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Significant Figures

Significant figures are nothing but the digits, which is used to establish the number. The term significant digits also are called as significant figures. We can identify the number of significant digits or significant figures by counting all the figures starting at the 1st non-zero digit located on the left. For example, 23.45 have four significant digits.

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Define Significant Figures

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The significant figures of a given number are those important digits, which carry the meaning contributing to its precision. For example, the number 5.678 has four significant figures. Significant figures provide accuracy to the numbers. Significant figures can also be termed as significant digits.

Significant Figures Rules

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The rules for significant figures are as follows:

(i) All non zero digits are significant. 12365 contains 5 significant figures.

(ii) All zeros occurring between the two non zero digits are significant. 109.0087 contain 7 significant figures.

(iii) All zeros to the right of a decimal point and to the left of a non-zero digit are never significant. 0.00987 contained 3 significant figures.

(iv) All zeros to the right of a decimal point are significant, if a non-zero digit does not follow them. 20.00 contain 4 significant figures.

(v) All zeros to the right of the last non-zero digit after the decimal point are significant. 0.0089700 contains 5 significant figures.

(vi) All zeros to the right of the last non-zero digit are not significant. 9080 contains 3 significant figures.

(vii) All zeros to the right of the last non-zero digit are significant, if they come from a measurement. 1090 m contains 4 significant figures.


Significant Figures Examples

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Below you could see significant figures examples, for adding significant figures, multiplying significant figures and dividing significant figures.

Solved Examples

Question 1: Identify the number of significant figures from the following.
48, 0.048, 5.4880, 6002, 4800
Solution:
48 - The number 48 is a non-zero number that has two significant figures.

0.048 - Zeroes placed before the other numbers are not significant figures and the number of significant figures in 0.048 is two.

5.4880 - Zeroes placed after the other numbers but after a decimal point are significant figures and the number of significant figures in 5.4880 is five.

6002 - The number 6002 has four significant figures because the Zeroes placed between the figures are always significant.

4800 - The number 4800 may have at least two significant figures. It also has three and four significant figures. That is:

4800 - 4.8 x 103 has two significant figures.

4800 - 4.80 x 103 has three significant figures.

4800 - 4.800 x 103 has four significant figures.


Question 2: Add the numbers 7.32, 7.21, and 23.96 and fund the number of significant figures in the solution.
Solution:
The given numbers are 7.32, 7.21, and 23.96.

The number 7.32 has three significant figures.

The number 7.21 has three significant figures

The number 23.96 has four significant figures.

Adding the numbers, we get:

7. 3 2

7. 2 1

2 3. 9 6 +
------------
3 7. 4 9
-------------

Therefore, the solution is 37.49.

37.49 can be rounded to 37.5

Therefore, the number of significant figures in 37.5 is three.


Question 3: Calculate the number of significant digits from the following calculations. 5.2 x 103 x 6.732 x 102
Solution:
When we divide or multiply the numbers the number of significant digits in the result is the equal as the least number of significant digits in any of the divided or multiplied terms.

5.2 x 103 has two significant digits, 6.732 x 102 has four significant digits, and the result will have two significant digits.

The number 7.5 x 106 is rounded to 7.5 x 106 since the number to the right of the last significant digit < 5.


Significant Figures Practice

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Below you could see the significant figures practice

Practice Problems

Question 1: How to Identify the number of significant figures from the following.
84, 0.084, 5.8480, 2005, 8400
Question 2: Solve the following addition 5.76 + 4.62 + 31.21 and find the number of significant figures in the solution.

Rounding Significant Figures

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A number is rounded off to the desired number of significant figures by dropping one or more digits from the right. When the first digit dropped is less than 5, the last digit retained should remain unchanged; when it is greater than 5, the last digit is rounded up. When the digit dropped is exactly 5, the number retained is rounded up or down to get an even number. When more than one digit is dropped, rounding off should be done in a block, not one digit at a time.

Rounding significant figures involve 2 rules to remember:

Rule One: See what is our rounding digit is asked to do and see the right side of number of digits the rounding of significant figures asked for. If that digit are less than 5, simply leave all digits to the right of it.

Rule Two: See what is our rounding digit is asked to do then see what the right side of number of digits the rounding of significant figures asked for. If that digit is 5 or greater than 5, add one to the rounding digit and drop all digits to the right of it.

Solved Examples

Question 1: Given 13.378912 correct to 3 significant figures.
Solution:
Look at the FOURTH figure after the decimal point: 13.378 | 912

The figure after the ‘cut-off point’ is a ‘9’

So round the number UP.

Answer:  13.379 to 3 significant figures.


Question 2: Given 42.378212 correct to 3 significant figures.
Solution:
Look at the FOURTH figure after the significant figures: 42.378 | 212

The figure after the ‘cut-off point’ is a ‘2’

So round the number UP.

Answer:  42.378 to 3 significant figures.


More topics in Significant Figures
Scientific Notation Absolute Error
Percentage Relative Error
NCERT Solutions
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