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Std 5 Mathematics · Chapter 2

2. Number Work

Solutions to Problem Sets 2 to 6 — six- and seven-digit numbers, place value, expanded form and comparison. Maharashtra State Board (Balbharati), Grade Five Mathematics, Part One.

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Key Idea: The Indian Place-Value Chart

Places from right to left: Units → Tens → Hundreds → Thousands → Ten thousands → Lakhs → Ten lakhs → Crores.
Commas: the first comma comes after three digits from the right (thousands), then after every two digits (lakhs, crores). Example: 27,65,043.
Reading: read ten lakhs and lakhs together, and ten thousands and thousands together. 18,35,614 is eighteen lakh thirty-five thousand six hundred and fourteen.
Writing in figures: fill every place. If a place has nothing, write 0 there. Eight lakh nine thousand and forty-three is 8,09,043, not 89043.

1 lakh = 1,00,000 = 100 thousand. 10 lakh = 10,00,000 = 1 million. 1 crore = 1,00,00,000.

Problem Set 2

1Using the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 write ten each of two-, three-, four- and five-digit numbers. Read the numbers.

Answers will vary. Here is one set of examples:

  • Two-digit: 10, 23, 37, 45, 58, 61, 74, 89, 92, 96
  • Three-digit: 105, 234, 360, 417, 529, 648, 703, 815, 987, 990
  • Four-digit: 1,024; 2,359; 3,480; 4,617; 5,092; 6,735; 7,208; 8,461; 9,053; 9,876
  • Five-digit: 10,293; 23,456; 34,078; 45,610; 56,789; 60,512; 71,304; 82,945; 90,617; 98,765

Reading examples: 45 is forty-five; 648 is six hundred and forty-eight; 7,208 is seven thousand two hundred and eight; 60,512 is sixty thousand five hundred and twelve.

A two-digit number cannot begin with 0, so 05 is not a two-digit number. The same applies to three-, four- and five-digit numbers.

2Fill in the blanks in the table below.
No.Devanagari numeralsInternational numeralsNumber written in words
(1)२,३५९2,359Two thousand, three hundred and fifty-nine
(2)३२,७५६32,756Thirty-two thousand, seven hundred and fifty-six
(3)६७,८५९67,859Sixty-seven thousand, eight hundred and fifty-nine
(4)१,०३४1,034One thousand and thirty-four
(5)२७,८९५27,895Twenty-seven thousand, eight hundred and ninety-five

Answers filled in are in bold. Row (1) is the example given in the textbook.

3As a part of the ‘Avoid Plastic Project’, Zilla Parishad schools made and provided paper bags to provision stores and greengrocers. Read the talukawise numbers of the bags and write the numbers in words.
  1. Kopargaon — 12,740: Twelve thousand seven hundred and forty
  2. Shevgaon — 28,095: Twenty-eight thousand and ninety-five
  3. Karjat — 31,608: Thirty-one thousand six hundred and eight
  4. Sangamner — 10,972: Ten thousand nine hundred and seventy-two
4How many rupees do they make?

(1) 20 notes of 1000 rupees, 5 notes of 100 rupees and 14 notes of 10 rupees.

20 × 1000 = 20,000 rupees
5 × 100 = 500 rupees
14 × 10 = 140 rupees
Total: 20,000 + 500 + 140 = 20,640 rupees

(2) 15 notes of 1000 rupees, 12 notes of 100 rupees, 8 notes of 10 rupees and 5 coins of 1 rupee.

15 × 1000 = 15,000 rupees
12 × 100 = 1,200 rupees
8 × 10 = 80 rupees
5 × 1 = 5 rupees
Total: 15,000 + 1,200 + 80 + 5 = 16,285 rupees
5Write the biggest and the smallest five-digit numbers that can be made using the digits 4, 5, 0, 3, 7 only once.

Biggest number: arrange the digits from the biggest to the smallest — 7, 5, 4, 3, 0. The biggest number is 75,430.

Smallest number: arranging from smallest to biggest gives 0, 3, 4, 5, 7. But a number cannot begin with 0, so put the next smallest digit, 3, first and 0 second. The smallest number is 30,457.

6The names of some places and their populations are given below. Use this information to answer the questions that follow.
Tala: 40,642 · Gaganbawada: 35,777 · Bodhwad: 91,256 · Moregaon: 87,012 · Bhamragad: 35,950 · Velhe: 54,497 · Ashti: 76,201 · Washi: 92,173 · Morwada: 85,890

(1) Which place has the greatest population? What is its population?

The biggest ten-thousands digit is 9, in Bodhwad (91,256) and Washi (92,173). Comparing the thousands digits, 2 > 1. So Washi has the greatest population, 92,173.

(2) Which place, Morwada or Moregaon, has the greater population?

Morwada: 85,890; Moregaon: 87,012. Both have 8 ten thousands; in the thousands place 7 > 5. So Moregaon has the greater population.

(3) Which place has the smallest population? How much is it?

The smallest ten-thousands digit is 3, in Gaganbawada (35,777) and Bhamragad (35,950). The thousands digits are both 5; in the hundreds place 7 < 9. So Gaganbawada has the smallest population, 35,777.

Problem Set 3

1Read the numbers and write them in words.
  1. 7,65,234 — Seven lakh sixty-five thousand two hundred and thirty-four
  2. 4,73,225 — Four lakh seventy-three thousand two hundred and twenty-five
  3. 3,27,001 — Three lakh twenty-seven thousand and one
  4. 8,75,375 — Eight lakh seventy-five thousand three hundred and seventy-five
  5. 1,50,437 — One lakh fifty thousand four hundred and thirty-seven
  6. 2,03,174 — Two lakh three thousand one hundred and seventy-four
  7. 6,47,851 — Six lakh forty-seven thousand eight hundred and fifty-one
  8. 9,00,999 — Nine lakh nine hundred and ninety-nine
  9. 5,75,010 — Five lakh seventy-five thousand and ten
  10. 4,03,005 — Four lakh three thousand and five
2Read the numbers and write them in figures.
  1. One lakh thirty-five thousand eight hundred and fifty-five = 1,35,855
  2. Seven lakh twenty-seven thousand = 7,27,000
  3. Four lakh twenty-five thousand three hundred = 4,25,300
  4. Nine lakh nine thousand ninety-nine = 9,09,099
  5. Seven lakh forty-nine thousand three hundred and sixty-two = 7,49,362
  6. Eight lakh = 8,00,000

Check the zeros: in (4) there are no ten thousands and no hundreds, so 0 goes in both those places — 9,09,099.

3Make five six-digit numbers, each time using any of the digits 0 to 9 only once.

Answers will vary. No digit is repeated within a number, and 0 is never placed first. Examples:

  1. 1,02,345 — One lakh two thousand three hundred and forty-five
  2. 3,68,907 — Three lakh sixty-eight thousand nine hundred and seven
  3. 4,59,120 — Four lakh fifty-nine thousand one hundred and twenty
  4. 7,25,068 — Seven lakh twenty-five thousand and sixty-eight
  5. 9,86,543 — Nine lakh eighty-six thousand five hundred and forty-three

Problem Set 4

1Read the numbers and write them in words.
  1. 25,79,899 — Twenty-five lakh seventy-nine thousand eight hundred and ninety-nine
  2. 30,70,506 — Thirty lakh seventy thousand five hundred and six
  3. 45,71,504 — Forty-five lakh seventy-one thousand five hundred and four
  4. 21,09,900 — Twenty-one lakh nine thousand nine hundred
  5. 43,07,854 — Forty-three lakh seven thousand eight hundred and fifty-four
  6. 50,00,000 — Fifty lakh
  7. 60,00,010 — Sixty lakh and ten
  8. 70,00,100 — Seventy lakh one hundred
  9. 80,01,000 — Eighty lakh one thousand
  10. 90,10,000 — Ninety lakh ten thousand
  11. 91,00,000 — Ninety-one lakh
  12. 99,99,999 — Ninety-nine lakh ninety-nine thousand nine hundred and ninety-nine
2Given below are the deposits made in the Women’s Co-operative Credit Societies of some districts. Read those figures.
  1. Pune — ₹ 94,29,408: Ninety-four lakh twenty-nine thousand four hundred and eight rupees
  2. Nashik — ₹ 61,07,187: Sixty-one lakh seven thousand one hundred and eighty-seven rupees
  3. Nagpur — ₹ 46,53,570: Forty-six lakh fifty-three thousand five hundred and seventy rupees
  4. Ahmadnagar — ₹ 45,43,159: Forty-five lakh forty-three thousand one hundred and fifty-nine rupees
  5. Aurangabad — ₹ 37,01,282: Thirty-seven lakh one thousand two hundred and eighty-two rupees
  6. Yavatmal — ₹ 27,72,348: Twenty-seven lakh seventy-two thousand three hundred and forty-eight rupees
  7. Sindhudurg — ₹ 58,49,651: Fifty-eight lakh forty-nine thousand six hundred and fifty-one rupees

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Problem Set 5

1Write the place value of the underlined digit.
  1. 78,95,210 — the digit 7 is in the ten lakhs place, so its place value is 70,00,000
  2. 14,95,210 — the digit 4 is in the lakhs place, so its place value is 4,00,000
  3. 3,52,749 — the digit 5 is in the ten thousands place, so its place value is 50,000
  4. 50,000 — the digit 0 is in the units place, so its place value is 0
  5. 89,99,988 — the digit 9 is in the ten thousands place, so its place value is 90,000

The place value of 0 is always 0, whichever place it is in.

2Write the numbers in their expanded form.
  1. 56,43,215 = 50,00,000 + 6,00,000 + 40,000 + 3,000 + 200 + 10 + 5
  2. 70,815 = 70,000 + 800 + 10 + 5
  3. 8,35,999 = 8,00,000 + 30,000 + 5,000 + 900 + 90 + 9
  4. 8,88,889 = 8,00,000 + 80,000 + 8,000 + 800 + 80 + 9
  5. 92,32,992 = 90,00,000 + 2,00,000 + 30,000 + 2,000 + 900 + 90 + 2
3Write the place name and place value of each digit in the following numbers.

(1) 35,705

  • 3 — Ten thousands place — place value 30,000
  • 5 — Thousands place — place value 5,000
  • 7 — Hundreds place — place value 700
  • 0 — Tens place — place value 0
  • 5 — Units place — place value 5

(2) 7,82,899

  • 7 — Lakhs place — place value 7,00,000
  • 8 — Ten thousands place — place value 80,000
  • 2 — Thousands place — place value 2,000
  • 8 — Hundreds place — place value 800
  • 9 — Tens place — place value 90
  • 9 — Units place — place value 9

(3) 82,74,508

  • 8 — Ten lakhs place — place value 80,00,000
  • 2 — Lakhs place — place value 2,00,000
  • 7 — Ten thousands place — place value 70,000
  • 4 — Thousands place — place value 4,000
  • 5 — Hundreds place — place value 500
  • 0 — Tens place — place value 0
  • 8 — Units place — place value 8
4The expanded form of the number is given. Write the number.
  1. 60,000 + 4000 + 600 + 70 + 9 = 64,679
  2. 9,00,000 + 20,000 + 7000 + 800 + 5 = 9,27,805
  3. 20,00,000 + 3,00,000 + 60,000 + 9000 + 500 + 10 + 7 = 23,69,517
  4. 7,00,000 + 80,000 + 4000 + 500 = 7,84,500
  5. 80,00,000 + 50,000 + 1000 + 600 + 9 = 80,51,609

In (4) there are no tens or units, so write 0, 0 in those places. In (5) there are no lakhs and no tens, so 0 goes in both those places: 80,51,609.

★An interesting dice game — how to play well

This is a game to play in class, so there is no fixed answer. A few tips help:

  • Game 1 and Game 2 (largest number wins): put a big throw such as 5 or 6 in a high place (ten lakhs or lakhs), and a small throw such as 1 or 2 in a low place (tens or units).
  • Game 2: you may also put a small throw in a high place of another player’s row to keep their number small.
  • Game 3 (smallest number wins): do the opposite — keep small throws for your own high places and large throws for your low places.

To find the winner, compare the ten-lakhs digits first, then the lakhs digits, and so on.

Problem Set 6

1Write the proper symbol, ‘<’ or ‘>’ in the box.
  1. 5,705 < 15,705 (15,705 has more digits)
  2. 22,74,705 > 12,74,705 (ten lakhs: 2 > 1)
  3. 35,33,302 > 35,32,302 (ten thousands: 3 > 2)
  4. 99,999 < 9,99,999 (9,99,999 has more digits)
  5. 4,80,009 < 4,90,008 (ten thousands: 8 < 9)
  6. 35,80,177 < 35,88,172 (thousands: 0 < 8)

(1) is solved in the textbook as an example.

2Solve the problems given below.

(1) The Swayamsiddha Savings Group made 3,45,000 papads while the Swabhimani Group made 2,95,000. Which group made more papads?

Compare the lakhs digits: 3 > 2, so 3,45,000 > 2,95,000. The Swayamsiddha Savings Group made more papads.

(2) Children of the Primary School in Ahmadnagar District collected 2,00,000 seeds while those in Pune District collected 3,25,000. Which children collected more seeds?

Lakhs digits: 3 > 2, so 3,25,000 > 2,00,000. The children of Pune District collected more seeds.

(3) The number of people who took part in the Republic Day flag-hoisting ceremony was 2,01,306 in Pandharpur taluka and 1,97,208 in Malshiras taluka. In which taluka did a larger number of people participate?

Lakhs digits: 2 > 1, so 2,01,306 > 1,97,208. More people took part in Pandharpur taluka.

(4) At an exhibition, the Annapoorna Savings Group sold goods worth ₹ 5,12,345. The Nirman Group sold goods worth ₹ 4,12,900. This figure was ₹ 4,33,000 for the Srujan Group and ₹ 5,11,937 for the Savitribai Phule group. Which group had the largest sales? Which group had the smallest? Write the sales figures in ascending order.

  • Annapoorna (5,12,345) and Savitribai Phule (5,11,937) both have 5 lakhs; comparing the thousands digits, 2 > 1. So the Annapoorna Savings Group had the largest sales, ₹ 5,12,345.
  • Nirman (4,12,900) and Srujan (4,33,000) both have 4 lakhs; comparing the ten-thousands digits, 1 < 3. So the Nirman Group had the smallest sales, ₹ 4,12,900.

Ascending order (smallest to largest):

₹ 4,12,900 < ₹ 4,33,000 < ₹ 5,11,937 < ₹ 5,12,345

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