significant figures

Significant figures are also known as significant numbers because they are given in the form of digits. The number of significant digits is found by counting all values ​​from the 1st non-zero digit to the left. These numbers are reliable and important to show the quantity of a length, volume, mass, measure, etc. When calculating significant numbers, arithmetic operations such as addition, subtraction, multiplication and division are used.

Significant figures

Significant figures are defined as the number of digits which is compulsory to give the accurate result of any experiment or a calculation. Significant figures are number of digits which is known reliably and also number which is uncertain. The accuracy increases when the number of significant figures increases.

Now consider an example of significant figures, when the period of oscillation of a simple pendulum is determined as 2.43 seconds, then the digits 2 and 4 are reliable and certain, and the digit 3 is uncertain. Therefore, the calculated value has three (3) significant figures.

Significant Figures Rules

The rules which are used for the determination of significant figures are given here.

1. Every non – zero digits are significant figures.e.g., 454.76 has 5 (five) significant figures.
2. All zeroes which lie between two non – zero digits are also significant figures.e.g., 703.004 has 6 (six) significant figures.
3. All zeros after decimal but before a non – zero digit is not considered a significant figure.e.g.,0.00465 has only 3 (three) significant figures.
4. All zeros which are at the right side of decimal and also at the right side of a non – zero digits are considered as significant figures.E.g., 0.64000 has 5 (five)significant figures
5. When the given number does not contain a decimal point, then the final zeroes are ambiguous and they are not considered as significant figures.E.g., 75000 has two (2) significant figures.But when the number which is obtained on the basis of actual (real) measurement, then all zeroes which are to the right of the last non zero digit are also considered as significant figures.E.g., 8070 has four (4) significant figures.
6. When a decimal is present at the end of a whole number, then all zeros which are at the right end just before the decimal are considered as significant figures.E.g., 13300. Has five (5) significant figures.
7. When the number contains both an integral part as well as a decimal part, then all zeros in the number are considered as significant figures.e.g., 34.40 has four (4) significant figures.

Rules for Rounding Significant Figures

A number is rounded to the needed number of significant digits by leaving one or more digits to the right. If the first digit on the left is less than the number 5, then the last digit must remain constant. If the first digit is more than the number 5, then the last digit of the significant figure is rounded up. If the remaining digit is exactly equal to the number 5, then the retained number is rounded up or down to get an even number. If more than one digit remains, round as a whole rather than one digit.

Rules for rounding a given number to the appropriate significant figures are given below.

1. When the digit after the last significant digit is more than the number 5, then the last digit of the significant figure (or significant digit) is raised by one (1).
2. When the digit after the last significant digit is less than the number five (5)), then the last digit of the significant figure (or significant digit) is left without making any changes.
3. When the digit after the last significant digit is equal to the number five (5), then the last digit of the significant figure (or significant digit) is not altered when the number is even and is increased by 1 when it is odd.

Accuracy

Accuracy is the agreement between a measured value and correct value. When a clock strikes twelve and the sun is directly overhead, then the clock is considered accurate.

The ability of an apparatus to measure an exact value is termed as accuracy. In other words, accuracy is the closeness of measured value to a value which is considered as standard. Accuracy is attained with small readings. The small reading reduces the error in calculation.

Precision

Precision is the repeatability of measurement or measured value. Precision is not necessary to know the standard value or true value.

The proximity or closeness of two or more measurements or measured value to each other is considered to be the precision of a material. If we weigh a given substance 4 (four) times and get 4.2 kg all the time, then our measurement is said to be very precise, but not necessarily that measurement is accurate.

Conclusion

Significant figures are defined as the number of digits which is compulsory to give the accurate result of any experiment or a calculation.

Every non – zero digits are significant figures.

e.g., 454.76 has 5 (five) significant figures.

All zeroes which lie between two non – zero digits are also significant figures.

e.g., 703.004 has 6 (six) significant figures.

All zeros after decimal but before a non – zero digit is not considered a significant figure.

e.g.,0.00465 has only 3 (three) significant figures.

A number is rounded to the needed number of significant digits by leaving one or more digits to the right.

Precision is the repeatability of measurement or measured value.

Accuracy is the agreement between a measured value and correct value.