Large Numbers in Practice

In our daily lives, we encounter a variety of measurements that help us understand and navigate the world around us. Let's discover how "large numbers" play a crucial role in different scenarios, from the classroom to the cosmos. Whether it's centimeters or kilometers, grams or kilograms, every unit has its place and purpose.

Length Measurement:

we use centimetre (cm) as a unit of length.For measuring the length of a pencil, the width of a book or notebooks etc., We use centimetres. Our ruler has marks on each centimetre.For measuring the thickness of a pencil, however, we find centimetre too big. We use millimetre (mm) to show the thickness of a pencil.

(a) 10 millimetres(mm) = centimetre(cm)

To measure the length of the classroom or the school building, we shall find centimetre too small. We use metre for the purpose.

(b) 1 metre(m) = centimetres(cm) = millimetres(mm)

Even metre is too small, when we have to state distances between cities, say, Delhi and Mumbai, or Chennai and Kolkata. For this we need kilometres (km).

How many millimetres(mm) make 1 kilometre(km)?

1 km = m

But 1 m = mm

1km= 1000 × mm

= mm

1.How many centimetres make a kilometre?

Solution:

We know that 1km=m

But, 1m=cm

So, 1km=1000 x 1m=1000 x 100cm =cm

Therefore,1km=100000cm

Weight Measurement

We go to the market to buy rice or wheat; we buy it in kilograms (kg).But items like ginger or chillies which we do not need in large quantities, we buy in grams (g).We know

1 kilogram(kg) = grams(g).

Have you noticed the weight of the medicine tablets given to the sick? It is very small. It is in milligrams (mg).

1 gram(g) = milligrams(mg).

Let us solve some problems.Once done with question1 then click on question2 button.

Q1

1. How many milligrams make one kilogram?

Sol:

We know that 1kg=g

But 1g=mg

1kg= 1000 x 1g =1000 x 1000mg =mg

Therefore, 1kg = 1000000 mg

Q2

2. A box contains 2,00,000 medicine tablets each weighing 20 mg. What is the total weight of all the tablets in the box in grams and in kilograms?

Sol:

No. of medicine tablets in a box=

Weight of each tablet=mg

weight of all tablets in the box= 2,00,000 X 20mg =mg

Let us convert it into grams.1g=mg

4000000mg in grams = 40000001000g =g

Let us convert it into kilograms.1kg=mg

4000000mg in kilograms = 40000001000000g =kg

The total weight of all the tablets in the box

i) in grams = 4000g

ii) in kilograms = 4kg

Capacity Measurement

What is the capacity of a bucket for holding water? It is usually 20 litres (l).Capacity is given in litres. But sometimes we need a smaller unit, the millilitres.A bottle of hair oil, a cleaning liquid or a soft drink have labels which give the quantity of liquid inside in millilitres (ml).

1 litre(l) = millilitres(ml).

Try these

A bus started its journey and reached different places with a speed of 60 km/hour. The journey is shown below:

1.(i)Find the total distance covered by the bus from A to D.

= AB + BC + CD : + + = km.

(ii)Find the total distance covered by the bus from D to G.

= DE + EF + FG : + + = km.

(iii)Find the total distance covered by the bus, if it starts from A and returns back to A.

Start from A and Return back to A = sum of all the distance covered = AB + BC + CD + DE + EF + EG +GA.

But from (i) and (ii) AD= AB + BC + CD = 9740km and DG=DE + EF + FG = 15520km.

So, Start from A and Return back to A = AD + DG + GA = 9740 + 15520 + 1290 = km.

(iv) Can you find the difference of distances from C to D and D to E?

= - = km.

(v)(a) Find out the time taken by the bus to reach A to B

Given:

distance from A to B =

Speed=

But speed = DistanceTime ; Time = distancespeed

= 417060 = hr

but 0.5 of an hour(=60 minutes) is 12 x 60minutes= minutes(Since,0.5='1/2')

Therefore,Time taken to travel from A to B is 69 hr 30 min.

(b) Find out the time taken by the bus to reach C to D

Given:

distance from C to D =

Speed=

But speed = DistanceTime; Time = distancespeed

= 216060 = hr

Therefore,Time taken to travel from C to D is 36 hr.

(c)Find out the time taken by the bus to reach E to G

Given

Distance from E to G= EF + FG = + = km

Speed=60 kmhr

But speed = DistanceTime; Time = distancespeed

= 738060 = hr

Therefore,Time taken to travel from C to D is 123 hr.

(d)Find out the time taken by the bus for total journey

Given

Total journey=Distance from A to A= km(hint:Done in Q1 (iii)bit)

Speed=60 kmhr

But speed = DistanceTime; Time = distancespeed

= 2655060 = hr

but 0.5 of an hour(=60 minutes) is 12 x 60minutes= minutes(Since,0.5=12)

Therefore,Time taken for total journey (i.e. travel from A to A) is 442 hr 30 min

Case based question

Things	Apples	Oranges	Combs	Tooth Brushes	Pencils	Note books	Soap cakes
Price	40 per kg	30 per kg	3 for each	10 for one	1 for one	6 for one	8 for one

Things

Apples

Oranges

Combs

Tooth Brushes

Pencils

Note books

Soap cakes

Price

40 per kg

30 per kg

3 for each

10 for one

1 for one

6 for one

8 for one

The sales during the last year

Things	Apples	Oranges	Combs	Tooth Brushes	Pencils	Note books	Soap cakes
quantity sold	2457 kg	3004 kg	22760	25367	38530	40002	20005

Things

Apples

Oranges

Combs

Tooth Brushes

Pencils

Note books

Soap cakes

quantity sold

2457 kg

3004 kg

22760

25367

38530

40002

20005

Question&Sol

(a) Can you find the total weight of apples and oranges Raman sold last year?

Weight of apples = kg

Weight of oranges = kg

Therefore, total weight of apples and oranges= 2457 kg + 3004 kg = kg

Therefore, the total weight of oranges and apples = 5461 kg.

(b) Can you find the total money Raman got by selling apples?

weight of apples= kg

Cost of apples per kg=

=Total money Raman got by selling apples= Cost of apples x weight of apples= 40 x 2457 = ₹.

Therefore,Total money Raman earned by selling apples=98280.

(c) Can you find the total money Raman got by selling apples and oranges together?

Money earned by selling apples=₹(from above bit)

Money earned by selling oranges= Total no. oranges(in kgs) x cost of 0ranges per kg (in ₹)

=kg x ₹=₹

Money earned by selling apples + Money earned by selling oranges =98280 + 90120 = ₹.

Therefore, total money earned by selling apples and oranges is ₹188400.

(d) Make a table showing how much money Raman received from selling each item. Arrange the entries of amount of money received in descending order. Find the item which brought him the highest amount. How much is this amount?

Things	Apples	Oranges	Combs	Tooth Brushes	Pencils	Note books	Soap cakes
Quantity sold	2457 kg	3004 kg	22760	25367	38530	40002	20005
Price	40 per kg	30 per kg	3 for each	10 for one	1 for one	6 for one	8 for one
Total price=Quantity sold x Price	₹	₹	₹	₹	₹	₹	₹

Things

Apples

Oranges

Combs

Tooth Brushes

Pencils

Note books

Soap cakes

Quantity sold

2457 kg

3004 kg

22760

25367

38530

40002

20005

Price

40 per kg

30 per kg

3 for each

10 for one

1 for one

6 for one

8 for one

Total price=Quantity sold x Price

₹

Arrange the above total prices in descending order:

Apples-98280

Oranges-90120

Combs-66280

Tooth Brushes-253670

Pencils-38530

Notebooks 240012

Soap cakes-160040

Item which brought him the highest amount =

Highest amount among all items= ₹.

Example1

Example 1 :Population of Sundarnagar was 2,35,471 in the year 1991. In the year 2001 it was found to be increased by 72,958. What was the population of the city in 2001?

Hint: The problem states that the population in 2001 was found to have by a certain amount from its population in 1991.

The word "increased" indicates that we need to the increase to the original population to find the new population.

Solution :

Given

Population of the city in 1991=

Increase in population by 2001=

Population of the city in 2001=

Population of the city in 1991 + Increase in population

=2,35,471+72,958=

Note: Here addition can be done by using expanded form also.Like (200000+30000+400+70+1)+(70000+2000+900+50+8).Now, group and add numbers with the same place values.

Example2

Example 2 : In one state, the number of bicycles sold in the year 2002-2003 was 7,43,000. In the year 2003-2004, the number of bicycles sold was 8,00,100. In which year were more bicycles sold? and how many more?

Hint: When we talk about which year sales are more then we are doing comparison.So the operation we perform is .

Solution : Clearly, 8,00,100 is than 7,43,000. So, in that state, more bicycles were sold in the year than in .

Difference = Sales in 2003-2004 - Sales in 2002-2003

= 800100 – 743000 =

Note: Check the answer by adding 743000 + 57100 =800100 (the answer is right)

Example3

Example 3 :The town newspaper is published every day. One copy has 12 pages. Everyday 11,980 copies are printed. How many total pages are printed everyday?

Hint:Here we need to 12 pages 11980 times.It is a repeated addition.Repeated addition is called.So in this problem we have to do .

Solution :

Given Numbers:

Pages per copy=

Copies printed daily=

Total Pages Printed= Pages per copy × Copies printed daily

Total pages = 12 × 11,980=

Therefore,everyday 1,43,760 pages are printed.

Example4

Example 4 :The number of sheets of paper available for making notebooks is 75,000. Each sheet makes 8 pages of a notebook. Each notebook contains 200 pages. How many notebooks can be made from the paper available?

Hint: The logical steps involve first converting sheets to pages and then converting pages to notebooks. To find the number of pages, each sheet gives 8 pages, so for 75,000 sheets, we can either add 8 pages 75,000 times or 75,000 by 8. To convert pages to notebooks, since each notebook requires 200 pages, we repeatedly subtract 200 from the total pages until less than 200 pages remain, which is the same as using .

Solution :

Given Numbers:

Total sheets of paper= sheets.

Pages per sheet= pages.

Pages per notebook= pages.

Calculate Total Pages Produced:

Total pages = Total sheets of paper × Pages per sheet

Total pages = 75,000 × 8=

So, 600,000 pages can be produced from the available sheets of paper.

Calculate the Number of Notebooks:

Number of notebooks = Total pages produced ÷ Pages per notebook

Number of notebooks = 600,000 ÷ 200 =

So, 3,000 notebooks can be made from the available paper.

Conclusion: The number of notebooks that can be made from the 75,000 sheets of paper is 3,000.

Conclusion:

Note that in all these units we have some words common like kilo, milli and centi. You should remember that among these:

kilo is the and milli is the .

- shows 1000 times greater.

- shows 1000 times smaller.

- i.e. 1 kilogram = grams.

- 1 gram = milligrams.

- Similarly, centi shows 100 times smaller, i.e. 1 metre = centimetres.

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