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CBSE · Class 7 · Mathematics

Chapter 1: Large Numbers Around Us

5 concepts · 40 practice questions with answers · Free to read

This lesson is also in: मराठी · हिंदी

Lakh, crore and arab

From daily life

A newspaper says 23,40,500 people visited a fair and a company earned ₹4,50,00,000. To read such numbers we need places beyond ten thousands: lakhs and crores.

Simple definition

In the Indian system the first group from the right has 3 digits (hundreds), then every group has 2 digits: thousands, lakhs, crores. 1 lakh = 100 thousand = 1,00,000 (5 zeros), 1 crore = 100 lakh = 1,00,00,000 (7 zeros), 1 arab = 100 crore = 1,00,00,00,000 (9 zeros).

Cr5,TL3L6,TTh0Th8,H4T2O05 crore36 lakh08 thousand4205,36,08,420

In the figure: 5,36,08,420 has 5 crore, 36 lakh, 8 thousand and 420. Name: five crore thirty-six lakh eight thousand four hundred twenty. (Cr = crore, TL = ten lakh, L = lakh, TTh = ten thousand, Th = thousand.)

Rule 1: Read in groups — Start from the left; read each group and say its unit: crore, lakh, thousand. Skip a group that is all zeros.

  • Easy: 3,45,000 = three lakh forty-five thousand.
  • Medium: 12,06,300 = twelve lakh six thousand three hundred.
  • Exam-type: 7,00,05,090 = seven crore five thousand ninety.

Rule 2: Write from the name — Put each part in its own place and fill missing places with 0.

  • Easy: Five lakh twenty thousand = 5,20,000.
  • Medium: Forty-two lakh seven = 42,00,007.
  • Exam-type: Nine crore eight lakh sixty = 9,08,00,060.

Rule 3: Value of a digit — The value of a digit is the digit times the value of its place.

  • Easy: In 4,25,000 the 4 stands for 4 lakh = 4,00,000.
  • Medium: In 8,64,25,317 the 6 is in the ten-lakh place: value 60,00,000.
  • Exam-type: In 7,58,41,206 the 5 is worth fifty lakh = 50,00,000.
Remember

In the Indian system the first comma comes after 3 digits from the right and then after every 2 digits.

Common mistake

Writing one lakh as 10,000 or 12,34,567 as 1,234,567 (that is the international style).

Shortcut

Count zeros: lakh 5, crore 7, arab 9. Memory clue: "3-2-2-2": three digits first, then pairs for thousand, lakh, crore.

Spot the difference

PointLakhCrore
Number1,00,0001,00,00,000
Zeros57
Relation100 thousand100 lakh

Practice questions

Easy
  1. 1Write 4,05,300 in words.
  2. 2Write "six lakh forty thousand" in digits.
  3. 3How many zeros are there in 1 crore?
Medium
  1. 4Write 3,02,08,000 in words.
  2. 5Write "twelve crore five lakh seven" in digits.
  3. 6In 7,58,41,206, what is the value of the digit 5?
Challenging
  1. 7Write 9 crore 9 lakh 9 thousand 9 hundred in digits.
  2. 8Which number comes just after 99,99,999? Name it.
Show answers (try them yourself first)
  1. 1four lakh five thousand three hundred
  2. 26,40,000
  3. 37
  4. 4three crore two lakh eight thousand
  5. 512,05,00,007
  6. 650,00,000 (fifty lakh)
  7. 79,09,09,900
  8. 81,00,00,000 — one crore

Indian and international systems

From daily life

An Indian newspaper writes a budget as 3,50,00,000 while a foreign website writes the same budget as 35,000,000. The amount is the same; only the commas and names differ.

Simple definition

The international system puts a comma after every 3 digits: thousand, million (1,000,000), billion (1,000,000,000). The Indian system uses 3-2-2-2.

Indian (3-2-2-2)3,50,00,000International (3-3-3)35,000,000

In the figure: The same digits 3,50,00,000 = 35,000,000. Only the commas move. It is 3 crore 50 lakh = 35 million.

Rule 1: Move the commas — Digits never change. Take the digits and put the commas of the other system.

  • Easy: 5,00,000 = 500,000.
  • Medium: 2,45,00,000 = 24,500,000.
  • Exam-type: 1,00,00,00,000 = 1,000,000,000: one arab = one billion.
Live figure

Indian and international systems

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Rule 2: Change the unit — 10 lakh = 1 million and 1 crore = 10 million. So lakh ÷ 10 = million, crore × 10 = million.

  • Easy: 30 lakh = 3 million.
  • Medium: 8 crore = 80 million.
  • Exam-type: 450 crore = 4,500 million.
Remember

1 billion = 100 crore = 1 arab. The value is the same, only the name changes.

Common mistake

Thinking 1 million = 1 crore. Actually 1 crore = 10 million.

Shortcut

Lakh → million: ÷ 10. Crore → million: × 10. Memory clue: "Lakh loses a zero, crore gains a zero" on the way to million.

Spot the difference

PointIndianInternational
Commas3-2-2-23-3-3
Big nameslakh, crore, arabmillion, billion
One lakh1,00,000100,000

Practice questions

Easy
  1. 1Write 8,40,000 in the international system.
  2. 2How many lakhs make 1 million?
  3. 3Write 25,00,000 in the international system.
Medium
  1. 4Convert 6 crore into million.
  2. 5Write 72,500,000 in the Indian system.
  3. 6Which is bigger: 4 million or 30 lakh?
Challenging
  1. 7Express 1 billion in lakh.
  2. 8A website shows 1,250,000,000 users. Write this in the Indian system and in crore.
Show answers (try them yourself first)
  1. 1840,000
  2. 210
  3. 32,500,000
  4. 460 million
  5. 57,25,00,000
  6. 64 million = 40 lakh, so 4 million is bigger
  7. 710,000 lakh
  8. 81,25,00,00,000 = 125 crore

Comparing and ordering large numbers

From daily life

Three towns have populations 18,45,000, 9,87,500 and 18,54,200. To say which town is biggest we compare the numbers just like scores.

Simple definition

More digits = bigger number. If the number of digits is equal, compare digit by digit from the left; the first place where they differ decides. Ascending = smallest to largest, descending = largest to smallest.

118845540200004 < 5 ⇒ 18,45,000 < 18,54,200

In the figure: Both have 7 digits. The first two digits are equal. At the third place 4 < 5, so 18,45,000 is smaller.

Rule 1: Count the digits first — The number with more digits is always bigger (no leading zeros).

  • Easy: 9,99,999 (6 digits) < 10,00,000 (7 digits).
  • Medium: 45,67,890 (7 digits) > 4,56,789 (6 digits).
  • Exam-type: 3,40,25,000 (8 digits) > 34,02,500 (7 digits).
Live figure

Comparing and ordering large numbers

In the app you can move this figure with your finger.

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Rule 2: Same digits? Compare from the left — Find the first place where the digits differ; the bigger digit there gives the bigger number.

  • Easy: 5,48,200 > 5,46,900 (8 > 6 in the thousands place).
  • Medium: 72,15,300 > 72,15,030 (3 > 0 in the hundreds place).
  • Exam-type: Ascending order of 6,05,000; 6,50,000; 5,99,999 is 5,99,999 < 6,05,000 < 6,50,000.
Remember

Compare only numbers written in the same system and with the same unit.

Common mistake

Judging by the biggest single digit, for example thinking 9,000 is bigger than 10,000 because 9 > 1.

Shortcut

First count digits, then compare from the left. Memory clue: "Length first, Left next" — longer number wins; if equal, the leftmost difference wins.

Spot the difference

PointAscendingDescending
Ordersmallest → largestlargest → smallest
Sign between<>
Example70,800 < 7,08,000 < 7,80,0007,80,000 > 7,08,000 > 70,800

Practice questions

Easy
  1. 1Which is bigger: 8,95,000 or 89,500?
  2. 2Which is smaller: 12,34,567 or 12,34,576?
  3. 3Put > or <: 5,00,000 ___ 4,99,999.
Medium
  1. 4Arrange in ascending order: 7,08,000; 7,80,000; 70,800.
  2. 5Arrange in descending order: 2,50,00,000; 25,00,000; 2,05,00,000.
  3. 6Make the greatest 6-digit number using the digits 3, 0, 7, 5, 1, 9 once each.
Challenging
  1. 7Make the smallest 7-digit number using 4, 0, 8, 2, 6, 1, 9 once each.
  2. 8Towns A, B, C have 12,40,500; 12,04,800 and 12,40,050 people. Which town has the most and which the least?
Show answers (try them yourself first)
  1. 18,95,000 (6 digits) is bigger than 89,500 (5 digits)
  2. 212,34,567 (6 < 7 in the ones place)
  3. 3>
  4. 470,800 < 7,08,000 < 7,80,000
  5. 52,50,00,000 > 2,05,00,000 > 25,00,000
  6. 69,75,310
  7. 710,24,689
  8. 8Most: A; least: B

Exact values, rounding and estimation

From daily life

A stadium sold exactly 48,372 tickets, but the news says "about 48,000". When the exact number is not needed, a close number is enough.

Simple definition

An exact value is the precise count. An approximate value is a nearby number got by rounding. To round to a place, look at the digit just to its right: 5 or more → round up; less than 5 → keep; then make the digits on the right 0.

48,00049,000middle 48,50048,372

In the figure: 48,372 lies between 48,000 and 49,000 and is before the middle 48,500, so it rounds to 48,000.

Live figure

Exact values, rounding and estimation

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Rule 1: Round to ten, hundred, thousand — Mark the rounding place, look at the next digit on the right, then decide.

  • Easy: 3,846 to the nearest ten = 3,850 (6 ≥ 5, round up).
  • Medium: 67,451 to the nearest hundred = 67,500 (51 is more than 50).
  • Exam-type: 2,49,500 to the nearest thousand = 2,50,000 (500 → up, 9 becomes 10).

Rule 2: Round to lakh and crore — Same rule: compare the rest of the number with half (50,000 for lakh, 50,00,000 for crore).

  • Easy: 7,38,000 to the nearest lakh = 7,00,000 (38,000 < 50,000).
  • Medium: 12,65,400 to the nearest lakh = 13,00,000 (65,400 ≥ 50,000).
  • Exam-type: 4,96,00,000 to the nearest crore = 5,00,00,000 (96 lakh ≥ 50 lakh).

Rule 3: Estimate by rounding first — Round every number to an easy value, then add, subtract or multiply.

  • Easy: 4,980 + 3,020 ≈ 5,000 + 3,000 = 8,000.
  • Medium: 49,800 × 20 ≈ 50,000 × 20 = 10,00,000.
  • Exam-type: 1,950 people, 48 seats per bus: 2,000 ÷ 50 = 40 buses (estimate).
Remember

Only the first dropped digit decides whether to round up.

Common mistake

Rounding 2,49,500 to 2,00,000 because 4 is small. The thousand digit is 9 and the next digit is 5, so go up.

Shortcut

Round, then calculate: easy numbers give quick answers. Memory clue: "Five or more, raise the score; four or less, let it rest."

Spot the difference

PointExact valueApproximate value
Example48,372about 48,000
Usebills, marks, countingnews, quick estimates

Practice questions

Easy
  1. 1Round 5,683 to the nearest ten.
  2. 2Round 74,238 to the nearest thousand.
  3. 3Which is an approximate value: "exactly 4,325 seats" or "about 4,300 seats"?
Medium
  1. 4Round 8,46,725 to the nearest lakh.
  2. 5Round 3,49,99,999 to the nearest crore.
  3. 6Estimate 9,870 + 6,140 by rounding each to the nearest thousand.
Challenging
  1. 7A number rounded to the nearest hundred is 7,300. What is the smallest whole number it can be?
  2. 8Estimate 4,950 × 38 by rounding.
Show answers (try them yourself first)
  1. 15,680
  2. 274,000
  3. 3"about 4,300 seats"
  4. 48,00,000
  5. 53,00,00,000 (49,99,999 < 50,00,000)
  6. 616,000 (10,000 + 6,000)
  7. 77,250 (7,250 rounds up to 7,300)
  8. 85,000 × 40 = 2,00,000

Multiplication shortcuts and large calculations

From daily life

A school buys 25 notebooks for each of 48 classes. Instead of long multiplication we can use a quick trick.

Simple definition

Multiplying a whole number by 10, 100, 1000 adds 1, 2, 3 zeros. Also 5 = 10 ÷ 2, 25 = 100 ÷ 4, 125 = 1000 ÷ 8, so multiplying by them means: divide, then add zeros.

48÷ 412× 1001,20048 × 25 = 1,200

In the figure: 48 × 25: divide 48 by 4 to get 12, then multiply by 100 to get 1,200.

Rule 1: Multiply by 10, 100, 1000 — Add as many zeros to the right as there are zeros in 10, 100 or 1000.

  • Easy: 47 × 100 = 4,700.
  • Medium: 305 × 1,000 = 3,05,000.
  • Exam-type: 12,50,000 × 10 = 1,25,00,000.

Rule 2: Shortcuts for 5, 25, 125 — n × 5 = (n ÷ 2) × 10; n × 25 = (n ÷ 4) × 100; n × 125 = (n ÷ 8) × 1000.

  • Easy: 64 × 5 = 32 × 10 = 320.
  • Medium: 84 × 25 = 21 × 100 = 2,100.
  • Exam-type: 96 × 125 = 12 × 1000 = 12,000.

Rule 3: Big calculations in stages — Break the problem into easy steps and use zeros to keep it short.

  • Easy: 200 × 15 = 2 × 15 × 100 = 3,000.
  • Medium: 600 km a day for 30 days = 6 × 3 × 1000 = 18,000 km.
  • Exam-type: A bus runs 400 km a day. Days to cover 3,84,400 km: 3,84,400 ÷ 400 = 961 days.
Remember

Adding zeros works for whole numbers; decimals are handled in a later chapter.

Common mistake

25 × 40: doing 25 × 4 = 100 and forgetting the extra zero. The answer is 1,000.

Shortcut

5 → half and add one zero; 25 → quarter and add two zeros; 125 → eighth and add three zeros. Memory clue: Partners: 5-2, 25-4, 125-8 (2, 4, 8 keep doubling).

Spot the difference

Multiply byDivide first byThen add
521 zero
2542 zeros
12583 zeros

Practice questions

Easy
  1. 1Find 90 × 1,000.
  2. 2Find 46 × 5 using 5 = 10 ÷ 2.
  3. 3Find 36 × 25 quickly.
Medium
  1. 4Find 88 × 125.
  2. 5Find 24 × 250.
  3. 6A tap leaks 25 litres a day. How many litres leak in 400 days?
Challenging
  1. 7A vehicle runs 250 km every day. In how many days will it cover 1 lakh km?
  2. 8Show that 5,000 × 2,000 = 1 crore.
Show answers (try them yourself first)
  1. 190,000
  2. 2230
  3. 3900
  4. 411,000
  5. 56,000
  6. 610,000 litres
  7. 7400 days
  8. 85 × 2 = 10 and 3 + 3 = 6 zeros, so 10 followed by 6 zeros = 1,00,00,000 = 1 crore