼ 0.000034 has only two significant figures. (This is

Zeros to the left of the first non zero digit are not significant. more easily seen if it is written as 3.4x10-5)

∼ 0.001111 has four significant figures.

Trailing zeros (the right most zeros) are significant when

there is a decimal point in the number. For this reason it is ∼ 400. has three significant figures

important to give consideration to when a decimal point is ∼ 2.00 has three significant figures

used and to keep the trailing zeros to indicate the actual ∼ 0.050 has two significant figures

number of significant figures.

∼ 470,000 has two significant figures

Trailing zeros are not significant in numbers without ∼ 400 or 4x102 indicates only one significant figure. (To

indicate that the trailing zeros are significant a decimal point must be

decimal points. added. 400. has three significant digits and is written as 4.00x102 in

scientific notation.)

Exact numbers have an infinite number of significant digits ∼ If you count 2 pencils, then the number of pencils is

but they are generally not reported. 2.000...

∼ The number of centimeters per inch (2.54) has an

Defined numbers also have an infinite number of significant

infinite number of significant digits, as does the

speed of light (299792458 m/s).

RULE(S):

1. ALL non-zero numbers (1,2,3,4,5,6,7,8,9) are ALWAYS significant.

2. ALL zeroes between non-zero numbers are ALWAYS significant.

3. ALL zeroes which are SIMULTANEOUSLY to the right of the decimal point AND at the end of the

number are ALWAYS significant.

4. ALL zeroes which are to the left of a written decimal point and are in a number >= 10 are

ALWAYS significant.

Significant Figures 5/2013 © SLC 1 of 2

Learningentre Significant Figures

C

Significant figures are the digits in a value that are known with some degree of confidence. As the number

of significant figures increases, the more certain the measurement. As precision of a measurement

increases, so does the number of significant figures.

There are conventions that must be followed for expressing numbers so that their significant figures are

properly indicated. These conventions are:

∼ 549 has three significant figures

All non zero digits are significant.

∼ 1.892 has four significant figures

∼ 4023 has four significant figures

Zeros between non zero digits are significant.

∼ 50014 has five significant figures

∼ 0.000034 has only two significant figures. (This is

Zeros to the left of the first non zero digit are not significant. more easily seen if it is written as 3.4x10-5)

∼ 0.001111 has four significant figures.

Trailing zeros (the right most zeros) are significant when

there is a decimal point in the number. For this reason it is ∼ 400. has three significant figures

important to give consideration to when a decimal point is ∼ 2.00 has three significant figures

used and to keep the trailing zeros to indicate the actual ∼ 0.050 has two significant figures

number of significant figures.

∼ 470,000 has two significant figures

Trailing zeros are not significant in numbers without ∼ 400 or 4x102 indicates only one significant figure. (To

indicate that the trailing zeros are significant a decimal point must be

decimal points. added. 400. has three significant digits and is written as 4.00x102 in

scientific notation.)

Exact numbers have an infinite number of significant digits ∼ If you count 2 pencils, then the number of pencils is

but they are generally not reported. 2.000...

∼ The number of centimeters per inch (2.54) has an

Defined numbers also have an infinite number of significant

infinite number of significant digits, as does the

speed of light (299792458 m/s).

RULE(S):

1. ALL non-zero numbers (1,2,3,4,5,6,7,8,9) are ALWAYS significant.

2. ALL zeroes between non-zero numbers are ALWAYS significant.

3. ALL zeroes which are SIMULTANEOUSLY to the right of the decimal point AND at the end of the

number are ALWAYS significant.

4. ALL zeroes which are to the left of a written decimal point and are in a number >= 10 are

ALWAYS significant.

Significant Figures 5/2013 © SLC 1 of 2

2.
2 of 2 5/2013 © SLC Significant Figures

POSTAL: PO BOX 2100, ADELAIDE, SA 5001

INTERNET: http://www.flinders.edu.au/SLC

E-MAIL: [email protected]

TEL: 61-8-8201 2518

REGISTRY BUILDING ANNEXE

STUDENT LEARNING CENTRE

ANSWERS

a) 654.389 becomes 654 because the first non-significant digit is 3.

b) 65.4389 becomes 65.4.

c) 654,389 becomes 654,000 because we need to put the zeros in to hold the place values.

d) 56.7688 becomes 56.8 because the first non-significant digit is 6.

e) 0.03542210 becomes 0.0354. Note that three significant figures is not the same as three decimal places,

which would give us 0.035.

f) 0.0041032 becomes 0.00410 because the final zero is a significant figure, being the third in the sequence 4,

1, 0, 3, 2.

g) 45.989 becomes 46.0 because we round the third significant digit up from 9 to 10. This increases the digit,

5, preceding it to 6 and makes the third digit zero.

g) 45.989 f) 0.0041032 e) 0.03542210 d) 56.7688 c) 654,389 b) 65.4389 a) 654.389

Give the following numbers to three significant figures:

EXERCISE:

(ii) Apply to Rules for Rounding Off .

(i) Decide where you want your rounded value to stop. The rounding process is as follows:

1,3,4 3 10.0 (= 1.00 E+1)

1 1 3,000,000 (= 3 E+6)

1,2,3,4 6 501.040

1,3 5 8.1000

1,4 1 0.0004 (= 4 E-4)

1,2,4 5 900.06

1 4 3.967

1 5 48,923

figures

Rule(s) significant Number

No. of

EXAMPLES:

POSTAL: PO BOX 2100, ADELAIDE, SA 5001

INTERNET: http://www.flinders.edu.au/SLC

E-MAIL: [email protected]

TEL: 61-8-8201 2518

REGISTRY BUILDING ANNEXE

STUDENT LEARNING CENTRE

ANSWERS

a) 654.389 becomes 654 because the first non-significant digit is 3.

b) 65.4389 becomes 65.4.

c) 654,389 becomes 654,000 because we need to put the zeros in to hold the place values.

d) 56.7688 becomes 56.8 because the first non-significant digit is 6.

e) 0.03542210 becomes 0.0354. Note that three significant figures is not the same as three decimal places,

which would give us 0.035.

f) 0.0041032 becomes 0.00410 because the final zero is a significant figure, being the third in the sequence 4,

1, 0, 3, 2.

g) 45.989 becomes 46.0 because we round the third significant digit up from 9 to 10. This increases the digit,

5, preceding it to 6 and makes the third digit zero.

g) 45.989 f) 0.0041032 e) 0.03542210 d) 56.7688 c) 654,389 b) 65.4389 a) 654.389

Give the following numbers to three significant figures:

EXERCISE:

(ii) Apply to Rules for Rounding Off .

(i) Decide where you want your rounded value to stop. The rounding process is as follows:

1,3,4 3 10.0 (= 1.00 E+1)

1 1 3,000,000 (= 3 E+6)

1,2,3,4 6 501.040

1,3 5 8.1000

1,4 1 0.0004 (= 4 E-4)

1,2,4 5 900.06

1 4 3.967

1 5 48,923

figures

Rule(s) significant Number

No. of

EXAMPLES: