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What was the length of the smallest pencil you have used?
How long is this pencil? Guess ________ cm
Measure it using a scale. How good is your guess?
We can see that Anju used a lens to make it look bigger.
Solution:
The smallest pencil that I had used was about 1 cm long.
I think the given pencil is more than 3 cm.
With the help of scale, the length of the pencil comes out to be 3.6 cm.
So, my guess was correct.
Disclaimer: The length of the smallest pencil that you have used varies from student to student. The answers provided here are for reference only.
What does 0.9 cm mean? It is the same as ______ millimetres. We can also say this is ninetenths of a cm. Right?
So 30.5 cm is the same as ______ cm and ______ millimetre.
About how many of the big frogs will fit on the 1 m scale? _______
If they sit in a straight line about how many of the small frogs will cover 1 m? _______
Solution:
We know that,
1 cm = 10 mm
So, 0.9 cm = 9 mm
0.9 cm means 9 mm
It is the same as 9 millimetres.
So 30.5 cm is the same as 30 cm and 5 millimetre.
Now, 30.5 cm = 30 cm and 5 mm
We know that,
1 m = 100 cm
Length of the biggest frog = 30.5 cm
Thus, a maximum of 3 big frogs can fit on 1m scale.
Length of each small frog = 0.9 cm
Thus, a maximum of 111 small frogs can sit in a straight line and cover 1 m.
(1) Length of the nail — 2 cm and ____ mm or 2. ____ cm.
(2)
The length of this lady finger (bhindi) is ______ cm and ______ mm. We can also write it as ______ cm.
(3) Using the scale on this page find the difference in length between candle 1 and candle 3.
Length of

Length in cm and mm 
Length in cm 
Candle 1  
Flame 1  
Candle 2  
Flame 2  
Candle 3  
Flame 3 
Solution:
(1) Length of nail = 2 cm 9 mm
Now, 10 mm = 1 cm
1 mm = $\frac{1}{10}$ cm
9 mm = 0.9 cm
So, 2 cm 9 mm = 2.9 cm
(2) Length of lady finger is 8 cm and 4 mm
Now, 10 mm = 1 cm
1 mm = $\frac{1}{10}$ cm
4 mm = 0.4 cm
So, 8 cm 4 mm = 8.4 cm
(3)
Length of

Length in cm and mm 
Length in cm 
Candle 1  2 cm 9 mm  2.9 cm 
Flame 1  1 cm 3 mm  1.3 cm 
Candle 2  4 cm 9 mm  4.9 cm 
Flame 2  1 cm 9 mm  1.9 cm 
Candle 3  6 cm  6.0 cm 
Flame 3  1 cm 9 mm  1.9 cm 
Guess the lengths to draw these things. Ask your friend to draw the same. After you make the drawing use a scale to measure the length. Whose drawing showed a better guess?
Guess its length and draw 
Measure of your drawing 
Measure of your friend's drawing 
An ant of length less than 1 cm 

Pencil of length about 7 cm 

A glass 11 cm high with water up to 5 cm 

A bangle of perimeter 20 cm 

A curly hair of length 16 cm 
Solution:
Disclaimer: Students are advised to prepare the answer on their own.
Which line is longer? A or B? Measure each line and write how long it is in centimetres. How good is your guess?
Which line is longer? C or D? Measure each line. How good is your guess?
Solution:
I think line B is longer than line A.
With the help of ruler, we get the measurement of line A as 4.6 cm and line B as 4.6 cm.
That means, both the lines are of same length. So, our guess was incorrect.
I think both the lines C and D are of same measurement.
With the help of ruler, we get the measurement as 3.2 cm for both the lines.
So, our guess was correct.
Disclaimer: The guess may vary from student to student. The answers provided here are for reference only.
What is the length of a 100 rupee note? Guess. Now measure it using a scale.
Now guess the length and width of many other things. Measure and find the difference between your measure and your guess.
Size of  Your guess in cm  Your measure in cm  
length  width  length  width  
100 Rupee note 10 Rupee note 20 Rupee note 5 Rupee note Post card MathMagic book 
Solution:
My guess:
Length of notebook = 25 cm
Breadth of notebook = 20 cm
Measure:
Length of notebook = 22.3 cm
Breadth of notebook = 18.3 cm
Difference in length between my guess and measure = 25 − 22.3
= 2.7 cm
Difference in breadth between my guess and measure = 20 − 18.3
= 1.7 cm
Size of 
Your guess in cm 
Your measure in cm 


length 
width 
length 
width 
100 Rupee note 
20 
10 
15.8 
7.3 
(1) How many paise does a matchbox cost? _______
(2) How many matchboxes can be got for Rs 2.50? _______
(3) How many rupees does the soap cost? ______
(4) Arun wanted to buy a soap. He has a fiverupee coin, 2 onerupee coins and 4 halfrupee coins. Write in rupees what money he will get back.
(5 a) An egg costs two and a half rupees. How much will one and a half dozen cost?
(b) How many pens can Kannan buy? How much money is left?
(6) The price of two pens is Rs ______. Can she buy two pens?
Solution:
We know that,
Re 1 = 100 paise
(1) Cost of a matchbox = Re 0.50
= 50 paise
(2) Cost of a matchbox = Rs 50 paise
Amount of money to buy matchboxes = Rs 2.50
= 2 rupees 50 paise
= 2 × 100 paise + 50 paise
= 200 paise + 50 paise
= 250 paise
So, number of matchboxes bought for Rs 2.50 = 250 ÷ 50
= 5
Thus, 5 matchboxes can be bought for Rs 2.50.
(3) Cost of a soap = Rs 8.75
(4) We know that,
Re 1 = 100 paise
Arun has a fiverupee coin, 2 onerupee coins and 4 halfrupee coins.
Now,
Rs 5 = 5 × 100 paise
= 500 paise
2 one rupee coins = 2 × 100 paise
= 200 paise
4 halfrupee coins = 4 × 50 paise
= 200 paise
Total money with Arun = 500 paise + 200 paise + 200 paise
= 900 paise
Cost of a soap = Rs 8.75
= 8 rupees 75 paise
= 8 × 100 paise + 75 paise
= 800 paise + 75 paise
= 875 paise
Money left with Arun after buying a soap = 900 paise − 875 paise
= 25 paise
= Rs 0.25
$\begin{array}{cccc}& 9& 0& 0\\ & 8& 7& 5\\ & 0& 2& 5\\ & & & \end{array}$
Thus, after buying a soap, Arun will get back Rs 0.25.
(5)
(a) Cost of an egg = Rs 2.50
= 2 rupees 50 paise
= 2 × 100 paise + 50 paise
= 200 paise + 50 paise
= 250 paise
Now, one dozen eggs = 12 eggs
So, one and a half dozen eggs = 12 + 6
= 18 eggs
Cost of 18 eggs = 18 × 250 paise
= 4500 paise
= Rs 45
Thus, cost of one and half a dozen eggs is Rs 45.
(b) Total money with Kannan = Rs 60
Cost of one and a half dozen eggs = Rs 45
Total money left with Kannan after buying eggs = Rs 60 − 45
= Rs 15
= 1500 paise
Now, Kannan uses the money that is left for purchasing pens.
Cost of a pen = Rs 6.50
= 6 rupees 50 paise
= 6 × 100 paise + 50 paise
= 600 paise + 50 paise
= 650 paise
Cost of 2 pens = 2 × 650 paise
= 1300 paise
= Rs 13
So, Kannan can buy only two pens with the amount of money that was left with him after purchasing eggs.
Now, money left with Kannan after purchasing pens = 1500 paise − 1300 paise
= 200 paise
= Rs 2
Thus, Kannan was left with Rs 2 after buying 2 pens.
(6) The price of two pens is Rs 13.
She can buy two pens.
Colourful Design
What part of this sheet is coloured blue?____/10
What part of the sheet is green? ____
Which colour covers 0.2 of the sheet?
Solution:
Total number of strips in the sheet = 10
Number of blue coloured strips = 1
So, part of the sheet that is blue = $\frac{1}{10}$
Thus, $\frac{1}{10}$of the sheet is blue.
Number of green coloured strips = 3
So, part of the sheet that is green = $\frac{3}{10}$
Thus, $\frac{3}{10}$ of the sheet is green.
Number of yellow coloured strips = 2
So, part of the sheet that is yellow = $\frac{2}{10}$
= 0.2
Thus, $\frac{2}{10}$ of the sheet is yellow.
Look at the second sheet. Each strip is divided into 10 equal boxes. How many boxes are there in all?
Is each box 1/100 part of the sheet?
How many blue boxes are there? ______
Is blue equal to 10/100 of the sheet? We saw that blue is also equal to 1/10 of the sheet. We wrote it as 0.1 of the sheet.
Can we say 10/100 = 1/10 = 0.10 = 0.1?
Think: Can we write ten paise as 0.1 of a rupee?
How many boxes are red? What part of the sheet is this? 15/____
Can we also write it as 0.15 of the sheet?
Now 3/100 of the sheet is black. We can say 0.____ sheet is black.
How many white boxes are there in the sheet?
What part of the second sheet is white? _____
Solution:
Number of boxes in 1 strip = 10
There are a total of 10 strips in the sheet.
So, number of boxes in 10 strips = 10 × 10
= 100
Yes, each box is $\frac{1}{100}$ part of the sheet.
There are 10 blue boxes in the sheet.
Yes blue equals to $\frac{10}{100}$ of the sheet.
It is given that blue is equal to $\frac{1}{10}$ of the sheet.
Now, $\frac{1}{10}=\frac{1\times 10}{10\times 10}=\frac{10}{100}$
Thus, $\frac{1}{10}$ is also equal to $\frac{10}{100}$ of the sheet.
And, $\frac{1}{10}$ = 0.1
So,
$\frac{10}{100}$ = $\frac{1}{10}$ = 0.10 = 0.1
Now, 100 paise = Re 1
So, we need ten 10 paise coins to make Re 1.
Thus, we can say that 10 paise is $\frac{1}{10}$ of a rupee.
Now, $\frac{1}{10}$ = 0.1
So, 10 paise is 0.1 of a rupee.
There are a total of 15 red boxes in the sheet.
Total number of boxes in the sheet = 100
Part of the sheet that is red = $\frac{15}{100}$
Now, $\frac{15}{100}=0.15$
So, 0.15 of the sheet is red.
It is given that $\frac{3}{100}$ of the sheet is black.
Now, $\frac{3}{100}=0.03$
So, we can say that 0.03 of the sheet is black.
There are a total of 22 white boxes in the sheet.
So, part of the sheet that is white = $\frac{22}{100}$
= 0.22
Thus, 0.22 of the sheet is white.
The school at Malappuram has its sports day.
The first five children in the Long Jump are:
Who is the winner in the long jump? _______
Write the names of the I, II and III winners on this stand.
Do you remember that 1 metre = 100 centimetres? So one centimetre is 1/100 of a metre. We also write 1 cm as _____ m 
Solution:
It is given that 4.50 m is longest jump.
Thus, Rehana is the winner in the long jump.
The 1st winner is Rehana, 2nd winner is Meena, and 3rd winner is Teena.
We know that, 100 cm = 1 m
so, 1 cm = $\frac{1}{100}$ m
1 cm = 0.01 m
So, we can also write 1 cm as 0.01 m.
Write in Metres
3 metre 45 centimetre  $\overline{){}_{}}$  metres 
99 centimetre  $\overline{){}_{}}$  metres 
1 metre and 5 centimetre  $\overline{){}_{}}$  metres 
Solution:
We know that ,
100 cm = 1 m
1 cm = $\frac{1}{100}$ m = 0.01 m
Now, 3 m 45 cm = 3 + $\frac{45}{100}$ m
= 3 + 0.45 m
= 3.45 m
99 cm = $\frac{99}{100}$ m
= 0.99 m
1 m 5 cm = 1 + $\frac{5}{100}$ m
= 1 + 0.05 m
= 1.05 m
3 metre 45 centimetre  $\overline{)3.45}$  metres 
99 centimetre  $\overline{)0.99}$  metres 
1 metre and 5 centimetre  $\overline{)1.05}$  metres 
What is Dinesh's height in metres?
_____ m _____ cm.
Solution:
Dinesh has to grow 45 cm more to reach the height of 2 m.
Now, 1 m = 100 cm
So, 2 m = 200 cm
Height of Dinesh = 200 − 45
= 155 cm
$\begin{array}{cccc}& 2& 0& 0\\ & & 4& 5\\ & 1& 5& 5\\ & & & \end{array}$
Now, 155 cm = 100 + 55 cm
= 1 m 55 cm
Thus, Dinesh's height is 1 m 55 cm.
Shivam Bank has a chart to show us how many Indian rupees we can get when we change the money of different countries.
Country 
Money 
Changed into Indian Rupees 
Korea Sri Lanka Nepal Hong Kong South Africa China U.A.E. U.S.A. Germany England 
Won Rupee (SL) Rupee Dollar (HK) Rand Yuan Dirham Dollar Euro Pound 
0.04 0.37 0.63 5.10 5.18 5.50 10.80 39.70 58.30 77.76 
Solution:
(A) The money of England will cost the most in Indian Rupees as 1 pound is equal to Rs 77.76
(B) We find from the chart that,
1 US dollars = Rs 39.70
= 39 rupees 70 paise
= 39 × 100 paise + 70 paise
= 3900 paise + 70 paise
= 3970 paise
10 US dollars = 10 × 3970 paise
= 39700 paise
= Rs 397.00
So, Mithun got Rs 397.00 from his uncle as a gift.
Money spent on school trip by Mithun = Rs 350.00
So, money left with Mithun = Rs 397.00 − 350.00
= Rs 47.00
$\begin{array}{ccccccc}& 3& 9& 7& .& 0& 0\\ & 3& 5& 0& .& 0& 0\\ & 0& 4& 7& .& 0& 0\\ & & & & & & \end{array}$
(C) Here, we are considering the exchange rates of Dirham in place of Saudi Riyal.
Salary of Majeed's father = 1000 Dirham
We find from the chart that,
1 Dirham = Rs10.80
= 10 rupees 80 paise
= 10 × 100 + 80 paise
= 1000 + 80 paise
= 1080 paise
So, 1000 Dirhams = 1000 × 1080 paise
= 1080000 paise
= Rs 10800
Therefore, salary of Majeed's father = Rs 10800.00
Salary of Arun's father = 2000 Sri Lankan Rupees
We find from the chart that,
1 Sri Lankan Rupee = Re 0.37
= 37 paise
So, 2000 Sri Lankan Rupees = 2000 × 37 paise
= 74000 paise
= Rs 740.00
Therefore, salary of Arun's father = Rs 740
Thus, Majeed's father gets more salary in Indian Rupees than Arun's father.
(D) Price of present bought by Leena's aunty = 30 Yuan
We find from the chart that,
1 Yuan = Rs 5.50
= 5 rupees 50 paise
= 5 × 100 + 50 paise
= 500 + 50 paise
= 550 paise
So, 30 Yuan = 30 × 550 paise
= 16500 paise
= Rs 165
So, the cost of the gift in Indian Rupees is Rs 165.00
(E)
(1) We find from the chart,
1 Won = Re 0.04
= 4 paise
We know that,
Re 1 = 100 paise
So, Rs 4 = 4 × 100 paise = 400 paise
Rs 400 = 400 × 100 paise = 40000 paise
Now, 4 paise = 1 Won
So, 400 paise = 400 ÷ 4 Won
= 100 Won
and 40000 paise = 40000 ÷ 4 Won
= 10000 Won
Thus, Astha can change 100 Won for Rs 4, and 10000 Won for Rs 400.
(2) We find from the chart,
1 Hong Kong Dollar = Rs 5.10
= 5 rupees 10 paise
= 5 × 100 + 10 paise
= 500 + 10 paise
= 510 paise
Total money with Astha = Rs 508
= 508 × 100 paise = 50800 paise
50800 paise = 50490 + 310 paise
50800 paise = 510 × 99 + 310 paise
50800 paise = 510 HKD + 310 paise
Now, 310 paise = 300 paise + 10 paise
= 3 rupees and 10 paise
= Rs 3.10
Thus, Astha can change 99 HKD for Rs 508 and Rs 3.10 is left with her.
Kiran went shopping with Rs 200. Look at the bill. The shopkeeper forgot to put the point correctly in the prices. Put the point in the correct place and find out the total amount of the bill.
Item  Quantity  Price (Rupees) 
Soap Green gram Tea Coconut Oil 
1 1 kg 250 gm 1 Litre 
1250 5025 2725 6000 
Total  ___________ 
Solution:
Item  Quantity  Price (Rupees) 
Soap Green gram Tea Coconut Oil 
1 1 kg 250 gm 1 Litre 
12.50 50.25 27.25 60.00 
Total  150.00 
The temperature in each city was noted at 3 pm on 16 January 2008.
(1) Which place had the highest temperature at 3 pm? Which place is the coolest at that time?
(2) How much higher is the temperature in Mumbai from that in Srinagar?
(3) How many degrees will the temperature need to rise for it to reach 40°C in Thiruvananthapuram?
(4) How much lower is the temperature of Kolkata from that in Chennai?
(5) The temperature in these cities was also noted at 3 am on the same day. Look at the table and answer the questions.
(a) Which place had the lowest temperature at 3 am? Imagine yourself to be there and describe how it would feel.
(b) What is the difference between the temperatures at 3 pm and 3 am in Chennai? In Bhopal?
City 
Temperature at 3 am 
Chennai  21.1 
Mumbai  19.0 
Th'puram  21.6 
Kolkata  13.1 
Bhopal  9.8 
Srinagar  1.3 
Guwahati  12.8 
Jaipur  10.2 
Solution:
(1) Mumbai had the highest temperature i.e. 35.1°C at 3 pm. Srinagar was the coolest place with the temperature of 8.1°C at 3 pm.
(2) Temperature of Mumbai at 3 pm = 35.1^{∘}C
Temperature of Srinagar at 3 pm = 8.1^{∘}C
Difference in temperature = 35.1^{∘}C − 8.1^{∘}C
= 27^{∘}C
(3) Temperature of Thiruvananthapuram at 3 pm = 33.5^{∘}C
Rise in the temperature needed to attain a temperature of 40^{∘}C = 40^{∘}C − 33.5^{∘}C
= 6.5^{∘}C
(4) Temperature of Chennai at 3 pm = 29.9^{∘}C
Temperature of Kolkata at 3 pm = 26.6^{∘}C
Difference between temperature = 29.9^{∘}C − 26.6^{∘}C
= 3.3^{∘}C
(5)
(a) Temperature of Srinagar at 3 am = 1.3^{∘}C
It will be very cold there.
(b) Temperature of Chennai at 3 pm = 29.9^{∘}C
Temperature of Chennai at 3 am = 21.1^{∘}C
Difference between temperature = 29.9^{∘}C − 21.1^{∘}C
= 8.8^{∘}C
Temperature of Bhopal at 3 pm = 25.9^{∘}C
Temperature of Bhopal at 3 am = 9.8^{∘}C
Difference between temperature = 25.9^{∘}C − 9.8^{∘}C
=16.1^{∘}C