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State Board · Class 5 · Mathematics

Lesson 2: Number Work

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

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Six-digit numbers and the lakh

From daily life

A shop sells a scooter for 99,999 rupees. If one more rupee is added, the price becomes 1,00,000 rupees, which is one lakh.

Simple definition

99,999 + 1 = 1,00,000, read as one lakh (लाख). One lakh = 100 thousand. A six-digit number is read with the lakhs first.

Number lineNumber line from 0 to 10 in steps of 0.5. Point A at 7. Point B at 6.5.012345678910ABnumbers are in lakhs

In the figure : On the number line A is at 7 lakh = 7,00,000 and B is on the half mark after 6 lakh, so B is at 6,50,000.

Rule 1: Know the lakh — One lakh = 100 thousand, so half a lakh = 50 thousand.

  • Easy : Two and a half lakh = 2,50,000.
  • Medium : 1000 notes of 100 rupees make 1,00,000 rupees, which is one lakh rupees.
  • Exam-type : 3,00,000 − 50,000 = 2,50,000, so three lakh minus fifty thousand is two and a half lakh.

Rule 2: Read six-digit numbers — Read the lakhs, then the thousands, then the hundreds, tens and ones.

  • Easy : 2,35,705 = two lakh thirty-five thousand seven hundred and five.
  • Medium : 8,00,363 = eight lakh three hundred and sixty-three.
  • Exam-type : 9,00,049 = nine lakh forty-nine. The zeros mean there are no thousands and no hundreds.
Remember

A lakh has five zeros. 1 lakh = 1,00,000.

Common mistake

Reading 1,00,000 as "ten thousand". It is one lakh = 100 thousand.

Shortcut

Memory clue: Lakh = 5 zeros, so the first comma from the right comes after 3 digits and the next after 2.

Spot the difference

NumberName
1,00,000one lakh
50,000half a lakh
2,50,000two and a half lakh

Practice questions

Easy
  1. 1Write 99,999 + 1 as a number.
  2. 2How many thousands make 1 lakh?
  3. 3Read 4,50,000.
Medium
  1. 4Read 6,07,209.
  2. 5How many 50-rupee notes make 1 lakh rupees?
  3. 6What is the number half way between 6,00,000 and 7,00,000?
Challenging
  1. 7Read 3,00,500 and 9,10,010.
  2. 8A school collected 2,30,000 rupees in donations. How much more is needed to reach 3 lakh?
Show answers (try them yourself first)
  1. 11,00,000
  2. 2100
  3. 3four lakh fifty thousand
  4. 4six lakh seven thousand two hundred and nine
  5. 51,00,000 ÷ 50 = 2000 notes.
  6. 66,50,000
  7. 7three lakh five hundred; nine lakh ten thousand and ten
  8. 83,00,000 − 2,30,000 = 70,000 rupees.

Writing six-digit numbers in figures

From daily life

A farmer sold his harvest for eight lakh, nine thousand and forty-three rupees. To write it correctly on a receipt, each place must be filled, with 0 where nothing is there.

Simple definition

To write a number in figures, write the digit of the highest place first and then a digit in every smaller place. Write 0 where a place is empty.

Rule 1: Place values in a grid — Put each part in its place: lakh, thousands, hundreds, tens, ones.

  • Easy : Four lakh twenty thousand five hundred = 4,20,500.
  • Medium : Six lakh two thousand eight = 6,02,008.
  • Exam-type : Eight lakh nine thousand forty-three = 8,09,043 (not 89,043). The 0 in the ten thousands place is needed.
Remember

An empty place always gets 0. Count the digits at the end: a six-digit number has 6 digits.

Common mistake

Writing seven lakh five as 7,5 or 75,000. The correct number is 7,00,005.

Shortcut

Memory clue: Fill every box of the place-value chart; if a box is empty, put 0.

Spot the difference

WordsFigures
five lakh ten5,00,010
two lakh four thousand2,04,000
nine lakh ninety9,00,090

Practice questions

Easy
  1. 1Write "three lakh" in figures.
  2. 2Write "five lakh ten" in figures.
  3. 3Write "one lakh five thousand" in figures.
Medium
  1. 4Write "seven lakh forty thousand six hundred" in figures.
  2. 5Write "two lakh seven" in figures.
  3. 6How many zeros does the number "four lakh two" have?
Challenging
  1. 7Write "nine lakh nine thousand nine" in figures.
  2. 8A bill reads "six lakh sixty thousand six". Rina writes 6,60,06. What is wrong, and what is right?
Show answers (try them yourself first)
  1. 13,00,000
  2. 25,00,010
  3. 31,05,000
  4. 47,40,600
  5. 52,00,007
  6. 64,00,002 has 4 zeros.
  7. 79,09,009
  8. 8One digit is missing. Right: 6,60,006.

Seven-digit numbers

From daily life

A city has ten lakh people. A bigger city has more than that: ten lakh is the first seven-digit number.

Simple definition

1,00,000 × 10 = 10,00,000, read as ten lakh, the smallest seven-digit number. One million = ten lakh. A new place, ten lakhs, comes to the left of the lakhs place.

Place value chartPlace value chart of the Indian system for the number 36,05,284. ten lakhs: 3, lakhs: 6, ten thousands: 0, thousands: 5, hundreds: 2, tens: 8, ones: 4.OnesThou.LakhsTL3L6TTh0Th5H2T8O4

In the figure : The chart shows 36,05,284. With the Indian system, put the first comma after 3 digits from the right and then after every 2 digits: 36,05,284.

Rule 1: Read a seven-digit number — Read the lakhs part first (ten lakhs and lakhs together), then thousands, hundreds, tens and ones.

  • Easy : 18,35,614 = eighteen lakh thirty-five thousand six hundred and fourteen.
  • Medium : 72,00,095 = seventy-two lakh and ninety-five.
  • Exam-type : 70,02,300 = seventy lakh two thousand three hundred.
Live figure

Seven-digit numbers

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

Open in the app

Rule 2: Place the commas — From the right put a comma after 3 digits, then after every 2 digits.

  • Easy : 1250000 = 12,50,000.
  • Medium : 3600528 = 36,00,528.
  • Exam-type : Count first: 4070900 has 7 digits, so it becomes 40,70,900. An 8-digit number like 40709000 becomes 4,07,09,000.
Remember

Ten lakh = one million = 10,00,000. Seven digits start from ten lakh.

Common mistake

Putting commas after every 3 digits (international style) while using Indian words. In the Indian system use 3, then 2, 2.

Shortcut

Memory clue: 3 – 2 – 2 from the right, like the rhythm of a song.

Spot the difference

NumberName
10,00,000ten lakh
25,00,000twenty-five lakh
99,99,999ninety-nine lakh ninety-nine thousand nine hundred ninety-nine

Practice questions

Easy
  1. 1What is 1,00,000 × 10?
  2. 2How many digits does 10,00,000 have?
  3. 3Read 25,00,000.
Medium
  1. 4Read 41,07,300.
  2. 5Put commas in 8504600.
  3. 6Write "sixty lakh forty-five thousand" in figures.
Challenging
  1. 7Write the smallest and the biggest seven-digit numbers.
  2. 8A town has 12,40,000 people and another has 9,90,000. Which is bigger and by how much?
Show answers (try them yourself first)
  1. 110,00,000 (ten lakh)
  2. 27
  3. 3twenty-five lakh
  4. 4forty-one lakh seven thousand three hundred
  5. 585,04,600
  6. 660,45,000
  7. 710,00,000 and 99,99,999
  8. 8The first, by 12,40,000 − 9,90,000 = 2,50,000.

Expanded form and place value

From daily life

A shopkeeper counts: 9 lakh + 5 thousand + 6. Putting each part in its place is called expanded form.

Simple definition

Adding the place values of the digits gives the expanded form (विस्तारित रूप). The place value (स्थानिक किंमत) of a digit is the digit × the value of its place.

Rule 1: Expanded form — Write each digit with its place value and add.

  • Easy : 95,04,506 = 90,00,000 + 5,00,000 + 4,000 + 500 + 6.
  • Medium : 27,65,043 has place values 20,00,000; 7,00,000; 60,000; 5,000; 0; 40; 3.
  • Exam-type : 4,00,000 + 90,000 + 200 = 4,90,200.
Place value chartPlace value chart of the Indian system for the number 4,80,25,316. crores: 4, ten lakhs: 8, lakhs: 0, ten thousands: 2, thousands: 5, hundreds: 3, tens: 1, ones: 6. Highlighted: ten lakhs.OnesThou.LakhsCroresTCrCr4TL8L0TTh2Th5H3T1O6

In the figure : In 4,80,25,316 the highlighted digit is 8, in the ten lakhs place, so its place value is 8 × 10,00,000 = 80,00,000. The 4 on its left is in the crores place.

Rule 2: Place value of one digit — Digit × value of its place.

  • Easy : In 59,30,478 the digit 5 is in the ten lakhs place, so its place value is 50,00,000.
  • Medium : In 4,80,25,316 the 4 is in the crores place: 4 × 1,00,00,000 = 4,00,00,000.
  • Exam-type : The digit 0 always has place value 0, wherever it is.
Place value chartPlace value chart of the Indian system for the number 3?,40,126 (a hidden digit is shown as ?). ten lakhs: 3, lakhs: ?, ten thousands: 4, thousands: 0, hundreds: 1, tens: 2, ones: 6.OnesThou.LakhsTL3L?TTh4Th0H1T2O63?,40,126

In the figure : In the puzzle the digits add up to 22. The visible digits are 3, 4, 0, 1, 2, 6 and add up to 16, so the hidden digit is 22 − 16 = 6.

Remember

The face value of a digit is the digit itself. The place value changes with the place.

Common mistake

Saying the place value of 5 in 5,000 is 5. It is 5 × 1,000 = 5,000.

Shortcut

Memory clue: Face value = the digit; place value = digit × place.

Spot the difference

NumberDigitPlace value
3,45,67833,00,000
3,45,678440,000
3,45,678770

Practice questions

Easy
  1. 1Write the place value of 6 in 6,00,000.
  2. 2What is the place value of 4 in 2,48,516?
  3. 3What is the place value of the digit 0 in 7,08,031?
Medium
  1. 4Write 54,06,289 in expanded form.
  2. 5Write the number: 30,00,000 + 2,00,000 + 700 + 5.
  3. 6In 83,76,245, what is the place value of 8 and of 7?
Challenging
  1. 7In 6,43,25,810 the digit 6 is in which place and what is its place value?
  2. 8The digits of a number add up to 20. The visible digits are 5, 3, 1 and 4. What is the hidden digit?
Show answers (try them yourself first)
  1. 16,00,000
  2. 240,000
  3. 30
  4. 450,00,000 + 4,00,000 + 6,000 + 200 + 80 + 9
  5. 532,00,705
  6. 68 → 80,00,000; 7 → 70,000.
  7. 7Ten crores place: 60,00,00,000.
  8. 85 + 3 + 1 + 4 = 13, so 20 − 13 = 7.

Comparing numbers, crores and abja

From daily life

A village has 8,90,000 people and a district has 82,00,000. Which is bigger? You compare by counting the digits first.

Simple definition

The number with more digits is bigger. If the digits are equal in number, compare from the highest place. 99,99,999 + 1 = 1,00,00,000 = one crore (कोटी), the smallest eight-digit number. After the crores come ten crores and abja (अब्ज).

Rule 1: Compare two numbers — First count the digits. If equal, compare ten lakhs, then lakhs, then ten thousands and so on.

  • Easy : 8,90,000 has 6 digits and 82,00,000 has 8 digits, so 8,90,000 < 82,00,000.
  • Medium : 45,23,000 > 45,19,999. Both have 7 digits and the same ten lakhs and lakhs digits (45 lakh and then 23 thousand against 19 thousand), so compare the thousands: 23 > 19.
  • Exam-type : Order 61,40,000, 6,14,000 and 61,04,000 from smallest: 6,14,000; 61,04,000; 61,40,000.

Rule 2: Crores and abja — Each place is ten times the place on its right.

  • Easy : 99,99,999 + 1 = 1,00,00,000 = one crore.
  • Medium : 8,45,12,706 = eight crore forty-five lakh twelve thousand seven hundred and six.
  • Exam-type : Zeros after 1: lakh 5, ten lakh 6, crore 7, ten crore 8, abja 9. India's 2011 population 1,21,01,93,422 = one abja twenty-one crore one lakh ninety-three thousand four hundred twenty-two.
Remember

More digits means a bigger number. Only when the digits are equal do we compare place by place.

Common mistake

Comparing 99,999 with 1,00,000 by looking at the first digit. 9 is bigger than 1, but 1,00,000 has more digits, so it is bigger.

Shortcut

Memory clue: Count digits first, compare places next.

Spot the difference

NumberName
1,00,00,000one crore
10,00,00,000ten crore
1,00,00,00,000one abja

Practice questions

Easy
  1. 1Which is bigger: 9,99,999 or 10,00,000?
  2. 2Write the smallest 8-digit number.
  3. 3What comes after 99,99,999?
Medium
  1. 4Put < or >: 54,32,100 __ 54,23,999.
  2. 5Arrange from the smallest: 3,40,500; 34,05,000; 3,04,500.
  3. 6Read 3,24,50,000.
Challenging
  1. 7Write "seven crore six lakh" in figures.
  2. 8A state has 2,40,00,000 voters and another has 2,04,00,000. Which has more and by how much?
Show answers (try them yourself first)
  1. 110,00,000, because it has more digits.
  2. 21,00,00,000 (one crore)
  3. 31,00,00,000 (one crore)
  4. 4>
  5. 53,04,500; 3,40,500; 34,05,000
  6. 6three crore twenty-four lakh fifty thousand
  7. 77,06,00,000
  8. 8The first, by 36,00,000.

Quick revision

  • 1 lakh = 1,00,000; 10 lakh = 10,00,000 (= 1 million); 1 crore = 1,00,00,000.
  • Write 0 in an empty place; the number with more digits is bigger.
  • Expanded form = sum of place values.