By studying this lesson, you will be able to,
● know the place value corresponding to the position of each digit in a whole number,
● know the value represented by each digit in a whole number and
● read and write in words numbers up to the billions period.
2.1 Place value
When writing numbers, we most often use the Hindu-Arabic number system. In this system, the ten digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 are used to write numbers.
When writing numbers, we most often use the Hindu-Arabic number system. In this system, the ten digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 are used to write numbers.
When writing numbers, we most often use the Hindu-Arabic number system. In this system, the ten digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 are used to write numbers.
As an example, the number ten is written as 10 using digits. The number ninety nine is written as 99 using digits. That is, the numbers 10 and 99 are written using two positions.
As an example, the number ten is written as 10 using digits. The number ninety nine is written as 99 using digits. That is, the numbers 10 and 99 are written using two positions.
As an example, the number ten is written as 10 using digits. The number ninety nine is written as 99 using digits. That is, the numbers 10 and 99 are written using two positions.
As an example, the number ten is written as 10 using digits. The number ninety nine is written as 99 using digits. That is, the numbers 10 and 99 are written using two positions.
Now, let us describe the place value corresponding to the position of each digit in a number and the value represented by each of the digits.
● Using thirty five beads, if chains containing ten beads each are made by threading the beads, there will be three chains of ten beads each, with five beads remaining.
The thirty five beads can be separated into three sets of ten beads each and five sets of one bead each.
That is,
Thirty five = 3 tens + 5 ones = 35
According to the above explanation, the 5 in 35 represents 5 ones. The position which 5 occupies is the 'ones place'. The place value of the position occupied by the digit 5 is taken as 1.
The 3 in 35 represents 3 tens. The position which 3 occupies is the 'tens place'. The place value of the position that the digit 3 occupies is 10.
In the following figure, each position has been marked using a square, and the position of each digit of 35 has been indicated.
We learnt that 35 = 3 tens + 5 ones.
In the same manner,
53 = 5 tens + 3 ones = 50 + 3,
65 = 6 tens + 5 ones = 60 + 5
and 99 = 9 tens + 9 ones = 90 + 9
That is, there is a value represented by a digit in a number, according to the position of the digit.
Now, let us find the value represented by each digit of 35.
The value represented by 3 in the number 35 = 3 tens = 30
The value represented by 5 in the number 35 = 5 ones = 5
The maximum value that can be represented by a digit in the ones place is 9.
The maximum value that can be represented by a digit in the tens place is 90.
The maximum number of counters that can be placed on a single rod of an abacus is 9.
Exercise 2.1
(1) Complete the following table.
2.2 Place value described further
The greatest number that can be written using two positions is 99. It has 9 tens and 9 ones. The number which is one greater than 99 is hundred.
The tens place and ones place are not sufficient to write the number hundred in digits. Hence the place value corresponding to the position to the left of the tens place is taken as 100 and that position is named as the hundreds place.
Therefore hundred is written using three positions as 100.
Now let us look at numbers which are written by using digits in three positions.
Several numbers which can be formed using the digits 2, 4 and 5 are given below. Consider the ways of using 5 in these numbers.
245 Two hundred forty five
254 Two hundred fifty four
524 Five hundred twenty four
In 245, the digit 5 is in the ones place.
The value represented by 5 in 245 = 5
ones = 5 In 254, the digit 5 is in the tens place.
The value represented by 5 in 254 = 5 tens = 50
In 524, the digit 5 is in the hundreds place.
The value represented by 5 in 524 = 5 hundreds = 500
It is clear that the value represented by 5 in the above numbers varies according to the position of 5.
The place value corresponding to the position of each digit in a number from right to left is respectively 1, 10, 100, 1000, 10000 etc.
Accordingly, when two successive digits of a number are considered, the place value corresponding to the position of the digit on the left is ten times the place value corresponding to the position of the digit on the right.
Now, let us name the positions that each of the digits 2, 4, 5, 6 and 7 occupies in the number 67524 by writing these digits in five positions.
67524 = 6 ten thousands + 7 thousands + 5 hundreds + 2 tens + 4 ones
Let us now consider the value represented by each digit in the number 67524.
4 is in the ones place of 67524.The value represented by 4 is 4.
2 is in the tens place of 67524. The value represented by 2 is 20.
5 is in the hundreds place of 67524. The value represented by 5 is 500.
7 is in the thousands place of 67524. The value represented by 7 is 7000.
6 is in the ten thousands place of 67524. The value represented by 6 is 60000.
Exercise 2.2
(1) In the number 99601,
(i) what is the value represented by 9, which is positioned fourth from the right?
(ii) what is the place value corresponding to the position of 0?
(iii) what is the value represented by 0 ?
(iv) what is the value represented by 9, which is positioned fifth from the right ?
(2) Complete the following table.
(3) Write down all the numbers of three positions, that can be written using each of the digits 4, 5 and 8 exactly once. For each of these numbers, write down the place value corresponding to the position of 8 and the value represented by 8.
(4) Using each of the digits 2, 4, 5 and 9 exactly once, write down, (i) the largest possible number of four positions and the value represented by each digit in that number. (ii) the smallest possible number of four positions and the value represented by each digit in that number.
2.3 Periods of numbers
The total number of students studying in several schools from grade 6 to 11 is 2836696.
See whether you can read the number of students given in the above statement. How numbers such as the above are read and written in words is described below.
Let us consider the number 2836696. Let us write this number by separating it into groups of three, starting from the ones place, as given below.
2 836 696
A group separated in the above manner is known as a period of numbers or number zone.
In this separation, the number of positions with digits in the last period, that is, the leftmost period, may be less than three. Only the digit 2 is in the last period of the above number.
Let us name the periods of this number as follows.
This number is read as two million eight hundred thirty six thousand six hundred ninety six.
Now, let us consider how the number 967476568 is read.
Let us first separate this number into periods from right to left as follows.
This number is read as nine hundred sixty seven million four hundred seventy six thousand five hundred sixty eight.
Let us also consider how the number 7686975623 is read. Let us first separate it into periods.
The period which comes after the millions period is named as the billions period.
This number is read as seven billion six hundred eighty six million nine hundred seventy five thousand six hundred twenty three.
To find out how the number 675278285676 is read, let us separate it into periods as follows.
This number is read as six hundred seventy five billion two hundred seventy eight million two hundred eighty five thousand six hundred seventy six.
Writing a number in this manner by separating it into groups of three positions, starting from the ones place and moving towards the left,is to represent the number in standard form.
Writing a number in this manner by separating it into groups of three positions, starting from the ones place and moving towards the left,is to represent the number in standard form.
Writing a number in this manner by separating it into groups of three positions, starting from the ones place and moving towards the left,is to represent the number in standard form.
The following table provides several examples of how numbers are read.The way of writing them in words is also the same.
The way of reading a number or writing a number in words is known as the name of the number.
In most financial documents, the amount is written down in words.
Exercise 2.3
(1) Write down each of the following numbers in standard form.
(i) 72350 (ii) 55000 (iii) 27201125 (iv) 300001279 (v) 299000001 (vi) 21345699
(2) Write down each of the following numbers which have been separated into periods in words.
(3) Write down each of the following numbers in standard form and then write them in the table separated into periods.
(i) 76735 (ii) 864657 (iii) 2769812 (iv) 47867619 (v) 763156561 (vi) 6746971256 (vii) 2765231
(4) Write down each of the following numbers in standard form and write down the name of the number as well.
(i) 50800435000 (ii) 43050800500 (iii) 585000430 (iv) 300001283 (v) 299000003 (vi) 272000023 (vii) 100200030000 (viii) 553000000 (ix) 47000005
(5) Write the following numbers, which have been given in words in standard form.
(i) Four hundred five thousand
(ii) Three hundred twenty five thousand five hundred
(iii) Four million eight hundred thousand
(iv) Six billion sixty million
(v) Eighteen million twenty four thousand fifty
(6)The distance between the earth and the sun is 149597870 in kilometers. Write this number in standard form and write it in words too.
(7) A businessman plans to deposit Rs 15006500 in a bank. How does he write this amount in word on a bank slip?
Miscellaneous Exercise
(1) Write down each of the following numbers by expanding in terms of the place value as shown in the example.
Example: 6745 = 6 thousands + 7 hundreds + 4 tens + 5 ones
(i) 24 (ii) 40 (iii) 546 (iv) 7163 (v) 92651
(2) Complete the following table.
(3) Using each of the digits 8, 6, 5, 3 and 1 exactly once, write down
(i) the largest possible number of four positions and the value represented by 3 in the number.
(ii) the smallest possible number of four positions and the value represented by 3 in the number.
(4) Write the following numbers in standard form and write also how they are read.
(i) 450050 (ii) 37504537 (iii) 212345699 (iv) 8432109640 (v) 2003040050 (vi) 143021000
(5) What is the smallest number that can be written using three different digits, which has the millions period as its last period? Write this number in words too.
(6) What is the greatest number, which has the billions period as its last period? Write this number in words too.
