7VM Class 07 | Ganit Prakash | Ch 1 Large Numbers Around
7VM Class 07 | Ganit Prakash | Ch 01 Large Numbers Around
Mangalyaan: India's Budget Space Mission
India's first interplanetary mission, Mangalyaan (Mars Orbiter Mission), was launched in 2013. Remarkably, it cost just 450 crore about 4,50,00,00,000 rupees-making it one of the most economical Mars missions ever. Over its journey, the spacecraft travelled nearly 65 crore km to reach Mars, far more cost-effectively than similar missions by other space agencies.
Number Names: Indian Systern
Number Name
1 One
10 Ten
100 Hundred
1,000 One thousand
10,000 Ten thousand
1,00,000 One lakh
10,00,000 Ten lakh
1,00,00,000 One crore
10,00,00,000 Ten crore
1,00,00,00,000 One Arab
10,00,00,00,000 Ten Arab
1,00,00,00,00,000 One kharab
10,00,00,00,00,000 Ten kharab
Reading and Writing Numbers
★ Read and Write each of the numbers given below in words:
(a) 17,45,000
(b) 65,24,003
(c) 8,23,90,510
(d) 8,09,01,405
(e) 3,50,00,601
(f) 90,24,03,107
(g) 5,17,45,000
(h) 7,65,24,003
(i) 78,23,90,510
(j) 68,09,01,405
(k) 3,00,600
(l) 5,04,085
(m) 27,30,000
(n) 70,53,138
Write the corresponding number in the Indian place value system for each of the following:
(a) Seventeen lakh forty-five thousand
(b) Sixty-five lakh twenty-four thousand three
(c) Eight crore twenty-three lakh ninety thousand five hundred ten
(d) Eight crore nine lakh one thousand four hundred five
(e) Three crore fifty lakh six hundred one
(f) Ninety crore twenty-four lakh three thousand one hundred seven
(g) Five crore seventeen lakh forty-five thousand
(h) Seven crore sixty-five lakh twenty-four thousand three
(i) Seventy-eight crore twenty-three lakh ninety thousand five hundred ten
(j) Sixty-eight crore nine lakh one thousand four hundred five
(k) Three lakh six hundred
(l) Five lakh four thousand eighty-five
(m) Twenty-seven lakh thirty thousand
(n) Seventy lakh fifty-three thousand one hundred thirty-eight
(o) One lakh twenty three thousand four hundred and fifty six
(p) Four lakh seven thousand seven hundred and four
(q) Fifty lakhs five thousand and fifty
(r) Ten lakhs two hundred and thirty five
★ Read each of the numbers given below in words:
(a) 17,45,000
(b) 65,24,003
(c) 8,23,90,510
(d) 8,09,01,405
(e) 3,50,00,601
(f) 90,24,03,107
(g) 5,17,45,000
(h) 7,65,24,003
(i) 78,23,90,510
(j) 68,09,01,405
(k) 3,00,600
(l) 5,04,085
(m) 27,30,000
(n) 70,53,138
Expanded Form
Break the number into parts based on their place values.
756219 = 700000 + 50000 + 6000 + 200 + 10 + 9
★ Write the following numbers in expanded form:
(a) 17,45,000
(b) 65,24,003
(c) 8,23,90,510
(d) 8,09,01,405
(e) 3,50,00,601
(f) 90,24,03,107
(g) 5,17,45,000
(h) 7,65,24,003
(i) 78,23,90,510
(j) 68,09,01,405
(k) 3,00,600
(l) 5,04,085
(m) 27,30,000
(n) 70,53,138
★ A different kind of calculator
Two of the many different ways to get 5072 are shown below:
These two ways can be expressed as:
(a) (50x100) + (7×10) + (2 × 1) = 5072
(b) (3×1000) + (20×100) + (72×1) = 5072
★ Find a different way to get 5072 and write an expression for the same.
Figure it Out
For each number given below, write expressions for at least two different ways to obtain the number through button clicks.
Think like Chitti and be creative.
(a) 8300
(b) 40629
(c) 56354
(d) 66666
(e) 367813
Land of Tens
In the Land of Tens, there are special calculators with special buttons.
1. The Thoughtful Thousands only has a +1000 button. How many times should it be pressed to show:
(a) Three thousand? 3 times
(b) 10,000? ____________
(c) Fifty three thousand? ___________
(d) 90,000? ______________
(e) One Lakh? ________________
(f) ____________? 153 times
(g) How many thousands are required to make one lakh?
2. The Tedious Tens only has a +10 button. How many times should it be pressed to show:
(a) Five hundred? _____________
(b) 780? _________
(c) 1000? _________
(d) 3700? ________
(e) 10,000? ___________
(f) One lakh? _____________
(g) ____________? 435 times
3. The Handy Hundreds only has a +100 button. How many times should it be pressed to show:
(a) Four hundred? ___________times
(b) 3,700? ________
(c) 10,000? __________
(d) Fifty three thousand? __________
(e) 90,000? __________
(f) 97,600? __________
(g) 1,00,000? __________
(h) _________? 582 times
(i) How many hundreds are required to make ten
thousand?
(j) How many hundreds are required to make one lakh?
(k) Handy Hundreds says, “There are some numbers which Tedious Tens and Thoughtful Thousands can’t show but I can.” Is this statement true? Think and explore.
▲ Ascending vs Descending Order
Ascending Order (Small → Big): It is also known as Increasing Order.
Descending Order (Big→ Small): It is also known as Decreasing Order.
Face Value vs Place Value
Face Value => The Name of digit itself
Place Value => The digit value of its position or period.
Example: In 756219,
Face value of 5 = 5
Place value of 5 = 50000
Face value of 6 = 6
Place value of 6 = 6000
Successor and Predecessor
Successor => Next number (Add 1 to get successor)
Successor of 99 = 99 + 1 = 100
Predecessor => Just before (Subtract 1 to get Predecessor)
Predecessor of 1,00 = 100 –1 = 99
Place Values (International or American System)
Number Name
One 1
Ten 10
Hundred 100
Thousand 1,000
Ten Thousand 10,000
Hundred Thousand 100,000
Million 1,000,000
Ten Million 10,000,000
Hundred Million 100,000,000
Billions 1,000,000,000
Ten Billions 10,000,000,000
Hundred Billions 100,000,000,000
Trillian 1,000,000,000,000
LARGE NUMBERS
1-Digit Numbers
0,1,2, to 9
2-Digit Numbers
10, 11, 12 to 99
3-Digit Numbers
100, 101, 102 to 999
4-Digit Numbers
1000, 1001, 1002 to 9999
5-Digit Numbers
10000, 10001, 10002 to 99999
6-Digit Numbers
100000, 100001, 100002 to 999999
7-Digit Numbers
1000000, 1000001, 1000002 to 9999999
8-Digit Numbers
10000000, 10000001, 10000002 to 99999999
Concept Highlights
★ 10,00,000 is the smallest 7-digit number, called Ten lakh.
★ 99,99,999 is the largest 7-digit number.
★ 1,00,00,000 is the smallest 8-digit number, called One crore.
★ 9,99,99,999 is the largest 8-digit number.
★ 10,00,00,000 is the smallest 9-digit number, called Ten crore.
★ 99,99,99,999 is the largest 9-digit number.
★ 1,00,00,00,000 is the smallest 10-digit number, called One arab.
6. Form the smallest and greatest 7-digit numbers using all digits only once.
(a) 3,0, 9, 2, 8, 7, 4
(b) 5, 6, 1, 3, 0, 2, 9
How many zeros does a hundred thousand have?
The number 9876501234 can be easily read by placing commas first:
(a) 9,87,65,01,234 9 arab 87 crore 65 lakhs 1 thousand and 234 or 987 crore 65 lakh 1 thousand 234 (in the Indian system).
(b) 9,876,501,234 9 billion 876 million 501 thousand 234 (in the American system).
Figure it Out
1. Read the following numbers in Indian place value notation and write their number names in both the Indian and American systems:
(a) 4050678
(b) 48121620
(c) 20022002
(d) 246813579
(e) 345000543
(f) 1020304050
2. Write the following numbers in Indian place value notation:
(a) One crore one lakh one thousand ten
(b) One billion one million one thousand one
(c) Ten crore twenty lakh thirty thousand forty
(d) Nine billion eighty million seven hundred thousand six hundred
3. Compare and write '<', '>' or '':
(a) 30 thousand _______ 3 lakhs
(b) 500 lakhs _______ 5 million
(c) 800 thousand _______ 8 million
(d) 640 crore _______ 60 billion
We shall come across even bigger numbers in later grades.
★ All large numbers are read using place values: lakh, crore, and so on.
★ Expanded form means breaking a number into sums based on place values.
EXACT AND APPROXIMATE VALUES
Rounding Up and rounding Down
There are two situations where it makes sense to round up and rounding down a number.
Rounding Up –> Rounding up is when the approximated number is more than the actual number.
For example, if a school has 843 people including students, teachers and staff: the principal might order 850 sweets instead of 800 sweets.
Rounding Down –> Rounding Down is when the approximated number is less than the actual number.
For example, if the cost of an item is ₹470, the shopkeeper may say that the cost is around ₹450 instead of saying it is around ₹500.lmk
There are situations where it is better to round down (rounding down is when the approximated number is less than the actual number).
? Think and share situations where it is appropriate to
(a) round up,
(b) round down,
(c) either rounding up or rounding down is okay and
(d) when exact numbers are needed.
★ In real life, we often don't need the exact number-a close estimate works just fine! Where do we use approximations?
★ The library has about 12,000 books. (The actual number is 12.378.)
★ The truck has a weight of nearly 3000 kilograms. (The actual weight is 3145 kilograms.)
★ Over 50,000 people visited the fair. (The actual number is 50,286.)
★ Close to 5200 runners participated in the city marathon. (The actual number is 5214.)
★ These are rounded numbers-easy to remember and useful for general information.
Rules to round a number:
Look at the digit immediate right to the place you want to round:
★ If it's 5 or more, round up. Increase the rounding digit by 1 and digits to its right becomes 0.
★ If it's 4 or less, round down. The rounding digit stays the same and digits to its right becomes 0.
Example: Round 6,74,38,291.
Rounded to the Nearest
Number to be Rounded
Rounded Value
Thousand
6,74,38.291
6,74,38,000
Ten Thousand
6,74,38,291
6,74,40,000
Lakh
6,74,38,291
6,74,00,000
Ten Lakh
6,74,38,291
6,70,00,000
Crore
6,74,38,291
Let us compare the exact and approximate values rounded to their highest places of numbers.
Example
Exact Value
Approximate Value
12,378
Books in a school library
12,000
Visitors at a science fair
49,286
50,000
Weight of a truck
3145 kg
3000 kg
Runners in a city marathon
5214
5000
Concept Highlights
➤Indian vs International Numeration System: Grouping and names differ-lakh vs million, crore vs billion.
➤ Place Value Grouping: Indian: 3, 2, 2...; International: 3, 3, 3... from right.
Exact vs Approximate Values: We round numbers for simplicity. Round up if digit to the right is 5 or more, else round down.
Estimation in Real Life: Approximations help communicate big data quickly and clearly.
Similarly, write the five nearest neighbours for these numbers:
(a) 3,87,69,957
(b) 29,05,32,481
Math Talk ?
I have a number for which all five nearest neighbours are 5,00,00,000. What could the number be? How many such numbers are there?
Roxie and Estu are estimating the values of simple expressions.
1. 4,63,128 + 4,19,682,
Roxie: "The sum is near 8,00,000 and is more than 8,00,000."
Estu: "The sum is near 9,00,000 and is less than 9,00,000."
(a) Are these estimates correct? Whose estimate is closer to the sum?
(b) Will the sum be greater than 8,50,000 or less than 8,50,000? Why do you think so?
(c) Will the sum be greater than 8,83,128 or less than 8,83,128? Why do you think so?
(d) Exact value of 4,63,128 + 4,19,682 =
2. 14,63,128 – 4,90,020
Roxie: "The difference is near 10,00,000 and is less than 10,00,000."
Estu: "The difference is near 9,00,000 and is more than 9,00,000."
(a) Are these estimates correct? Whose estimate is closer to the difference?
(b) Will the difference be greater than 9,50,000 or less than 9,50,000? Why do you think so?
(c) Will the difference be greater than 9,63,128 or less than 9,63,128? Why do you think so?
(d) Exact value of 14,63,128-4,90,020 =
1.5 Patterns in Products
Roxie and Estu are playing with multiplication. They encounter an interesting technique for multiplying a number by 10, 100, 1000, and so on.
A Multiplication Shortcut
Roxie evaluated 116 × 5 as follows: 58
= 116 × 5
= (116 × 10)/ 2
= 58 × 10
= 580.
N × 5 = = (N × 10)/ 2
Estu evaluated
824 × 25 as follows:
824 × 25 20600.
= (824 × 100)/4
= 206
? Using the meaning of multiplication and division, can you explain why multiplying by 5 is the same as dividing by 2 and multiplying by 10?
Math Talk
? Figure it Out
1. Find quick ways to calculate these products:
(a) 2 * 1768 * 50
(b) 72 × 125 [Hint: 125 = 1000 1 8
(c) 125 × 40 × 8 × 25
2. Calculate these products quickly.
(a) 25 × 12 =
(b) 25 × 240 =
(c) 250 × 120 =
(d) 2500 × 12 =
(e) ____ × ______ = 1200000000
How Long is the Product?
In each of the following boxes, the multiplications produce interesting patterns. Evaluate them to find the pattern. Extend the multiplications based on the observed pattern.
Practice Time 1
1. Choose the correct answer.
(a) The smallest 7-digit number is:
(1) 9,99,999
(ii) 10,00,000
(iii) 1,00,000
(b) How many digits does the number 8,40,50,309 have?
(i) 6
(ii) 8
(iii) 9
(c) The place value of 2 in 4,82,73,610 is:
(i) 20,00,000
(ii) 2,00,000
(iii) 2,00,00,000
2. Rewrite the following numbers in the Indian Number System with commas. Also write number names.
(a) 1745000
(b) 6524003
(c) 82390510
(d) 80901405
(e) 35000601
(f) 902403107
(g) 51745000
(h) 76524003
(i) 782390510
(j) 680901405
3. Rewrite the following numbers in the International Number System with commas. Also write.
(a) 1745000
(b) 6524003
(c) 82390510
(d) 80901405
(e) 35000601
(f) 902403107
(g) 51745000
(h) 76524003
(i) 782390510
(j) 680901405
4. Expand the numbers.
(a) 1745000
(b) 6524003
(c) 82390510
(d) 80901405
(e) 35000601
(f) 902403107
(g) 51745000
(h) 76524003
(i) 782390510
(j) 680901405
5. Write the place value and face value of the underlined digit.
(a) 1745000
(b) 6524003
(c) 82390510
(d) 80901405
(e) 35000601
(f) 902403107
(g) 51745000
(h) 76524003
(i) 782390510
(j) 680901405
5. Arrange in ascending and descending order.
(a) 98,21,045; 10,00,000; 1,20,25,000; 50,00,010
(b) 45,10,789; 45,10,788; 1,00,00,000
6. Form the smallest and greatest 7-digit numbers using all digits only once.
(a) 3,0, 9, 2, 8, 7, 4
(b) 5, 6, 1, 3, 0, 2, 9
7. Write the standard numeral.
(a) 30,00,000 + 4,00,000 + 2000 + 60 + 8
(b) 3,00,00,000 + 70,00,000 + 50,000 + 3000 + 400 + 2
8. Creative Thinking Create a 9-digit number using only odd digits. Then, write it in words and expand it.
9. Analytical Thinking Tara said, "In the number 45,07,623, the digit 5 is in the lakhs place and has a value of 5,00,000." Her friend replied, "No, 5 is in the thousands place." Who is correct? Explain using the place value chart.
10. A government housing project was announced for 70,000 people. If 1000 people are allotted homes every week, in how many weeks will everyone receive their home?
11. A state government budgeted 28,74,00,000 for building 200 new classrooms across schools. If each classroom costs the same, what is the cost of building one classroom?
Figure it Out
1. According to the 2011 Census, the population of the town of Chintamani was about 75,000. How much less than one lakh is 75,000?
2. The estimated population of Chintamani in the year 2024 is 1,06,000. How much more than one lakh is 1,06,000?
3. By how much did the population of Chintamani increase from 2011 to 2024?
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