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The solutions provided by Vedantu follow up with the updated version of the CBSE curriculum. The subject matter experts at Vedantu have done extensive and proper research to design the NCERT Solutions for Class 4 Maths Chapter 1. CBSE Class 4 Maths Chapter 1 is made in such a way so that it is understandable to every student. By going through the CBSE Class 4 Maths Chapter 1 Solutions, one can get a very clear concept of mathematics at the root level. This can help the child to solve complex problems on their own.
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Class 4 Maths Chapter 1 Building with Bricks are provided to help revise the concepts at your pace and practice to perfection.
The numbers that are significantly larger than those typically used in our everyday life are large. Large numbers are usually used for instance in simple counting or monetary transactions. The term large number typically refers to large positive integers. It also more generally refers to large positive real numbers but it may also be used in other contexts.
The very large numbers occur in the fields such as mathematics, cryptography, and statistical mechanics as well as in cosmology. Sometimes people also refer to numbers as being â€˜astronomically largeâ€™. Although it is very easy to mathematically define the numbers that are much larger even than those used in astronomy.
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A scientific was created to handle the wide range of the values that occur in scientific study.
For example, 1.0 x 109 means one billion because 1 is followed by nine zeros to see how large the number is.
The number of cells in a human body is estimated at 3.72 x 10^{13}.
The number of bits on a computer hard disk as of 2020 typically is about 10^{13}, 1-2 TB.
The number of neuronal connections in the human brain is estimated at 10^{14}.
The mass of the earth consists of about 4 x 10^{51} nucleons.
The total number of DNA base pairs within the entire biomass on the earth. As a possible approximation of the global biodiversity, it is estimated at (5.3 +3.6) x 10^{37}.
The number of atoms in the observable universe is estimated as 10^{80}.
The lower bound on the game tree complexity of chess which is also known as Shannon Number is estimated at around 10^{120}.
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In the formation of the numbers with the given digits, we all might say that a particular number is an arranged group of digits. Numbers can be formed with or without the repetition of the digits. Let us look into the examples that are formed without the repetition of digits.
With the digits 2 and 6, the numbers formed are 26 as well as 62.
With the digits 5 and 9, the numbers formed are 59 and also 95.
With the digits 9 and 4, the numbers formed are 94 and 49.
But with the digits 0 and 5, only one number that is 50 can be formed. The number 05 is not a two-digit number.
Similarly, three digits numbers are also formed without the repetition of a single number.
For Example,
The numbers 2, 3, 4 can form six numbers 234, 243, 342, 423, 432 of three digits.
The numbers 4, 6, 9 can form six numbers like 469, 496, 649, 694, 946, 964 of three digits.
The numbers 3, 7, 8 can form six numbers like 378, 387, 738, 837, 873 of three digits.
But the numbers 0, 1, and 5 can only form 4 numbers of three digits are 105, 150, 501, 510.
Some more examples of four-digit numbers without the repetition of a number.
The numbers 1, 2, 3, 4 can form four digit numbers like 1234, 1243, 1324, 1423, 1432, 2134, 2143, 2314, 2341, 2413, 2431, 3124, 3142, 3421, 3412, 3214, 3241, 4123, 4132, 4213, 4231, 4312, 4321.
We can observe that when the numbers of the digits are increased more and more numbers are formed. We are very much familiar with the formation of numbers with two or three digits. We also should know that, the procedure of forming the greatest as well as the smallest numbers having definite digits.
The face value of any number can be the representation as to the value of the digit itself. For example, the face value of the digit 3 in the number 356 is 3 itself. The face value of the digit 7 in the number 765 if 7 itself. The face value of the digit 6 in the number 689 is 6 itself.
The place value always represents the position of a digit in a number. For example, the place value of the digit 7 in the number 765 is hundredth that is 7 x 100 = 700th. The place value of the digit 6 in the number 678 is hundredth that is 6 x100 = 600th.
The major difference between place value as well as face value is that the place value deals with the position of the digit and the face value represents the actual value of a digit. The number system is available and is very crucial for characterizing the digits into the groups of tens, hundreds, and also even thousands.
You must first understand the key differences that separate the place value from the face value. In the place value, the number system begins from 0 to the tens, hundreds, thousands, and so on. Place value is defined as the digit multiplied wherever it is placed, it can be either by hundreds or by the thousands. Whereas the face value is simply defined as the digit itself within a number.
The place value of 0 is 0. The face value of 0 is also 0. The place value of a digit should be multiplied by the digit value of the position where it is located. On the other hand, the face value of a digit always remains the same and that too irrespective of the position where it is located.
For Example, the place value as well the face value for every digit 4657
The face value of 7 is 7.
The place value of the number 7 is also 7.
The face value of 5 is 5.
The place value of 5 is 50.
The face value of 6 is 6.
The place value 6 is 600.
The face value of 4 is 4.
The place value of 4 is 4000.
The expanded form of a number shows the expanded forms of a number including expanded notation form, expanded factor form, expanded exponential form as well as word form.
Expanded form or the expanded notation is a way of writing numbers to see the math value of individual digits. When the numbers are separated into individual place values and decimal places then they can also form a mathematical expression. The number 5,325 in the expanded notation form is 5,000 + 300 + 20 + 5 = 5325.
One can also write numbers using the expanded form in multiple ways. For Example, the number 5,325 can be written as 5325 in the standard form. The expanded form of the number 5325 is 5000 + 300 + 20 + 5 = 5325. The Expanded factors form of the number 5325 is
(5 x 1000) + (3 x 100) + (2 x 10) + (5 x 1) = 5325Â
The Expanded Exponential form of the number 5325 is (5 x 10^{3}) + (3 x 10^{2}) + (2 x 10^{1}) + (5 x 10^{0}) = 5325.
The word form of the number 5325 is Five thousand three hundred and twenty-five.
The phrase â€˜standard formâ€™ refers to the scientific number notation in England and Great Britain that the US calls â€˜scientific notationâ€™. The standard form in Great Britain and the scientific notation in the USA mean essentially the same thing when referring to the notation used in the representation of the very large or very small numbers such as 4.959 x 10^{12} or 1.66 x 10^{-24}.
Predecessors are the numbers that come just before a number. On the other hand, the number that comes immediately after a particular number is called its successor. The predecessor of a given number is always less than the given number. On the other hand, the successor of a given number is one more than the given number.
The successor of a whole number is the number obtained by adding 1 to the number. The successor of 0 is 1, the successor of 1 is 2, the successor of 2 is 3, the successor of 3 is 4, and so on. Every number has a successor as we can add 1 to any number. We can also observe that every whole number has its successor.
The number which comes just before a particular number is called the predecessor of it. The predecessor of a whole number is one less than it. Clearly, the predecessor of 1 is 0, the predecessor of 2 is 1, the predecessor of 3 is always 2, and so on. The whole number 0 does not have a predecessor. We can also observe that every whole number except the number 0 has its predecessor. Also, if suppose â€˜aâ€™ is the successor of â€˜bâ€™, then â€˜bâ€™ is the predecessor of â€˜aâ€™.
Examples to find the successor and the predecessor of a particular number.
The successor of 1000 is 1000 + 1 = 1001 whereas the predecessor of 1000 is 1000 - 1 = 999.
The successor of 11999 is 11999 + 1 = 12000 whereas the predecessor of 11999 is 11999 - 1 = 11998.
The successor of 400099 + 1 = 400099 whereas the predecessor of 400099 is 400099 - 1 = 400100.
The successor of 1000001 is 1000001 + 1 = 1000002 whereas the predecessor of 1000001 is 1000001 - 1 = 1000000.
The successor of 999 is 999 + 1 = 1000 whereas the predecessor of 999 is 999 - 1 = 998.
To find the predecessor of a number one should subtract by 1 to get the predecessor of that number. On the other hand to find the successor of a number one must add 1 to the given number to find the successor.
When children first learn to count they also learn the number sequence usually up to ten, but without an understanding of what the numbers mean. Next, they learn to count objects and the numbers of the things that are in front of them and then learn 1:1 correspondence when counting. During this stage the kids are learning the number sequence and that the numbers continue past 10. They learn how to count up to the higher numbers like 20 or 30. And eventually, they learn to count up to 100 and that numbers up to 100 can be split up into tens and ones.
When comparing numbers, it is very crucial to know the value of the most significant digit in each of the numbers. This will also tell you how large each number can be.
The most significant digit is the first non-zero digit the number contains. The number with the largest value, most significant digit will be bigger unless it is a negative number.
In the number 3458, the most significant digit is 3 which has a value of 3000. In the number 56.47, the most significant digit is 5 which has the value 50. In the number 0.0825, the most significant digit is 8 which has a value of 0.08. Now, if the two numbers are both positive integers that are whole numbers then looking at the number of the digits the number has will show you which is bigger. We often use the symbols like <> and also = while comparing two numbers.
While comparing the numbers up to 100 you need to look at the value of the ten digits unless the number is 100. The number with the larger tens digit will be bigger as the tens digit will be the most significant. The only exception is if either of the numbers is negative. Look at the comparing negative number section. If the numbers have the same ten digits then one needs to look at the oneâ€™s digit and also see which one is more.
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1. What are Some Simple Tricks to Count?
Ans: Using fingers to count is an old trick for beginners. Efficiency in the abacus may also help a lot in counting. However, the most important concept that helps a lot is multiplication tables. It is good to memorize the tables up to 20. Division by short method should be practised more and more.
Cross-verifying the result is also important such as subtraction, adding the difference with the number subtracted will give the original number. Carry forward and borrow should be calculated mentally to reduce the time taken. Splitting numbers into ones, tens, hundreds, and so on, and decimal places should be mentally marked properly in calculations.
2. What can you do When you are Stuck in Counting?
Ans: You may forget some of the borrows and carry while doing calculations involving large numbers. It is very important to find out the error quickly or else the counter will go wrong. The first thing to be noticed is whether the result you are getting is abnormal.
If yes, then stop calculating at that point, and go back one or two steps, and check the steps again.
If no error is found, go back right to the start of the problem and try to find any error if at all in the beginning part.
If again no error is found then go ahead and finish the problem.
Do not stop at halfway through a particular line of calculation, else you may forget the borrows carryforwards which you have taken.
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