Chapter 1:Unit 12. Rounding off, Accuracy and Precision

Accuracy and Precision

Rounding off: To write the final answer with proper sig. fig. we must round off the original answer. It can be done in two ways:

If the first number that must be dropped is 4 or less, drop it and all remaining numbers

If the dropped number that must be dropped is 5 or greater, round the number up by adding 1 to the last digit that will be retained. Example: a number 66.453 can be written in many different significant figures:

• 4 significant figure: 66.45
• 3 significant figures: 66.5
• 2 significant figures: 66
• 1 significant figure: 70 (reduces significant figure but value of the number is not changed)

Raising to a power using powers of ten:

1. Raise the number to the correct power.
2. Multiply the exponents.

Example (2.0 x 10³)⁴  =  16 x 10¹²  =  1.6 x 10¹³

(Use correct scientific notation; use correct number of significant figures)

Finding roots using powers of ten:

1. If the exponent is not evenly divisible by the root, rewrite the number with a new power of ten that is evenly divisible.
2. Find the root of the number,

Divide the exponent by the root to be taken.

Example:

Accuracy: It means how close a number is compared to the true value. Mathematically accuracy is determined. when a measured number is evaluated with respect to the significant figures of a number considered to be true value.

For example: The true value of the length of a pen is 15.63 cm. 15.6 cm is less accurate than 15.63 cm.

Precision:  It means how reproducible the measured number is compared to the true value. It also means how consequent measurements of an object are close to each other Mathematically, it is determined when the measured number is compared to the number of decimal places in the significant digits.

For example, measurement of 25.612 is more precise than 25. Precision always depends on instrument.

Watch the following video for Accuracy and Precision:

Questions:

1. Round off the following number to 3 significant figures
   a) 6715
   b) 415

2.      A student conducted an experiment five times and gets a solution concentration of 4.9M, 5.1M, 5.8M, and 5.2M. The true concentration of the solution is 5.0M. What do you think about he precision and accuracy of the measurement?

Ans: 1. a) 6720

b)102

2.Imprecise and inaccurate.

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