## Units and Measurement

### significant figures

**Significant Figures**

Rule for counting significant numbers

(2) In a whole number the zeros on the right side of the given number are non-significant.

45400 [significant number is 3]

(3) All the zeroes between two non –zeroes digit are significant.

Example: 21001 [significant number is 5]

200.0 --- significant number 3

(3) if the number is less than one the zero on right side of the decimal and to the left of non-zero digit are not significant.

0.00102 [significant number is 3]

0.000007 [significant number is 1]

2.00007 [significant number is 6]

Special rule

0.7 [significant number is 1]

0.70 [significant number is 2]

0.700 [significant number is 3]

**Changing in unitary: **

0.00003 = 3 × 10^{-5 }[significant number is 1]

1.17 × 10^{6} = [significant number is 3]

**Accuracy** indicates how close our measurement is to the true value.

**Precision** is measured by least count of the measuring instrument and it is indicated by number of significant figure in the value.

- Precising depends on significant number.

Example: if you have a wall clock having only hour and minutes hands and does not have second hand so it will not give précising measure.

It is necessary that accuracy has precision no it is possible that if precise observation may not be accurate.

Rounding the numbers by significant numbers.

If digit to be dropped is 5 or 5 followed by zero then précising digit will be increased by 1 and if it is odd. But there will be not changed if it will be even.

Actual Operation

Propagation of significant number in mathematical operation.

Addition and substraction

In result significant figure after decimal will be equal to minimum significant figures in any quantity that is added.

Example :

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