The measurement is the base of all experiments in a world of science and technology.
The quality of a measurement can be described using terms such as :
The value of every measurement contains some uncertainty. These uncertainties are called errors.
Accuracy is the closeness of a measured value to the actual value or true value.
In a shop, you purchased 3.5 kg apple measured using traditional balance, on the way you weight the same pack of apple ina different shop which is digitals balnce and found that it actually weight only 3.3 then, the measurement is considered inaccurate. If the purchased apple measures the same 3.5 kg then the measurement is considered as accurate.
Precision: is the closeness of two or more measurements to each other.
The pack of apple is weighted for five or more time, and get 3.5 kg for each time, then your measurement is very precise. If the measurement varies then it is considered as imprecise.
Approximation: is the process of finding a number, which is acceptably close to the exact value of the measurement of a physical quantity.
Continuing the same example, if the apple weighs differently in different balances but most of the time (or all the time) the value is above 3.3 kg then we can conclude that the pack of apple is approximately 3.3 kg.
Try an activity:
Calculate the approximate ‘heartbeat’ of a man in a day.
Consider the heart beats per minute as 72 times.
Given: \(1\) day ; Heart beats rate \(=\) \(72\) per minute approximately.
To find: The approximate heart beat rate of man in \(1\) day.
Approximate heart beat rate of man in \(1\) days:
Approximate heart beat rate in one day \(=\) \(1 day\) \(×\) \(heart\ beat\ rate\) \(×\) \(60 seconds\) \(×\) \(24 hours\).
\(=\) \(1\) \(×\) \(72\) \(×\) \(60\) \(×\) \(24\)
Thus, the approximation of heart beat rate of man in \(1\) day is \(103680\).
Rounding off numbers: While rounding off a number, if a last digit is greater than 5 then it should be changed or increased by one. The following are a few steps to be followed in rounding off numbers.
Rule for Round off:
Step 1: Identify the last digit to be kept.
Step 2: The following digit is less than \(5\). So, retain it as the same number. (or) The following digit is equal to or greater than \(5\). Then, the number is increased by one.
Example 1: Round off the number \(1.344\).
To find: The round off the number \(1.344\) to two decimal places.
Round off the number \(1.344\):
Step: 1 Identify the last digit to be kept.\(4\) is the last digit to be kept.
Step: 2 The following digit, because \(4\) is less than \(4\). So, retain it as \(4\).
Thus, the round off the number is \(1.34\).
Example 2: Round off the number \(1.456\).
To find: The round off the number \(1.456\) to two decimal places.
Round off the number \(1.456\):
Step: 1 Identify the last digit to be kept. \(5\) is the last digit to be kept.
Step: 2. The following digit, because \(6\) is greater than \(5\). So, increase \(5\) by one as \(6\).
Thus, the round off the number is \(1.46\).