Quantitative Aptitude

Number System and Digits

380 Questions

Number system and digits questions test the ability to manipulate numbers, identify significant digits, and form specific values. These problems often require finding missing digits or determining the properties of large sums. They form a vital component of the quantitative aptitude section.

Number formationMissing digitsSignificant digitsLargest and smallest numbersDigit sum properties

Number System and Digits Questions

Multiple choice maths 5-digit numbers expanded form introduction to numbers and number systems numbers in general form

Numeral for sixty million and sixty six is

  1. $60,000,060$
  2. $60,000,066$
  3. $6,000,066$

  4. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

In international numbering system
The 1st period consists of - ones, tens and hundred.
The 2nd period consists of - thousand, $10$ thousand and $100 $ thousands.
The 3rd period consists of - million, $10$ million and $100$ million.
$\therefore $  Numeral for sixty million and sixty six $=60,000,066$
Option B is correct.

Multiple choice maths 5-digit numbers expanded form introduction to numbers and number systems numbers in general form

If a new number is formed by interchanging the tens and thousands place digits of $8727$, then what is the relation between them?

  1. New number is greater than original number.

  2. New number is smaller than original number.

  3. New number is equal to the original number.

  4. Can't be determined
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Original number $= 8727$
After interchanging tens and thousands of place digits, we get $2787$.
So, new member is smaller than original number.

Multiple choice maths 5-digit numbers expanded form introduction to numbers and number systems numbers in general form

In a two digit number, if number in units place is $8$ and number in tens place is $y$ then that number is __________.

  1. $y+8$
  2. $y+80$
  3. $10y+8$
  4. $80y$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Lets take an example of $23$
The digit at units place$=3$
The digit at tens place$=2$
The number$=2\times10+3=23$
In the question
The digit at units place is $8$
Thus, the number $=y\times10+8=10y+8$

Multiple choice maths 5-digit numbers expanded form introduction to numbers and number systems numbers in general form

The number of digits in $5^{30}$ is ,$(\log _{10}2=0.3010)$

  1. $30$
  2. $22$
  3. $21$
  4. $none\ of\ these$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let x = 5^30. Taking log base 10 gives log(x) = 30 * log(5) = 30 * log(10/2) = 30 * (1 - log(2)) = 30 * (1 - 0.3010) = 30 * 0.699 = 20.97. The number of digits is the floor of log(x) plus 1, which is 20 + 1 = 21 digits.

Multiple choice maths 5-digit numbers expanded form introduction to numbers and number systems numbers in general form

Numeral for ninety million ninety thousand ninety is

  1. $9090095$
  2. $90090090$
  3. $909090$

  4. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
We know that,

$1$ million $= 1000000$, therefore, $90$ million $= 90000000$

$1$ thousand $= 1000$, therefore, $90$ thousand $= 90000$

Thus, ninety million ninety thousand ninety is

$=90000000+90000+90=90090090$

Hence, numeral for ninety million ninety thousand ninety is $90090090$.
Multiple choice maths 5-digit numbers expanded form introduction to numbers and number systems numbers in general form

The positive two-digit integers $x$ and $y$ have the same digits, but in reverse order. Which of the following must be a factor of $x + y$? 

  1. $6$
  2. $9$
  3. $10$
  4. $11$
  5. $14$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

$\Rightarrow$  Let two positive integers are $x=17$ and $y=71$.

$\Rightarrow$  $x+y=17+71=88$
$\Rightarrow$  $88=11\times 2 \times 2\times 2$
$\therefore$   From the factors given in the options, $11$ will be the factor of $x+y$.

Multiple choice maths 5-digit numbers expanded form introduction to numbers and number systems numbers in general form

The digits in the tens place and units place of a two digit number are $t$ and $u$ respectively. If $1$ is placed between them, what is the value of the three digit number so formed?

  1. $100u+t+10$
  2. $100t+10+u$
  3. $10t+u+1$
  4. $100t+10u+1$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the number in one's place be $ u$ and the number in ten's place be $10t$.

According the the question 
$\Rightarrow 10t + 1+ u $
Hence now the 10t will become 100t as it will take hundred's digit place and 1 will become 10 as it will take ten's digit place.
Hence the value  of 3 digit number will be $ 100t + 10 + u $.

Multiple choice maths 5-digit numbers expanded form introduction to numbers and number systems numbers in general form

The difference between a two-digit number and the number obtained by interchanging the digits is 36. What is the difference between the sum and the difference of the digits of the number if the ratio between the digits of the number is 1 : 2 ?

  1. 4

  2. 8

  3. 16

  4. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$\because $ The number is greater than the number obtained in reversing the digits and the ten's digit is greater than the unit's digit
Let ten's and unit's digit be $2x$ and $x$ respectively
Then, $(10\times 2x+x)-(10x+2x)=36$
$9x=36$
$x=4$
Required difference$=(2x+x)-(2x-x)=2x=8$

Multiple choice maths concept of directed numbers and number line subtraction of directed numbers subtraction of integers subtraction of integers on number line

What would be the difference between the place values of the digits at the tens and units places of a number formed by the addition of the greatest six-digit number and the smallest three-digit number?

  1. $81$
  2. $72$
  3. $63$
  4. $54$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The greatest 6 digit number is $=999999$.

The smallest 3 digit number is$=100$.
Therefore there sum$=1000099$.
The tens place value=$90$ and units place vaue $=9$.
Therefore the difference is $81$ .

Multiple choice logarithm and its uses basic mathematical concepts physics

The characteristic of a number having $m$ $(m>1)$ digits is given by,

  1. $m-1$
  2. $m+1$
  3. $m$

  4. None of the above
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

If a number is $N>0$, then $\log _{10}N$ will have two parts, the integral part is known the characteristic and the decimal part is known as mantissa.

$2$ digit belongs from $[10,100]$ where $\log _{10}10=1$ and $\log _{10}100=2$
Similarly, $m$ digit number belongs from $[10^{m-1},10^m]$, where $\log _{10}10^{m-1}=m-1$ and $\log _{10}10^m=m$.
Thus any number between $[10^{m-1},10^m]$ will have $m-1$ as the integral part.
Thus the characteristic of a number having $m$ digits is given by $m-1$.