Video Lectures 1.4 Measurement and Significant Figures

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Issacs Teach

**Accuracy**

Accuracy is a measure of the difference between the true value (the value to be measured) and the value measured by an instrument.

**Precision**is depends totally on the instrument and it is the difference between measurements of the same dimension made number of times. It is expressed as the difference between one measurement and the arithmetic mean of the number of measurements.

**Significant figures**: Significant figures in a number are include all the certain digits plus one doubtful digit.

If a number has 4 significant figures or digits, it means 3 of them are certain and fourth one is doubtful.

Rules for determining the number of significant figures

1. All non-zero digits are significant

Decimal place does not determine the number of significant figures.

2. A zero becomes significant in case it comes between two non-zero numbers.

3. The zeros at the beginning of a number are not significant.

For example 0.0004 has only one significant figure.

4. All zeros placed to right of a number are significant. They represent the precision of the measuring scale.

For example 267.000 has six significant figures.

(The precision does not come by writing the number. It comes because the instrument has the ability to read a number certainly up to that level of measurement.)

Rules of calculations involving significant figures

Rule 1. The final result of addition or subtraction should be reported up to the same number of decimal places as are present in the term having the least number of decimal places.

Example- addition of three numbers

6.414

2.3

0.501

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9.215 is the answer but the answer should be reported up to one decimal place only as 2.3 is the term having least number of decimal places.

Hence correct answer is 9.2

Rule 2. In multiplication or division, the final result should be reported up to the same number of significant figures as are present in the term with the least number of significant figures.

Example: 4.2345*1.25 = 5.293125

The final result should be reported up to three significant figures only as 1.25 has three significant figures. Hence the correct answer to be reported is 5.29.

Rounding off figures of retention of significant figures.

i) If the digit coming after the desired number of significant figures happens to be more than 5, the preceding digit or figure is increased by 1.

ii) If that digit is less than 5, it is neglected and hence the preceding significant figure remains unchanged.

iii) If that digit happens to be 5, the preceding digit is increased by one in case it is odd number. If preceding digit is an even number, it remains the same.

If the problem has number of steps, the rounding off is to be done at the final answer level only.

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