place-value-representation MCQs for UPSC Prelims

28 practice questions on place-value-representation from the A Story of Numbers section of the UPSC Prelims syllabus. 28 come with a written explanation. Try the sample set below - the answer stays hidden until you ask for it.

8 Easy 14 Medium 6 Hard

Sample questions

Q1
hard

Consider these statements about whole numbers. (i) A zero written at the left end, as in $047$, changes the value of the number. (ii) A zero written inside, as in $407$, changes the value of the number. Which statement(s) are correct?

  1. A Both (i) and (ii)
  2. B Only (i)
  3. C Neither (i) nor (ii)
  4. D Only (ii)
Show answer and explanation

Correct answer: D - Only (ii)

A leading zero marks a place above the highest digit, and that place holds nothing, so $047$ is still $47$ and (i) is false. A zero inside pushes every digit on its left into a higher place, so $407$ is far larger than $47$ and (ii) is true. Only (ii) stands.

Q2
medium

A student adds $407+186$ and writes $583$. Which mistake produced that answer?

  1. A The carry from the ones column was never added into the tens
  2. B The zero was treated as a one
  3. C The hundreds were added twice over
  4. D The numbers were subtracted instead of added
Show answer and explanation

Correct answer: A - The carry from the ones column was never added into the tens

The ones give $7+6=13$, so $3$ is written and $1$ is carried. Ignoring that carry leaves the tens as $0+8=8$ and produces $583$ instead of the correct $593$. The hundreds were added once, the zero was used correctly, and subtracting would have given $221$.

Q3
hard

A four-digit number is made using each of the digits $3$, $0$, $7$ and $5$ exactly once. What is the largest such number, and what is its digit $5$ worth?

  1. A $5730$, with the $5$ worth $5000$
  2. B $7530$, with the $5$ worth $500$
  3. C $7350$, with the $5$ worth $50$
  4. D $7530$, with the $5$ worth $50$
Show answer and explanation

Correct answer: B - $7530$, with the $5$ worth $500$

To make the largest number the digits are placed in decreasing order, giving $7530$, where the $5$ occupies the hundreds place and is worth $500$. Reading it as a tens digit gives $50$. The number $7350$ is smaller than $7530$, and $5730$ starts with the smaller digit $5$, so it is smaller still.

Q4
easy

A number in expanded form is $4000+300+7$. What is the number?

  1. A $4370$
  2. B $43007$
  3. C $437$
  4. D $4307$
Show answer and explanation

Correct answer: D - $4307$

The tens place has no part in the sum, so a zero fills it and the number is $4307$. Leaving the empty place out gives $437$. Putting the $7$ in the tens place gives $4370$. Writing two zeros for one empty place gives $43007$.

Q5
medium

A number has $3$ in the thousands place and $9$ in the tens place, with zeros in every other place. What is the number?

  1. A $3900$
  2. B $390$
  3. C $3009$
  4. D $3090$
Show answer and explanation

Correct answer: D - $3090$

Thousands $3$, hundreds $0$, tens $9$ and ones $0$ give $3090$. Putting the $9$ in the hundreds place gives $3900$. Dropping the thousands place gives $390$, and putting the $9$ in the ones place gives $3009$.

Q6
easy

Which number is one hundred more than $907$?

  1. A $917$
  2. B $1007$
  3. C $1907$
  4. D $908$
Show answer and explanation

Correct answer: B - $1007$

Adding one hundred to $907$ gives $1007$, in which the zero holds the empty tens place. Adding to the tens instead gives $917$. Adding a thousand gives $1907$. Adding one to the ones gives $908$.

Q7
medium

Assertion (A): Writing a large number in a place-value system needs more symbols than writing it in an additive system. Reason (R): In a place-value system a single digit can stand for a large amount because of the place it occupies.

  1. A Both A and R are true, and R is the correct explanation of A
  2. B Both A and R are true, but R is not the correct explanation of A
  3. C A is true, but R is false
  4. D A is false, but R is true
Show answer and explanation

Correct answer: D - A is false, but R is true

A is false: $9999$ needs four digits in our system but thirty-six signs in an additive one, so place value uses far fewer symbols. R is true, since the leading $9$ means nine thousand purely because of where it sits. The assertion fails while the reason stands.

Q8
hard

A number has the expanded form $5\times1000+0\times100+4\times10+9$. A second number is made by exchanging the digits in the thousands and tens places. How does the value change?

  1. A It rises by $990$
  2. B It falls by $10$
  3. C It falls by $1000$
  4. D It falls by $990$
Show answer and explanation

Correct answer: D - It falls by $990$

The first number is $5049$, and exchanging the thousands digit $5$ with the tens digit $4$ gives $4059$. The change is $5049-4059=990$, a fall because the larger digit has moved to a much smaller place. It cannot rise, and the change is neither a plain $10$ nor a plain $1000$.

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