New Countdown Book-4

 

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Numbers and Arithmetic Operations

In this unit students will learn to: •  identify place values of digits up to one hundred million •  read and write numbers in words and numerals up to one hundred million •  compare and order numbers up to 8 digits •  add and subtract numbers up to 6 digits •  •  •  • 

multiply numbers up to 5 digits by numbers up to 3 digits divide numbers up to 4 digits by numbers up to 2 digits solve simple sums involving four operations solve real-life problems involving four operations

 MA  MATHS FLASH You have already learnt: • to to   read and write numbers in words and figures up to 6 digits • to to   identify place value of numbers up to 6 digits • to to   compare and order 6-digit numbers • to to   represent numbers on a number line • to to   add and subtract numbers up to 4 digits • to to   multiply and divide 2-digit numbers by a 1-digit number

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KEY  vocabulary million, place value, compare, order, operation, multiplier, multiplicand, product, divisor, dividend, quotient, remainder, commutative law

Numbers and Arithmetic Operations   1

 

Numbers Now we will work with numbers up to 9 digits that is hundred million. Let us consider the following place value chart. Millions HM

1

TM

Thousands HTh T Th 1 0

M

Ones

Th 0

H 0

T 0

U 0

 6-digit number

1

0

0

0

0

0

0

 7-digit number

1

0

0

0

0

0

0

0

 8-digit number

0

0

0

0

0

0

0

0

 9-digit number

From the above chart we conclude that as the number of digits increases the value of the number also increases. A 7-digit number is a million, 8-digit number is ten million, and 9-digit number is hundred million. Now as an example consider a 7-digit number 2 489 652 and place it in the place value chart. M

HTh TTh

2

4

Th

H

T

U

9

6

5

2

8

This shows that a 7-digit number goes up to one million. When we place 23,896,108 in a place value chart we notice that a 8-digit number goes up to ten million. TM 2

M 3

HTh TTh 8 9

Th 6

H 1

T 0

U 8

While a 9-digit number 630 057 789 goes up to hundred million.

1

HM

TM

M

6

3

0

Numbers and Arithmetic Operations

HTh TTh 0

5

2

Th

H

T

U

7

7

8

9

1

 

 Examples::  Examples

1.  Write 682 952 602 in words.  Solutio n  Solution

First place the number in the place value chart.

HM

TM

M

6

8

2

HTh TTh 9

5

Th

H

T

U

2

6

0

2

Now we can easily write the number in word as: Six hundred and eighty-two million, nine hundred and fifty-two thousand, six hundred and two. 2.  Write the given number in figures:

 

Twenty five million, nine hundred and nine thousand, four hundred and thirty-seven.

 Soluti  Solution: on:

Make a place value chart and write the number in it. TM

M

2

5

HTh TTh 0

9

Th

H

T

U

9

4

3

7

Hence the required number is 25 909 437. 3. 3.   Write the value of the ringed digit in the number 489 8 3 2 416  Solution: n:  Solutio

Place the number in the place value chart. HM TM M HTh TTh Th 4

8

9

8

3

2

H

T

U

4

1

6

The value of 3 is thirty thousand or 30 000. 4.  Write the number 469 825 136 in expanded form.  Solutio n:  Solution:

400 000 000 + 60 000 000 + 9 000 000 + 800 000 + 20 000 + 5000 + 100 + 30 + 6

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3

Numbers and Arithmetic Operations   1

 

5.  The given number is written in expanded form, find the value. 5.    500 000 000 + 90 000 000 + 6 000 000 + 000 000 + 20 000 + 1000 + 500 + 40 + 1  Solution:  Soluti on:

The required value can be obtained by adding up all the numbers vertically. The required number is 596 021 541

Comparing and ordering 8-digit numbers Comparing numbers is the same as knowing which number is smaller and which number is the bigger. Let us take an example of two 6-digit numbers, 698 721 and 698 831 To compare these numbers, follow the given steps. numbers bers in it 1.  Make a place value chart and write both the num HTh

TTh

Th

H

T

U

6

9

8

7

2

1

6 9 8 8 3 1 2.  Now check the place value of e each ach digit starting from the largest place – hundred thousand.

3.  We see that the numbers in HTH, TTH and Th are equal, but in the 3.  hundred place, 8 hundred is greater than 7 hundred which makes 698 831 greater than 698 721. 4.  Symbolically, it is denoted as 698, 831

>

698 721.

The open side of the symbol indicates the greater number. Now, let us compare two 8-digit numbers, 46 251 881 and 46 270 430. Following the steps we write the numbers in the place values TM

M

HTh TTh

4

6,

2

4

6,

2

Th

H

T

U

5

1,

8

8

1

7

0,

4

3

0

Starting from the left we find that 70 thousand in greater than 50 thousand.

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Numbers and Arithmetic Operations

4

1

 

Therefore, or

46 270 430 > 46 261 881 46 251 881  73 921 516 > 73 921 016

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Numbers and Arithmetic Operations   1

 

 Exercise 1a   1. 1.   Fill in the blanks.   a.  In 49 8 52 610, the place value of the ringed digit is .   b.  5 000 000 + 200 000 + 00 000 + 0 0000 000 + 400 + 50 + 9 =      

.

c.  Insert space to express 725895213 in International number system. . d.  The predecessor of 8 001 001 is . 316 6 999 is . e.  The successor of 2 31

  2.  State whether the following are true or false.   a.  The predecessor of 60 000 000 is 60 000 999. ( )   b.  The successor to 189 561 100 is 189 561 200. ( ) numbe er at on one e milli illion on pl plac ace e ha hass si six x zero zeroes es on it itss righ right. t. (   c.  A numb   d.  Place value is the value of the position of a digit in a number. ( )

)

  e.  The place value of 6 in 10 682 817 is 600 000. ( ) correctt answer from the given options.   3.  3.  Select the correc   a.  The predecessor of 61 15 999 is   6 015 999 6 115 989 6 115 998 6 116 000   b.  Eighty million, four hundred and ninety thousand in figures is   80 490 000 80 400 9000   804 900 000 8 049 000 successor of 5 49 62 111 is   c.  The successor   55 062 111 64 962 111   54 962 101 54 962 112              

d.  8 463 11 110 0 written in expanded form is 8 + 463 + 110 8 000 000 + 400 000 + 60 000 + 3000 + 100 + 10 800 000 + 400 + 60 + 3 + 100 + 10 800 000 + 40 000 + 6000 + 300 + 10 843 43 002 is e.  The predecessor of 7 8 7 843 001 7 834 000 7 835 002 8 834 003

  4.  Write the given numbers in words. a.  3 000 000 b.  b.  140 000 000 c. c.   217 000 000  

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Numbers and Arithmetic Operations

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d.  50 000 000

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  5. 5.   Write in figures with correct spac spacings. ings.   a.  Nine million b.  Twenty four million c.    c.  Seven hundred and five million d.  Ten million 9 hundred   6.  Write the given numbers in words. a.  1 289 056 b.  27 389 100 c.  613 421 005  

d.  497 560

  7.  Write the place value of the circled digit.   a. a.   7   8 9 452 100 b. b.   14 0 09 838   c.  25   6  943 100 d.  86 24   7   120   8.  8.  Write the predecessor of:   a.  60 129 808   c.  256 943 100

b.  497 215 010 d.  630 713 455

  9.  9.  Write the successors of:   a.  146 780 000   c.  871 600 009

b.  59 899 989 d.  106 343 201

  10.  a.  Write the017 num numbers bers in expande expanded d form: 200 00 b.  83 153 206 a.  7 2   c.  917 245 985 d.  164 205 789  11. 1.   Fill the blank with >,