### 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. 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 $$1.46$$.