Question

How many inches is $3cm$?

Answer 1

Hint:
Start with using the information that says one inch is equal to the length of $2.54$ centimeter to form an equation, i.e. $1{\text{ inch}} = 2.54{\text{ cm}}$ . Now we can find the length in inches for one centimeter by dividing both sides of this equation by $2.54$. Now for finding the required measurement, multiply the newly obtained equation by $3$.

Complete step by step solution:
Here in this problem, we are given a length of $3cm$ and we need to find the equivalent of this length in the unit ‘inch’.
A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, which is used as a standard for measurement of the same kind of quantity. An inch is defined as the measurement unit used in Imperial and the US Customary measurement systems. It is the unit of length. The unit centimeter is also used to measure the length, and used in the International System of Units, which is the current form of the metric system. It is represented using the notation “cm”.
Since we know that the length of one inch is the same as the length of $2.54cm$ .
$ \Rightarrow 1{\text{ inch}} = 2.54{\text{ cm}}$
But we know the value in centimeters, so let’s find the relation for one centimeter
$ \Rightarrow \dfrac{1}{{2.54}}{\text{ inch}} = \dfrac{{2.54}}{{2.54}}{\text{ cm}} \Rightarrow {\text{1 }}cm = \dfrac{1}{{2.54}}inch$
So, for a length of $3cm$ as given in the question, we can simply multiply both the side of the above relation with $3$
$ \Rightarrow {\text{1 }}cm = \dfrac{1}{{2.54}}inch \Rightarrow 1 \times 3{\text{ }}cm = \dfrac{1}{{2.54}} \times 3{\text{ }}inch$
Now we can simplify this by solving both RHS and LHS:
$ \Rightarrow 1 \times 3{\text{ }}cm = \dfrac{1}{{2.54}} \times 3{\text{ }}inch \Rightarrow 3{\text{ }}cm = \dfrac{1}{{2.54}} \times 3 = 1.18{\text{ }}inch$

Therefore, the length of $3cm$ is equal to $1.18 \text{inches}$.

Additional Information:
For a better understanding of the same concept let us take another case to solve. Let’s find how much a length of $10cm$ will be in inches.
Here we have to multiply $10$ in the equation ${\text{1 }}cm = \dfrac{1}{{2.54}}inch$
$ \Rightarrow 1 \times 10{\text{ }}cm = \dfrac{1}{{2.54}} \times 10{\text{ }}inch \Rightarrow 10cm = 3.937inch$
Thus, we get that the length of ${\text{10 c}}m$ is equal to the length of $3.937$ inch.

Note:
Be careful with the type of units we are dealing with here. An alternate approach to the solution of this problem is through the unitary method, which is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.