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

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

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

Correct answer: C - $7530$, 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 $437$
  2. B $4307$
  3. C $4370$
  4. D $43007$
Show answer and explanation

Correct answer: B - $4307$

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

Correct answer: A - $3090$

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

Correct answer: D - $1007$

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

Correct answer: C - 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 $1000$.

Practice all 28 place-value-representation questions free

Timed practice, instant scoring, and explanations for every question. Free forever - no card, no catch.

Start practicing I am a teacher - create a test

More A Story of Numbers topics

early-number-systems 26