Question

Find the product of the following : \[25m{\text{ }}15cm\] by \[9\].

Answer 1

Hint: We have to find the value of the product of the given expression. We solve this question using the concept of multiplication of terms and the concept of conversion of measurement of units. We first convert the units of the given expression into measurement of unit into centimetre and then we will multiply the obtained value of the measurement of unit by \[9\] and then we again convert the value obtained after multiplication into units of measurements in metre by using the relation between metre and centimetre.

Complete step-by-step solution:
Given :
\[25m{\text{ }}15cm\] by \[9\]
We know that the relation between m and cm is given as :
\[1m = 100{\text{ }}cm\]
The units can be written as :
\[25m{\text{ }}15cm = 25 \times \left( {100} \right) + 15\]
\[25m{\text{ }}15cm = 2500 + 15\]
The units of the given expression is written as :
\[25m{\text{ }}15cm = 2515cm\]
Now, we have to multiply the measurement in \[cm\] by \[9\].
On multiplication, we get the value as :
\[25m{\text{ }}15cm{\text{ }}by{\text{ }}9 = 2515 \times 9\]
On solving, we get
\[25m{\text{ }}15cm{\text{ }}by{\text{ }}9 = 22635cm\]
We can also write the expression as :
\[25m{\text{ }}15cm{\text{ }}by{\text{ }}9 = 22600 + 35\]
Now, using the relation between m and cm, we can write the expression as :
\[1cm = \dfrac{1}{{100}}m\]
Using this, we get
\[25m{\text{ }}15cm{\text{ }}by{\text{ }}9 = 22600 \times \dfrac{1}{{100}} + 35\]
Also, we can write it as :
\[25m{\text{ }}15cm{\text{ }}by{\text{ }}9 = 226m{\text{ }}35cm\]
Hence, the product of the given expression \[25m{\text{ }}15cm\] by \[9\] is \[226m{\text{ }}35cm\].

Note: While doing these types of questions in which we have to use the concept of unit of measurements , we have to take care of the units of conversion and their particular relation. Many times we mistakenly take the wrong relation or the wrong units. May sure that the units are placed at every point where needed; this helps to reduce the possible errors while solving the question. Using the system of units we can also change the units of a quantity of length into the units of quantity of volume.
One cubic centimetre can also be stated as one thousandth of a litre.
\[1cc = \dfrac{1}{{1000}}L\]
A system of units can be changed into another system of units without affecting the actual value of the quantity. Some more conversions are stated below :
\[1km = 1000m\]
\[1km = 100000cm\]
\[1km = 1000000mm\]