# Digits and Numbers

We will discuss here how to solve different types of problems related to digits and numbers.

1. The number of digits in (48^4 × 5^12) is

(a) 18

(b) 16

(c) 14

(d) 12

Solution:

48^4 × 5^12

= (16 × 3)^4 × 5^12

= (2^4)^4 × (3)^4 × (5)^12

= (2)^16 × (3)^4 × (5)^12

= (2 × 5)^12 × (2 × 3)^4

= (10)^12 × (6)^4

= 1296 × 10^12

Therefore, the required number of digits = 4 + 12 = 16

2. All the prime numbers from 2 to 200 are multiplied together. How many zeros are there at the end of the product on the right?

(a) 21

(b) 22

(c) 24

(d) 25

Solution:

Number of zeros at the end of 2 × 4 × 6 × 8 × ........... × 200

= 200/(5 × 2) + 200/(5^2 × 2)

= 20 + 4

= 24

Note: Number of zeros at the end of the product 2 × 4 × 6 × 8 × ........... 2n = 2n/(5 × 2) + 2n/(5^2 × 2) + 2n/(5^3 × 2) + ...............

3. Numbers 10, 20, 30, 40, ........ , 980, 990, 1000 are multiplied together. The number of zeros at the end of the product (on the right) will be

(a) 124

(b) 120

(c) 111

(d) 110

Solution:

Number of zeros at the end of 10 × 20 × 30 × 40 × ............ × 1000 = 1000/(5 × 2) + 1000/(5^2 × 2) + 1000/(5^3 × 2) = 100 + 20 + 4 = 124

Note: Number of zeros at the end of the product of 10 × 20 × 30 × 40 × ............ × 10n = 10n/(5 × 2) + 10n/(5^2 × 2) + 10n/(5^3 × 2) + .........

4. The quotient of two positive integers is 9/5 and their product is 11520. The difference of these two numbers is:

(a) 60

(b) 64

(c) 74

(d) 70

Solution:

Quotient of division = 9/5

Therefore, the ratio of two numbers = 9 : 5

Now, 9x + 5x = 11520

or, 45x^2 = 11520

or, x^2 = 256

or, x = 16

Therefore, the required difference (9x - 5x) 4x = 4 × 16 = 64

5. The sum of a rational number and the reciprocal of that rational number is 13/6. The number is:

(a) 12/13

(b) 5/6

(c) 3/2

(d) 13/12

Solution:

Let, the rational number be a/b

Therefore, its reciprocal number be b/a

Now, a/b + b/a = 13/6

or, (a^2 + b^2)/ab = 13/6

or, (a^2 + b^2)/ab = (3^2 + 2^2)/(3 × 2)

Therefore, the required number = 3/2

Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.

## Recent Articles

1. ### Tangrams Math | Traditional Chinese Geometrical Puzzle | Triangles

Apr 17, 24 01:53 PM

Tangram is a traditional Chinese geometrical puzzle with 7 pieces (1 parallelogram, 1 square and 5 triangles) that can be arranged to match any particular design. In the given figure, it consists of o…

2. ### Time Duration |How to Calculate the Time Duration (in Hours & Minutes)

Apr 17, 24 01:32 PM

We will learn how to calculate the time duration in minutes and in hours. Time Duration (in minutes) Ron and Clara play badminton every evening. Yesterday, their game started at 5 : 15 p.m.

3. ### Worksheet on Third Grade Geometrical Shapes | Questions on Geometry

Apr 16, 24 02:00 AM

Practice the math worksheet on third grade geometrical shapes. The questions will help the students to get prepared for the third grade geometry test. 1. Name the types of surfaces that you know. 2. W…

4. ### 4th Grade Mental Math on Factors and Multiples |Worksheet with Answers

Apr 16, 24 01:15 AM

In 4th grade mental math on factors and multiples students can practice different questions on prime numbers, properties of prime numbers, factors, properties of factors, even numbers, odd numbers, pr…