
Q) What is place value of 2 in 2341?
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Q) Write the number 56798 in expanded form?
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Q) Expand 78456 ?
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Q) Write the numeral Sixtytwo lakh five?
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Q) Write the predecessor of the number 67,67,909?
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Q) 1 million is equal to?
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Q) 1 billion is equal to?
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Q) LXI=?
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Q) place value of 1 in 1024
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Q) Identify the greatest and smallest numbers of 45,453,3546,78
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Q) 14 lies between the numbers.
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Q) 1 cm __________ mm
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Q) Find the greatest and smallest numbers in 24,53,29,62,13,75,11 ?
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Q) Round off 3934554 to the nearest ten in number?
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Q) Compare 567654 and 567646 using >,< or= ?
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Q) Write the hindu and arabic numerals for the following:
(a) CLIV?
(b) CX?
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Q) Solve the following using the roman numerals
(a) XCXI  XV?
(b) LIX+CL+CV?
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Q) Write the definition of shifting digits?
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Q) What is sum?
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Q) What is difference?
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Q) What is product?
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Q) What is quotient?
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Q) A man saves $ 653 every month. Estimate the amount of money saved by him in two year?
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Q) A packet can hold 231 screws. Estimate the number of packet required to pack 34,46,876 screws?
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Q) In a town, there are 6,200 men,3,876 women,and 2,908 children. find the estimate population of the town by rounding off the numbers to the nearest hundred?
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Q) There are 2982 coins in a red bag and 2301 coins in a green bag. Estimate the the total number of coins to the nearest hundred in both the bag?
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Q) A shopkeeper has 5653 kg of sugar. He sells 53 kg of sugar every day. Estimate how much sugar is left after a days sale to the nearest hundred ?
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Q) What is rounding off the numbers?
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Q) Round of number which is nearest to the 560000?
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Q) Simplify (105 x 45)+9?
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Q) Write the greatest 5digit number ending in 1
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Q) Write three successors of 865.
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Q) 9999 + 999 = ?
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 Introduction
 Larger numbers
 Estimation by rounding off the numbers
 Rounding of Numbers
 Given two numbers, one with more digits is the greater number. If the number of digits in two given numbers is the same, that number is larger, which has a greater leftmost digit. If this digit also happens to be the same, we look at the next digit and so on.
 In forming numbers from given digits, we should be careful to see if the conditions under which the numbers are to be formed are satisfied. Thus, to form the greatest four digit number from 7, 8, 3, 5 without repeating a single digit, we need to use all four digits, the greatest number can have only 8 as the leftmost digit.
 The smallest four digit number is 1000 (one thousand). It follows the largest three digit number 999. Similarly, the smallest five digit number is 10,000. It is ten thousand and follows the largest four digit number 9999. Further, the smallest six digit number is 100,000. It is one lakh and follows the largest five digit number 99,999. This carries on for higher digit numbers in a similar manner.
 Use of commas helps in reading and writing large numbers. In the Indian system of numeration we have commas after 3 digits starting from the right and thereafter every 2 digits. The commas after 3, 5 and 7 digits separate thousand, lakh and crore respectively. In the International system of numeration commas are placed after every 3 digits starting from the right. The commas after 3 and 6 digits separate thousand and million respectively.
 Large numbers are needed in many places in daily life. For example, for giving number of students in a school, number of people in a village or town, money paid or received in large transactions (paying and selling), in measuring large distances say between various cities in a country or in the world and so on.
 Remember kilo shows 1000 times larger, Centi shows 100 times smaller and milli shows 1000 times smaller, thus, 1 kilometre = 1000 metres, 1 metre = 100 centimetres or 1000 millimetres etc.
 There are a number of situations in which we do not need the exact quantity but need only a reasonable guess or an estimate. For example, while stating how many spectators watched a particular international hockey match, we state the approximate number, say 51,000, we do not need to state the exact number.
 Estimation involves approximating a quantity to an accuracy required. Thus, 4117 may be approximated to 4100 or to 4000, i.e. to the nearest hundred or to the nearest thousand depending on our need.
 In number of situations, we have to estimate the outcome of number operations. This is done by rounding off the numbers involved and getting a quick, rough answer.
 Estimating the outcome of number operations is useful in checking answers.
 Use of brackets allows us to avoid confusion in the problems where we need to carry out more than one number operation.
 We use the HinduArabic system of numerals. Another system of writing numerals is the Roman system.
Ancient method of counting. Why numbers are required.
Ancient method of counting :
 Facts clearly state that counting sense in humans emerged long before the names of the numbers 1,2,3,4......
 In ancient times,the method of counting was based on distinct,uniform objects like fingers,stones,knots and lines.
For Example :
Kharosthi Numerals : Indian writing found in third century B.C.
Here, 1 is represented by I line,2 is represented by II,3 is represented by III and so on.... this is more of a symbolic representation to counting rather than a numerical representation.
Why numbers are required :
 Numbers are required to count concrete objects.
 Numbers help to create sequence by arranging smaller to bigger and bigger to smaller.
 Helps in creating order.
Shifting digits
Definition :
Let us consider set of certain numbers :
Examples :
Exchange digit at hundreds place to the digit at ones place
1.2.3.Introducing 10000
As we all know that 99 is the largest two digit number,1 added to 99 gives us the smallest 3 digit number.
99+1 =100 ( smallest three digit number )
Similarly,
999+1 =1000 (smallest four digit number )
Largest 3 digit number + 1 = smallest 4 digit number.
9999+1 =10000 (smallest five digit number )
Largest 4 digit number + 1 = smallest 5 digit number.
10  →  1×10 
100  →  10×10 
1000  →  10×100 
10000  →  10×1000 
10000 is actually 10 times 1000.so it is 10000 
So,we concluded that
Greatest single digit number+1=Smallest 2 digit number 
Greatest 2 digit number +1=Smallest 3 digit number 
Greatest 3 digit number +1=Smallest 4 digit number 
Greatest 4 digit number +1=Smallest 5 digit number 
1.2.4 :Revisiting place value
Let us consider few examples.
 28 = 20 + 8 = 2 × 10 + 8
 528 = 500 + 20 + 8 = 5 × 100 + 2 × 10 + 8 × 1
 4528 = 4000 + 500 + 20 + 8 = 4 × 1000 + 5 × 100 + 2 × 10 + 8 × 1
 64528 = 60000 + 4000 + 500 + 20 + 8 = 6 × 10000 + 4 × 1000 + 5 × 100 +2 × 10 + 8 × 1.
Let us illustrate above example using a table :
Number  Ten Thousand  Thousand  Hundreds  Tens  Ones 

28  2  8  
528  5  2  8  
4528  4  5  2  8  
64528  6  4  5  2  8 
Expansion of numbers:
Example :
Number  Number Name  Expansion 
50000  Fifty Thousand  5 × 10000 
28000  Twenty Eight Thousand  2 × 10000 + 8 × 1000 
68250  Sixty Eight Thousand Two Fifty  6 × 10000 + 8 × 1000 + 2 × 100 + 5 × 10 
89264  Eighty Nine Thousand Two Hundred and Sixty Four 
8 × 10000 + 9 × 1000 + 2 × 100 + 6 × 10 + 4 × 1 
1.2.5 Introducing 100000:
Greatest 5 digit number.
Adding 1 to the greatest 5 digit number gives the smallest 6 digit number.
Example :
99,999 + 1 =100000 ( This number is one lakh )
10 × 10000 = 100000
Let us consider 6 digit number in the expanded form for example.
8,56,243 = 8 × 100000 + 5 × 10000 + 6 × 1000 + 2 × 100 + 4 × 10 + 3 × 1.
This number has 3 in one's place,4 in ten's place,2 in hundred's place,6 in thousand's place,5 in ten thousands place and 8 in lakhs place and the number is "eight lakhs fifty six thousand two hundred and forty three".
Few more examples of expansion :
Number  Number Name  Expansion 
500000  Five Lakh  5 × 100000 
450000  Four Lakh Fifty Thousand  4 × 100000 + 5 × 10000 
398029  Three Lakh Ninety Eight Thousand and Twenty Nine 
3 × 100000 + 9 × 10000 + 8 × 1000 + 2 × 10 + 9 × 1 
 Introduction to larger numbers
 How to write large numbers  Introduction to comma system.
Example :
9,99,999 + 1 = 1000000 ( It is ten lakh )
Similarly, the greatest 7 digit number gives us the smallest 8 digit number.
99,99,999 + 1 = 10000000 ( It is one crore )
Pattern or sequence of numbers :
9+1  =  10 
99+1  =  100 
999+1  =  1000 
9,999+1  =  10000 
99,999+1  =  100000 
9,99,999+1  =  1000000 
99,99,999+1  =  10000000 
Indian system to numeration :
Values of the place in the Indian system of numeration are one's,ten's,hundred's, thousand's,ten thousand's,lakh,ten lakh,crore and so on.....
Following place value chart can be used to identify the digit in any place in the Indian system.
Periods  Crores  Lakhs  Thousands  Ones  
Places  Tens  Ones  Tens  Ones  Tens  Ones  Hundred  Tens  Ones 
International system of numeration:
Values of the places in international system of numeration are one's,ten's, hundred's,thousand's,ten thousand's,hundred thousand's,millions,ten million and so on....
Following place value chart can be used to identify the digit in any place in the international system.
Periods  Billions  Million  Thousand  Ones  
Places  Hundred  Tens  Ones  Hundred  Tens  Ones  Hundred  Tens  Ones  Hundred  Tens  Ones 
Comparison of the Indian and international system of numeration:
Indian numeration 
Crore  Ten Lakhs  Lakh  Ten thousand  Thousand  Hundred  Tens  Ones 

Numbers  10000000  1000000  100000  10000  1000  100  10  0 
International numeration 
Ten millions 
Million  Hundred Thousands 
Ten Thousands 
Thousand  Hundred  Tens  Ones 
Finding a value that is close enough to the right answer, usually with some thought or calculation involved.
Example: Rahul's estimation of 150 bricks to build a wall was very good as they were only 5 bricks left.
Estimation only finds the approximate value which is a value close to the actual value.
This method is commonly used to round off the numbers nearest to tens, hundreds, thousands and so on..... Estimating sum, difference, product and quotient
Estimating sum, difference, product and quotient
Example: let us consider numbers 14 and 18 on the number line.
14 lies between 10 and 20.we observe that the gap between 10 and 14 is less than the gap between 14 and 20 i.e., 14 is nearer to 10 than 20, so we round off 14 to 10,that is to the nearest ten.
Similarly, if we consider the number 18 which is more nearer to 20 than 10, we will round off 18 to 20 which is the nearest ten
First example shows rounding of 14 to the nearest ten.
Second example shows rounding of 18 to the nearest ten.
But if a number is equidistant from 10 and 20 both it is rounded off from 10 and 20.
Example: let us consider numbers 18652 and 53468.
a) Consider the digits in the thousands place of the given number.
b) If it is less than 5, replace the digits in thousands, hundreds, tens and ones by 0, keeping the digits in other places as they are.
c) If it is 5 or more than 5,replace the digits in thousands,hundreds,tens,and ones by 0 and increase the digit in ten thousands by 1.
i. 18652
Since, the digit in the thousands place is 8, and 8 > 5, so when rounded off the number nearest to ten thousand is 20000.
ii. 53468
In the number 53468, the digit in the thousands place is 3 and 3 < 5, so when rounded off the number nearest to ten thousand is 50000
Example :let us consider numbers 470518 and 621059
a) Consider the digits in the ten thousands place of the given number.
b) If it is less than 5, replace the digits in the ten thousands, thousands, hundreds, tens and ones by 0, keeping the digits in other places as they are.
c) If it is 5 or more than 5, replace the digits in ten thousands, thousands, hundreds, tens, and ones by 0 and increase the digit in lakhs by 1.
I. 470518
Since, the digit in the ten thousands place is 7 and 7 > 5, so the rounded off number is 500000.
II. 621059
In the number 621059, the digit in the ten thousands place is 2 and 2 < 5, so the rounded off number is 600000.