Theory:

The measurement is the basis of all experiments in the world of science and technology.
 
The quality of a measurement can be described using terms such as : 
  • Error
  • Accuracy
  • Precision
  • Approximation
  • Roundoff
Errors:
The value of every measurement contains some uncertainty. These uncertainties are called errors.
Accuracy:
Accuracy is the closeness of a measured value to the actual value or true value.
 
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Measuring the weight of apples
Example:
In a shop, you purchased 3.5 kg apple measured using traditional balance. On the way, you weigh the same pack of apples in a different shop with a digital balance and found that it actually weighs only \(3.3\) \(kg\). In this case, the measurement is considered inaccurate. If the purchased apple measures the same \(3.5 kg\), then the measurement is considered as accurate.
Precision:
It is the closeness of two or more measurements to each other.
Example:
When the pack of apples is weighted for five or more times, and you get \(3.5 kg\) for each time, then your measurement is very precise. If the measurement varies, then it is considered as imprecise
Approximation: 
It is the process of finding a number, which is acceptably close to the exact value of the measurement of a physical quantity.
Example:
Considering the above example, if the apple weighs differently in different balances, but most of the time (or all the time), the value is above \(3.3 kg\). We can conclude that the pack of apples is approximately \(3.3 kg\).
  
Try an activity: 
Calculate the approximate ‘heartbeat’ of a man in a day.
Consider the heartbeats per minute as 72 times.
Given
  \(1\) day ; Heart beats rate \(=\) \(72\) per minute approximately.

To find:
The approximation of the heartbeat rate of man in \(1\) day.

Approximate heartbeat rate of man in \(1\) days:
 
Approximate heartbeat rate in one day \(=\) \(1 day\) \(×\) \(heart\ beat\ rate\) \(×\) \(60 seconds\) \(×\) \(24 hours\).

\(=\) \(1\) \(×\) \(72\) \(×\) \(60\) \(×\) \(24\)
 
\(=\) 103680

Thus, the approximation of the heartbeat rate of man in \(1\) day is \(103680\).
 
Rounding off: 
While rounding off a number, if the last digit is greater than five, 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 \(1.344\).
 
Given:
  \(1.344\).
 
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.
 
Step: 2 The following digit is \(4\), because the last digit \(4\) is less than \(5\). So, we retain it as \(4\).
 
Thus, the round off the number is \(1.34\).
  
Example 2: Round off the number \(1.456\).
 
Given:
\(1.456\).
 
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.
 
Step: 2. The following digit is \(6\), because \(6\) is greater than \(5\). So, increase \(5\) by one as \(6\).
 
Thus, the round off the number is \(1.46\).