Class 6 Maths · Original EZT practice
Knowing Our Numbers (Class 6): original worked practice
A misplaced zero can change a count by lakhs. Practise reading, comparing and estimating numbers, then use a different check to catch the mistake before trying a fresh question.
9 original worked examples, 9 fresh self-check questions and 4 mixed questions, with explained answers. These are not copied textbook exercises, an official chapter index or a full answer key. No affiliation with NCERT is claimed.
Official sources for topic and edition context, checked 17 October 2026:
Choose, solve, check, then try a fresh question.
Before calculating, read the method prompt and name the condition that makes it useful. Write your own attempt. Open the steps only when you need them, and use the check to catch a wrong sign, unit or interpretation. Finish with the fresh question before reading its answer.
Read a number without losing a zero
Choose the method: Use Indian groups: ones, thousands, lakhs and crores. A zero holds a place even when it adds nothing.
EZT practice question
Write 8,03,64,209 in words and expanded form.
Show the worked solution
- Read the groups: 8 crore, 3 lakh, 64 thousand, 209.
- The non-zero place values are 8,00,00,000; 3,00,000; 60,000; 4,000; 200; 9.
Answer: Eight crore three lakh sixty-four thousand two hundred nine; 8,00,00,000 + 3,00,000 + 60,000 + 4,000 + 200 + 9.
Check: Adding the place values gives 80,364,209. The ten-lakh and tens places stay zero.
Watch for this: Do not read the group 03 as thirty lakh.
Now try it yourself
Write 5,00,40,018 in words.
Check your answer
Five crore forty thousand eighteen.
The lakh group is 00; the thousands group is 40, not 4.
Same digit, different value
Choose the method: Multiply the digit by its place value, then subtract the two values.
EZT practice question
Find the difference between the values of the two 6s in 6,28,64,105.
Show the worked solution
- The left 6 is in the crore place: 6,00,00,000.
- The other 6 is in the ten-thousand place: 60,000.
- Subtract 60,000 from 6,00,00,000.
Answer: 5,99,40,000
Check: 59,940,000 + 60,000 = 60,000,000.
Watch for this: A digit value is not its position number: the two 6s do not have equal place values.
Now try it yourself
Find the difference between the values of the two 8s in 8,14,82,930.
Check your answer
7,99,20,000
The two values are 8,00,00,000 and 80,000.
Change the grouping, not the number
Choose the method: Indian commas use a final group of three and then groups of two. International commas use groups of three throughout.
EZT practice question
Write 73,46,218 using international commas and words.
Show the worked solution
- Remove the commas to get 7346218.
- Group from the right in threes: 7 | 346 | 218.
Answer: 7,346,218; seven million three hundred forty-six thousand two hundred eighteen.
Check: Both notations contain the identical digit string 7346218.
Watch for this: Commas do not change a digit or create an extra zero.
Now try it yourself
Write 6,208,415 with Indian commas and words.
Check your answer
62,08,415; sixty-two lakh eight thousand four hundred fifteen.
Group 62 | 08 | 415 from the right.
Convert millions and lakhs
Choose the method: One million is ten lakh; one crore is ten million. State the conversion before multiplying.
EZT practice question
A fictional library network records 3.7 million loans. Write the count in Indian notation.
Show the worked solution
- 3.7 million = 3,700,000.
- Group the same integer as 37 | 00 | 000.
Answer: 37,00,000; thirty-seven lakh loans.
Check: 37 × 1,00,000 = 37,00,000.
Watch for this: This is a made-up count for practice, not a claim about a real library.
Now try it yourself
Write 4.6 crore as millions.
Check your answer
46 million
One crore is ten million, so 4.6 × 10 = 46.
Order positive integers
Choose the method: For positive integers written without leading zeros, more digits means a larger number. With equal lengths, compare left to right.
EZT practice question
Order 68,240; 6,82,400; 68,024; 6,28,400 from smallest to greatest.
Show the worked solution
- The five-digit integers come before the six-digit integers.
- 68,024 < 68,240 because their hundreds digits differ.
- 6,28,400 < 6,82,400 because their ten-thousands digits differ.
Answer: 68,024 < 68,240 < 6,28,400 < 6,82,400
Check: The ordered list has five, five, six and six digits.
Watch for this: Digit-count comparisons need this positive-integer setting; decimal numbers need place alignment.
Now try it yourself
Which is larger: 9,07,602 or 9,70,260?
Check your answer
9,70,260
Both have six digits and start with 9. Compare the next place: 7 is greater than 0.
Build an integer using every digit once
Choose the method: For the greatest arrangement, sort descending. For the smallest, use the smallest non-zero digit first, then the remaining digits ascending.
EZT practice question
Use 6, 0, 8, 3, 1 once each to form the greatest and smallest five-digit integers.
Show the worked solution
- Descending order is 8, 6, 3, 1, 0.
- For the smallest integer start with 1; then put 0, 3, 6, 8.
Answer: Greatest 86,310; smallest 10,368
Check: Both arrangements use the five supplied digits once and start with a non-zero digit.
Watch for this: 03816 names a four-digit integer, so it is not an eligible five-digit answer.
Now try it yourself
Use 5, 0, 9, 2, 4 once each to form the greatest and smallest five-digit integers.
Check your answer
Greatest 95,420; smallest 20,459
Choose 2 first for the smallest; place 0 immediately after it.
Round to a named place
Choose the method: For these non-negative integers use the usual half-up rule: at an exact halfway point choose the higher multiple. Inspect the digit immediately to the right of the named place.
EZT practice question
Round 6,354 to the nearest ten, hundred and thousand.
Show the worked solution
- Nearest ten: the ones digit is 4, so choose 6,350.
- Nearest hundred: the tens digit is 5, so choose 6,400.
- Nearest thousand: the hundreds digit is 3, so choose 6,000.
Answer: 6,350; 6,400; 6,000
Check: 6,354 is 4 from 6,350 and 46 from 6,400. Its distance from 6,000 is 354, smaller than 646 from 7,000.
Watch for this: A result can round down at one place and up at another.
Now try it yourself
Round 8,650 to the nearest hundred using the stated half-up convention.
Check your answer
8,700
It is exactly halfway between 8,600 and 8,700; this page chooses the higher multiple.
An estimate checks scale, not exactness
Choose the method: Round to a stated place, calculate the estimate, and compare it with the exact result. Two factors can round in opposite directions.
EZT practice question
Estimate 47 × 53 by rounding each factor to the nearest ten, then find the error.
Show the worked solution
- 47 rounds up to 50; 53 rounds down to 50.
- Estimate: 50 × 50 = 2,500.
- Exact value: (50 - 3)(50 + 3) = 2,500 - 9 = 2,491.
Answer: Estimate 2,500; exact 2,491; the estimate is 9 too high.
Check: 47 × 53 = 47 × (50 + 3) = 2,350 + 141 = 2,491.
Watch for this: An estimate near the answer does not prove the exact calculation, and opposite rounding does not always cancel.
Now try it yourself
Estimate 58 × 62 to the nearest ten, then give the exact result and error.
Check your answer
Estimate 3,600; exact 3,596; estimate 4 too high.
Both round to 60. The exact product is (60 - 2)(60 + 2) = 3,600 - 4.
Read standard Roman groups
Choose the method: Use standard modern school notation for 1 to 3,999. Subtractive pairs are IV, IX, XL, XC, CD and CM; V, L and D do not repeat.
EZT practice question
Write 68 and 247 in Roman numerals, then read DCCXLVI.
Show the worked solution
- 68 = 50 + 10 + 5 + 3: L + X + V + III.
- 247 = 200 + 40 + 7: CC + XL + VII.
- DCCXLVI = 500 + 200 + 40 + 6.
Answer: 68 = LXVIII; 247 = CCXLVII; DCCXLVI = 746.
Check: Each numeral breaks into descending hundreds, tens and ones groups.
Watch for this: Not every smaller symbol may subtract from every larger one. Historical inscriptions sometimes use other conventions.
Now try it yourself
Write 89 in standard Roman numerals and explain why IXX is not the standard spelling for 19.
Check your answer
89 = LXXXIX; 19 = XIX, not IXX.
89 = 80 + 9. For 19 write 10 + 9, using the allowed subtractive pair IX.
Try a mixed set
Choose a method or explanation before opening each answer.
1. A learner says 6,50,000 and 650,000 are different counts. Correct the claim.
Show answer and reason
They are the same count.
Removing commas from both gives 650000; only the grouping system differs.
2. How many four-digit positive integers are there?
Show answer and reason
9,000
They run from 1,000 through 9,999 inclusive: 9,999 - 1,000 + 1 = 9,000.
3. Round 24,950 to the nearest thousand using half-up rounding.
Show answer and reason
25,000
It is 50 below 25,000 and 950 above 24,000.
4. Does 7,225 ending in 25 prove it is the greatest arrangement of 7, 2, 2, 5?
Show answer and reason
No. The greatest arrangement is 7,522.
This is a digit-arrangement question. Sort the permitted digits descending, including both copies of 2.
Know the rule but lose track of the steps?
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Questions about this practice page
- Which Class 6 Chapter 1 does this page cover?
- It covers selected skills associated with the older Knowing Our Numbers chapter. Current Ganita Prakash Chapter 1 is Patterns in Mathematics; check your own edition before using this page.
- How do lakhs and millions fit together?
- One lakh is 100,000; ten lakh is one million. One crore is ten million. Write the same digit string before moving commas to avoid adding or dropping zeros.
- Can zero ever be written at the start?
- Yes, in codes or padded notation. But a leading zero adds no numerical value: 04 and 4 name the same integer. A required five-digit integer must start with a non-zero digit.
- Does a close estimate prove my exact answer?
- No. An estimate checks the size of an answer. Its error depends on what was rounded and how; calculate the exact result or an error bound when accuracy matters.
- Are these textbook exercises or tutor-authored answer keys?
- No. These are original EZT practice questions and explanations, not copied textbook exercises or an official answer key. No specific tutor authorship or current exam coverage is claimed.