Students often refer to Kerala State Syllabus SCERT Class 5 Maths Solutions and Class 5 Maths Chapter 2 Number World Questions and Answers Notes Pdf to clear their doubts.
SCERT Class 5 Maths Chapter 2 Solutions Number World
Class 5 Maths Chapter 2 Number World Questions and Answers Kerala State Syllabus
Number World Class 5 Questions and Answers Kerala Syllabus
Question 1.
How many two-digit numbers are there with 0? How many without 0?
Answer:
There are 9 Two-digit numbers with 0. For a two-digit number to contain 0, it must be in the tens place. So, we have 10, 20, 30,…, 90. 0 cannot be the first digit.
For two-digit numbers without 0, both the tens and unit places can take any digit from 1 to 9. So, we have 11, 12, 13, …, 98, 99. There are 9 choices for the tens place and 9 choices for the units place, resulting in 9 × 9 = 81 numbers.
Question 2.
i) How many three-digit numbers are possible with two 0?
ii) How many three-digit numbers are there with only one 0?
iii) How many three-digit numbers are there without any zero?
Answer:
i) Number of three-digit numbers possible with two zeros = 9,0 cannot be in the 1st digit
i.e., The two zeroes should be in the tens and unit places, So there are 9 three-digit numbers with two zeros.
ii) The zero cannot be in the hundreds place, as that would make it a 2-digit number.
So, the zero can only have two possible positions: the tens or units place.
The zero in the tens place: In this case, we have 9 options (1-9) for the hundreds place, 1 option for the tens place (0), and 9 options (1-9) for the units place. This gives 9 × 9 = 81 numbers.
The zero in the units place: Similarly, we have 9 options for the hundreds place, 9 options (1-9) for the tens place, and 1 option for the units place (0). This gives 9 x 9 x 1 = 81 numbers.
So, in total, we have 81 + 81 = 162 three-digit numbers with only one zero.
iii) For the first digit:
Since we cannot have 0 in the first place, there are 9 options (1 to 9).
For the second and third digits
For each of the remaining two digits, we have 9 options (0 is not allowed, but the other 9 digits are).
Therefore, the total number of 3-digit numbers (with no zeros) is:
9 (options for the first digit) × 9 (options for the second digit) × 9 (options for the third digit) = 729
So, there are 729 three-digit numbers (with no zeros).
Question 3.
How many two-digit numbers are there with the same digit repeated? How many three-digit numbers with the same digit repeated thrice?
Answer:
For two-digit numbers with the same digit repeated, you have 11, 22, 33, 44, 55, 66, 77, 88, and 99. So, there are 9 such numbers.
For three-digit numbers with the same digit repeated thrice, you have 111, 222, 333, 444, 555, 666, 777, 888, 999 and 999,
So, there are 9 two-digit numbers with the same digit repeated and 9 three-digit numbers with the same digit repeated thrice.
Question 4.
There are some numbers that read the same when the digits are put in the reverse order.
For example, 46764. Such numbers are called palindromic numbers.
i) How many two-digit numbers are palindromes?
ii) How many three-digit numbers?
iii) Four-digit numbers?
Answer:
i) For a two-digit number to be palindrome, the two digits must be zero There are 9 palindromic numbers with two digits:
11, 22, 33, 44, 55, 66, 77, 88, 99.
ii) For a three-digit number to be palindrome, The first and third digits must be the same
The first digit can’t be 0 for a three-digit number So first and third digits be any of the nine digits 1-9;
The second digit be any of the ten digits 0-9
Thus, there are 9 × 10 = 90three digit palindromic numbers
iii) For a three-digit number to be palindrome, The first and third digits must be the same
The first digit can’t be 0 for a three-digit number So first and third digits be any of the nine digits 1-9;
The second digit be any of the ten digits 0-9 .
Thus, there are 9 × 10 = 90 three-digit palindromic numbers.
iv) For a three-digit number to be palindrome, The first and fourth digits must be the same
The first digit can’t be 0 for a three-digit number
So first and fourth digits be any of the nine digits 1-9;
Also, the second and third digits must be the same
The second and third digits be any of the ten digits 0-9
Question 5.
How many four-digit numbers can be made using all the digits 1,2,3, 4? What is the sum of all these?
Answer:
In each place, 1, 2, 3, and 4 must occur equally often,
The possible numbers where 1 is at the thousands place are 1234, 1324, 1432, 1342, 1423, 1243
The possible numbers where 2 is at the thousands place are 2134, 2314, 2413, 2341, 2431, 2413
The possible numbers where 3 is at the thousands place are 3124, 3241, 3421, 3412, 3214, 3142
The possible numbers where 4 is at the thousands place are 4123, 4213, 4312, 4321, 4132, 4231
Therefore, there are 4 × 6 = 24 possible numbers that can be made using the given digits.
Since it’s a four-digit number, each digit will appear 24/4 = 6 times in each of the units, tens, hundreds, and thousands places.
Therefore, the sum of digits in the unit place is
6(1 + 2 + 3 + 4 ) = 6(10) = 60
Similarly at tens, hundreds, thousands places.
So, 60 + (60 × 10) + (60 × 100) + (60 × 1000) = 66,660
Intext Questions And Answers
Question 1.
How many four-digit numbers are possible with 1,3, 5, 7 as the digits?
Answer:
The possible numbers where 1 is at the thousands place are:
1357, 1375, 1537, 1573, 1735, 1753.
The possible numbers where 3 is at the thousands place are:
3157, 3175, 3715, 3751, 3517, 3571.
The possible numbers where 5 is at the thousands place are:
5137, 5173, 5317, 5371, 5713, 5731.
The possible numbers where 7 is at the thousands place are :
7135, 7153, 7315, 7351, 7531, 7513.
Therefore, there are 4 × 6 = 24 possible numbers that can be made using the given digits.
Class 5 Maths Chapter 2 Kerala Syllabus Number World Questions and Answers
Question 1.
Ziad and Meera are making numbers with digit cards. These are the cards they have:
a) What is the largest number they can make with these cards?
b) And the smallest?
Answer:
a) 876540.
b) 405678
Question 2.
The prices of cars bought by Ramu, Raju, Gopu and Saju are given below Ramu- Rs. 449180 Raju- Rs. 448991 Gopu- Rs. 440894 Saju- Rs. 448911
a) Who bought the car with the highest price? How much?
b) Write the highest price in words
c) Who bought the car with the lowest price? How much?
Answer:
a) Ramu-449180
b) Four lakh forty-nine thousand one hundred and eighty.
c) Gopu – Rs. 44089
Question 3.
Write the number according to the place value.
a) 8 lakh 3 ten thousand 6 thousand 7 hundred 3 tens and 2 ones.
b) Which among the following represents seven lakh two thousand four hundred and thirty- two?
(1) 72432 (2) 720432 (3) 702432 (4) 724320
Answer:
a) 836732
b) 702432
Question 4.
In class 1, there are 435268 children. Write the total number of students in class 1 in words.
Answer:
Four lakh thirty-five thousand two hundred sixty-eight.
Question 5.
a) What is the largest four-digit number?
b) What is the next number?
c) And the largest five-digit number?
d) What is the next number? How do we find it? ‘
Answer:
a) 9999 (Nine thousand nine hundred ninety-nine)
b) 10000 (Ten thousand)
c) 99999 (Ninety-nine thousand nine hundred and ninety-nine)
d) 100000 (one lakh.) By adding one with 99999 99999 + 1 = 100000 (lakh)
Class 5 Maths Chapter 2 Notes Kerala Syllabus Number World
Numbers are like magical symbols that help us count, measure, and understand the world around us. From the tiniest ant to the grandest mountains, everything can be represented and understood using numbers.
Imagine a world without numbers. Flow would we know how many candies we have or how old we are? Numbers make counting possible! Whether it’s counting the number of stars in the sky or the petals on a flower, numbers help us make sense of quantities.
Number That Counts
It is easy to start with the smallest number and make it bigger and bigger. In this section, we have seen how to make bigger numbers and how to read them easily by giving their place values. In this manner, we can read bigger numbers.
Growing Numbers
Here we discuss about how to count and categorize numbers based on their digit compositions across different ranges, from one-digit to four-digit numbers.
1. Number That Counts
2. Growing Numbers
1. Number That Counts
We have learnt, many things about Numbers, It is easy to start from the smallest number and make it bigger and bigger
1 one
10 Ten
100 Hundred
1000 Thousand
10000 Ten Thousand
Every time the digit 1 shifts one place to the left, it becomes ten times as large. So by shifting 1 to the left like this, we get
Adding more zeroes we get 10 crore, 100 crore and so on. In other countries, these numbers are known by different names. It goes like ten billion, hundred billion and thousand billion is called trillion. We need these big numbers in many situations, such as for the calculation of the population in Kerala. The numbers which have only zero after digit 1 are named like this. How do we read other types of numbers?
For, example. How do we read the number 362880?
We can start from the left.
3 Three
62 SixtyTwo
880 Eight Eighty
362880 – Three lakh sixty-two thousand eight hundred eighty
There’s another way to read 362880. Start from the right with 0 and count places to the left as one, ten, hundred and so on:
0 One
8 Ten
8 Hundred
2 Thousand
6 Ten thousand
3 Lakh
Then the number can be read as “Three lahks, sixty-two thousand eight hundred eighty”.
We can also read numbers by counting digits:
- One-digit numbers 1 to 9
- Two-digit numbers 10 to 99
- Three-digit numbers 100 to 999
- Four-digit numbers 1000 to 9999
- Five-digit numbers 10000 to 99999
- Six-digit numbers 100000 to 999999
- Seven-digit numbers 1000000 to 9999999
And we can continue
Flow do we read the number 234567?
Since it is a six-digit number, it is more than a lakh
So we read it as Two lakh thirty-four thousand five hundred sixty-seven.
Read the given statements.
1. In 2023, the minimum distance between the Earth and the Moon is 356569 kilometres and the maximum is 406458 kilometres.
We read it as, In Two thousand twenty-three, the minimum distance between the Earth and the moon is Three lakh fifty-six thousand five hundred sixty-nine kilometres and the maximum is Four lakh six thousand four hundred fifty-eight kilometre
2. According to the 2011 census, the population of Kerala was 33406061, and the total population of India was 1210854977.
We read it as, According to Two thousand eleven census, the population of Kerala was Thirty – Three million four hundred six thousand and sixty-one and the total population of India was One billion two hundred ten million eight hundred fifty- four thousand nine hundred seventy -seven
3. The product of all the numbers from 1 to 11 is 39916800.
We read it as, The product of all the numbers from 1 to 11 is Thirty -nine million nine hundred sixteen thousand eight hundred
2. Growing Numbers
There are only nine one-digit numbers, 1, 2, 3,9.
There are 99 numbers from 1 to 99, So to find the number of two-digit numbers, we have to subtract one-digit numbers from these, i.e., 99 – 9 = 90. So there are 90 two-digit numbers
From the numbers 1 to 999 we have to remove those from 1 to 99.
So there are 999 – 99 = 900 three-digit numbers
Karprekar Number
Karprekar Number is a number that, when we take a four-digit integer from the largest and smallest numbers from its digits and then subtract these two numbers. Continuing with this process of forming and subtracting, we will always arrive at the number 6174.
Palindromic Number
A number that remains the same even if its digits are reversed is called a palindromic number.
For example 14641, 32123, 99, 1001 etc
- Each digit in a number has a place value, which determines its position and worth in the number.
- The place value increases by a factor of 10 as you move from right to left in a number: ones, tens, hundreds, thousands, etc.
