NCERT Solutions for Class 9 Political Science Chapter 2

August 8, 202239 Insightful Publications

We generally measure solids in units of kilograms or grams. But, what about liquids like milk or water we drink, the oil used in daily cooking? How do we measure them? We measure those liquids by a unit called a **litre**. We also use millilitres to measure a small quantity of liquids.

A metric unit of volume that is a thousand cubic centimetres is known as a litre. Small quantities of liquids are measured in millilitres \(\left( {{\rm{mL}}} \right).\) Large amounts are measured in litres \(\left( {\rm{L}} \right).\) The conversion of litres to millilitres is given by \(1\,{\rm{L}} = 1000\,{\rm{mL}}{\rm{.}}\) This article will discuss the meaning of litres, conversion of litres to millilitres, applications of litres and millilitres, and solve the problems on the same.

Look at the figure, Aarna is drinking milk in a glass, and Aarav is drinking milk from a mug. If both the mug and the glass are filled to the brim, can you say who drinks more milk? No, we cannot predict who is drinking more milk.

Similarly, we can’t say which of the below pots, \(A\) or \(B,\) has more water in it.

To know who drinks more or which vessel contain more, we need to measure the liquids and express them in the same unit. The standard unit of measuring liquids is litre.

Liquids like milk, petrol, oil, etc., are measured in litres. Small quantity measurements like medicinal liquids are measured in millilitres. A litre can be sub-divided into \(1000\) equal portions. Each such part is called a millilitre.

Thus, \(1\,{\rm{litre}} = 1000\,{\rm{milliletres}}\)

\({\rm{L}}\) denotes litre.

Millilitre is denoted by \({\rm{mL}}\) or \({\rm{ml}}.\)

The standard-sized containers used for measuring liquids are given below.

The first kind of container is generally used to measure milk, whereas the second kind of container is used to measure petrol and oil.

We have learnt that a metre is bigger than a centimetre, and a kilogram is heavier than a gram. Similarly, a litre is more than a millilitre.

Suppose Partha has one litre of milk. He can measure it in one time by \({\rm{1}}\)-litre container or \(2\) times by \(500\,{\rm{mL}}\) container.

Therefore, \(1\,{\rm{L}} = 2 \times 500\,{\rm{mL}}\)

Similarly, \(1\,{\rm{L}} = 5 \times 200\,{\rm{mL}}\)

\(1\,{\rm{L}} = 1 \times 500\,{\rm{mL + 2}} \times {\rm{200}}\,{\rm{mL + 1}} \times {\rm{100}}\,{\rm{mL}}\)

\(1\,{\rm{L}} = 10 \times 100\,{\rm{mL}}\)

That is, \(1\,{\rm{L}}\) can be measured in different ways.

Litres are used in measuring the capacity of milk, cooking oils, kerosene, petrol, etc.

Millilitres are used in measuring the capacity of medicinal liquids like syrup and measuring the chemicals. Also, a small quantity of cooking oil, ketchup etc., are measured in millilitres.

By using the relation \(1\,{\rm{L}} = 1000\,{\rm{mL,}}\) we would be able to convert litres to millilitres and millilitres to litres.

We multiply the number of litres by \(1000\) to convert litres into millilitres.

**Example:** Convert \(3\,{\rm{litres}},\,5\,{\rm{litres}}\) and \(10\,{\rm{litres}}\) into millilitres.**Solution:** \(3\,{\rm{litres = 1000}} \times {\rm{3}}\,{\rm{millilitres}} = 3000\,{\rm{mL}}{\rm{.}}\)

\(5\,{\rm{litres = 1000}} \times 5\,{\rm{millilitres}} = 5000\,{\rm{mL}}{\rm{.}}\)

\(10\,{\rm{litres = 1000}} \times 10\,{\rm{millilitres}} = 10000\,{\rm{mL}}{\rm{.}}\)

So, from the above example, we can clearly understand that, to convert litres into millilitres, put \(3\) zeroes to the right of the number of litres.

**Example:** Convert \(4\,{\rm{litres}}\,{\rm{289}}\,{\rm{millilitres}}\) to \({\rm{mL}}.\)**Solution:** \(4\,{\rm{litres}}\,289\,{\rm{millilitres}} = 4\,{\rm{litres}} + 289\,{\rm{millilitres}}\)

\( = 1000 \times 4\,{\rm{mL}} + 289\,{\rm{mL}}\)

\( = 4000\,{\rm{mL}} + 289\,{\rm{mL}}\)

\( = 4289\,{\rm{mL}}\)

Therefore, \(4\,{\rm{litres}}\,289\,{\rm{millilitres}} = 4289\,{\rm{mL}}.\)

Conversion of millilitres to litres or into litres and millilitres is done in the same way as converting grams to kilograms or kilograms to grams \(1000\,{\rm{mL}} = 1\,{\rm{L}}.\)

**Example:** Convert into litres and millilitres.

(a) \(8000\,{\rm{mL}}\)

(b) \(5826\,{\rm{mL}}\)

(c) \(4089\,{\rm{mL}}\)**Solution:** (a) \(8000\,{\rm{mL}} = 8\,{\rm{L}} + 0\,{\rm{mL}} = 8\,{\rm{L}}\)

(b) \(5826\,{\rm{mL}} = 5000\,{\rm{mL}} + 826\,{\rm{mL}} = 5\,{\rm{L}}\,826\,{\rm{mL}}\)

(c ) \(4089\,{\rm{mL}} = 4000\,{\rm{mL}} + 89\,{\rm{mL}} = 4\,{\rm{L}}\,89\,{\rm{mL}}\)

The number formed by the last three digits on the right represents \({\rm{mL}},\) and the remaining digits represent litres.

We know that we can write \(1\,{\rm{litre}} = 1000\,{\rm{millilitre}}.\) In the same manner, we can write the below in terms of millilitres.

\(1\,{\rm{litre}} = 1000\,{\rm{millilitre}}\)

\(\frac{1}{2}\,{\rm{litre}} = 500\,{\rm{millilitre}}\)

\(\frac{1}{4}\,{\rm{litre}} = 250\,{\rm{millilitre}}\)

\(\frac{3}{4}\,{\rm{litre}} = 750\,{\rm{millilitre}}\)

The addition and subtraction of litres and millilitres are the same as the sum and difference of grams and kilograms. While doing the operations on capacity measures, always write millilitres in three digits and then perform the required operation like whole numbers.

**Example:** Add \(11\,{\rm{litre}}\,390\,{\rm{millilitres}}\) and \(9\,{\rm{litre}}\,920\,{\rm{millilitres}}\)**Solution: **Write the given data column-wise and start adding as shown below from the right end.

Therefore, \(11\,{\rm{litres}}\,390\,{\rm{millilitres}} + 9\,{\rm{litre}}\,920\,{\rm{millilitres}} = 21\,{\rm{litres}}\,90\,{\rm{millilitres}}.\)

**Example: **Subtract \(13\,{\rm{litres}}\,800\,{\rm{millilitres}}\) from \(21\,{\rm{litres}}\,750\,{\rm{millilitres}}.\)**Solution:** Write the given data column-wise and start subtracting as shown below from the right end.

Therefore, \(21\,{\rm{litres}}\,750\,{\rm{millilitres}} – 13\,{\rm{litre}}\,800\,{\rm{millilitres}} = 7\,{\rm{litres}}\,950\,{\rm{millilitres}}.\)

Finding the product and quotient of the capacity measures is the same as the multiplication and division of kilograms and grams. This means we need to first convert the litres to millilitres or millilitres to litres, and then we start multiplying or dividing the given capacity as whole numbers.

**Example:** A jar can hold \(4\,{\rm{litres}}\,250\,{\rm{millilitres}}\) of honey. How much honey will be needed to fill \(4\) jars?**Solution:** Here, we multiply \(4\,{\rm{litres}}\,250\,{\rm{millilitres}}\) by \(4.\)

\( \Rightarrow 4 \times \left( {4\,{\rm{litres}}\,250\,{\rm{millilitres}}} \right)\)

\( = 4 \times \left( {4000\,{\rm{millilitres}}\,{\rm{ + }}\,250\,{\rm{millilitres}}} \right)\)

\( = 4 \times 4250\,{\rm{mL}}\)

Now,

Therefore, required honey \( = 17000\,{\rm{millilitres}} = 17\,{\rm{litres}}.\)

**Example:** Rosy prepared \(14\,{\rm{litres}}\,500\,{\rm{millilitres}}\) syrup. She wants to fill it in \(5\) bottles. How much syrup will each bottle hold?**Answer:** We divide \(14\,{\rm{litres}}\,500\,{\rm{millilitres}},\) by \(5.\)

\(14\,{\rm{litres}}\,500\,{\rm{millilitres}} = 14 \times 1000\,{\rm{millilitres}} + 500\,{\rm{millilitres}}\)

\( = 14000\,{\rm{millilitres}} + 500\,{\rm{millilitres}}\)

\( = 14500\,{\rm{millilitres}}\)

Now, we divide \(14500\) by \(5\)

Therefore, syrup in each bottle \( = 2900\,{\rm{millilitres}} = 2000 + 900\,{\rm{millilitres}} = 2\,{\rm{litres}}\,900\,{\rm{millilitres}}\)

** Q.1. Mohini bought \(28\,{\rm{litres}}\,250\,{\rm{millilitres}}\) petrol for her car in January \(2018\) and \(53\,{\rm{litres}}\,900\,{\rm{millilitres}}\) in February \(2018.\) How much petrol did she buy in two months?** Petrol bought in January \(2018 = 28\,{\rm{litres}}\,250\,{\rm{millilitres}}\)

Ans:

Petrol bought in February \(2018 = 53\,{\rm{litres}}\,900\,{\rm{millilitres}}\)

We know that \(28\,{\rm{litres}}\,250\,{\rm{millilitres}} = \left( {28 \times 1000 + 250} \right){\rm{millilitres}} = \left( {28000 + 250} \right){\rm{mL}} = 28250\,{\rm{mL}}\)

And \(53\,{\rm{litres}}\,900\,{\rm{millilitres}} = \left( {1000 \times 53 + 900} \right){\rm{millilitres}} = \left( {53000 + 900} \right){\rm{mL}} = 53900\,{\rm{mL}}\)

Therefore, the total amount of petrol bought in two months \( = 28250\,{\rm{mL + 53900}}\,{\rm{mL}}\)

\( = {\rm{53900}}\,{\rm{mL}}\)

\( = 56\,{\rm{litres}}\,750\,{\rm{millilitres}}\)

So, the total amount of petrol bought by Mohini n January and February is \(56\,{\rm{L}}\,750\,{\rm{mL}}{\rm{.}}\)

** Q.2. Pankaj bought \(80\,{\rm{litres}}\,500\,{\rm{millilitres}}\) diesel for his truck. He used \(70\,{\rm{litres}}\,900\,{\rm{millilitres}}\) of it. How much diesel is still in the truck?** Total amount of diesel Pankaj bought \( = 80\,{\rm{litres}}\,500\,{\rm{millilitres}} = \left( {80 \times 1000 + 500} \right){\rm{mL}} = \left( {80000 + 500} \right){\rm{mL}} = 80500\,{\rm{mL}}\)

Ans:

Amount of diesel used \( = 70\,{\rm{litres}}\,900\,{\rm{millilitres}} = \left( {70 \times 1000 + 900} \right){\rm{mL}} = \left( {70000 + 900} \right){\rm{mL}} = 70900\,{\rm{mL}}\)

The total amount of diesel left in the truck \( = \) Amount of diesel Pankaj bought \(-\) Amount of diesel

\({\rm{ = }}\left( {80500 – 70900} \right){\rm{mL}}\)

\( = 9600\,{\rm{mL}}\)

\( = 9\,{\rm{litres}}\,600\,{\rm{millilitres}}\)

Therefore, the total amount of diesel left in the Pankaj’s truck \( = 9\,{\rm{L}}\,600\,{\rm{mL}}\)

** Q.3. Fifteen empty jars are to be filled with tomato ketchup. How much ketchup will be required if each jar can hold \(2\,{\rm{litres}}\,250\,{\rm{millilitres?}}\)** Number of jars to be filled with tomato ketchup \( = 15\)

Ans:

Each jar can hold \( = 2\,{\rm{litres}}\,250\,{\rm{millilitres}} = \left( {2 \times 1000 + 250} \right){\rm{mL}} = \left( {2000 + 250} \right){\rm{mL}} = 2250\,{\rm{mL}}\)

Therefore, the amount of ketchup required \({\rm{ = }}\left( {15 \times 2250} \right){\rm{mL}} = 33750\,{\rm{mL}}\)

** Q.4. \(11\,{\rm{litres}}\,250\,{\rm{millilitres}}\) milk is to be boiled in \(9\) pots. How much milk will be there in one pot?** Amount of milk boiled in \(9\) pots \( = 11\,{\rm{litres}}\,250\,{\rm{millilitres}} = \left[ {\left( {11 \times 1000} \right) + 250} \right]{\rm{mL}} = \left( {11000 + 250} \right){\rm{mL}} = 11250\,{\rm{mL}}\)

Ans:

Amount of milk in one pot \(= 11250 \div 9 = 1250\,{\rm{mL}} = 1000\,{\rm{mL}} + 250\,{\rm{mL}}\)

Therefore, the amount of milk in one pot is \(1\,{\rm{L}}\,250\,{\rm{mL}}.\)

** Q.5. Arun bought \(30\,{\rm{litre}}\) petrol for his car. He went to see the Taj and used \(\frac{3}{4}\) of the petrol. How much petrol is left in his car?** Amount of petrol Arun bought \( = 30\,{\rm{litres}}\)

Ans:

Amount of petrol used by Arun to visit the Taj \( = \frac{3}{4}\) of \(30\,{\rm{litres}} = \frac{3}{4} \times 30 = 7.5 \times 3 = 22.5\,{\rm{litres}}\)

Amount of petrol left in Arun’s car \( = \left( {30 – 22.5} \right){\rm{litres}} = 7.5\,{\rm{litres}}\)

\( = 7\,{\rm{litres}}\,500\,{\rm{millilitres}}\)

Therefore, the total amount of petrol left in Arun’s car \( = 7\,{\rm{litres}}\,500\,{\rm{millilitres}}\)

In the above article, we have studied the meaning of litres, uses of litres and millilitres, conversion of litres to millilitres and millilitres to litres. Also, we have learnt the addition and subtraction of litres and millilitres and multiplication and division of litres and millilitres. Also, we have solved some example problems based on the litre and millilitre.

**Learn About Comparing Quantities**

The answers to the most commonly asked questions about Litre are provided here:

A metric unit of volume that is a thousand cubic centimetres is known as a litre. A litre can be sub-divided into \(1000\) equal portions. Each such part is called a millilitre.Q.1. What is the meaning of 1 litre?Ans: Thus, \(1\,{\rm{litre}} = 1000\,{\rm{millilitres}}.\) |

The best example we can tell for litre is a one-litre water bottle, one-litre cooking oil etc., which we use in our daily life.Q.2. What is an example of 1 litre?Ans: |

To convert litres into millilitres, put \(3\) zeroes to the right of the litres as \(1\,{\rm{L}} = 1000\,{\rm{mL}}.\)Q.3. How do we convert litres to millilitres?Ans: |

Q.4. What are the uses of litres? Litres are used in measuring the capacity of milk, cooking oils, kerosene, petrol, etc.Ans: |

Q.5. What are the uses of millilitres?Ans: Millilitres are used in measuring the capacity of medicinal liquids like syrup and measuring the chemicals. Also, a small amount of cooking oil, ketchup etc., are measured in millilitres. |

*We hope this detailed article on the concept of litre in maths helped you in your studies. If you have any doubts, queries or suggestions regarding this article, feel free to ask us in the comment section and we will be more than happy to assist you. Happy learning!*