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Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating repeating decimal expansion: (i) 13/3125 (ii) 17/8 (iii) 64/455 (iv) 15/1600 (v) 29/343 (vi) 23/(2352) (vii) 129/(225775) (viii) 6/15 (ix) 35/50 (x) 77/210

Solutions: To state whether the following rational numbers will have a terminating decimal expansion or a non-terminating repeating decimal... View Article

Prove that the following are irrationals: (i) 1/√2 (ii) 7√5 (iii) 6 + √2

Solution: Let us assume 1/√2 is a rational number Let us assume 1/√2 = r where r is a rational number On further calculation we... View Article

There is a circular path around a sports field. Sonia takes 18 minutes to drive one round of the field, while Ravi takes 12 minutes for the same. Suppose they both start at the same point and at the same time, and go in the same direction. After how many minutes will they meet again at the starting point?

Given that Sonia takes 18 minutes to drive one round of the field, while Ravi takes 12 minutes for the same. Find out After how many minutes will... View Article

Check whether 6ⁿ can end with the digit 0 for any natural number n.

Given A number 6n Find out We need to check whether it can end with zero Solution We know that any number is multiplied by 5 or 10 or by the... View Article

Find the LCM and HCF of the following pairs of integers and verify that LCM × HCF = product of the two numbers. (i) 26 and 91 (ii) 510 and 92 (iii) 336 and 54

Answer: In arithmetic, the least common multiple or LCM of two numbers say a and b, is denoted as LCM (a,b). The LCM is the smallest or least... View Article

Express each number as a product of its prime factors: (i) 140 (ii) 156 (iii) 3825 (iv) 5005 (v) 7429

On taking the LCM of 140, we will get the product of its prime factor. Therefore, 140 = 2 × 2 × 5 × 7 × 1 =... View Article

An army contingent of 616 members is to march behind an army band of 32 members in a parade. The two groups are to march in the same number of columns. What is the maximum number of columns in which they can march?

Given An army contingent of 616 members is to march behind an army band of 32 members in a parade. Find out The maximum number of columns in... View Article

Give examples to show that friction is both a friend and a foe.

(i) Friction allows us to grip and catch different objects. (ii) It helps us to walk comfortably on the surface. (iii) It helps to minimize the... View Article

Iqbal has to push a lighter box and Seema has to push a similar heavier box on the same floor. Who will have to apply a larger force and why?

The force of friction between the two surfaces will increase if the two surfaces are pressed harder against each other. Thus, larger force will... View Article

Explain why sportsmen use shoes with spikes.

Spikes increase the surface of the shoes & make it rough which results in an increase in friction. This helps to have more grip on the floor... View Article

You spill a bucket of soapy water on a marble floor accidently. Would it make it easier or more difficult for you to walk on the floor? Why?

It is difficult to walk because when soapy water falls on the floor then the friction between the feet and floor reduces significantly. Thus, the... View Article

Alida runs her toy car on dry marble floor, wet marble floor, newspaper and towel spread on the floor. The force of friction acting on the car on different surfaces in increasing order will be (a) wet marble floor, dry marble floor, newspaper and towel. (b) newspaper, towel, dry marble floor, wet marble floor. (c) towel, newspaper, dry marble floor, wet marble floor. (d) wet marble floor, dry marble floor, towel, newspaper

The answer is (a) wet marble floor, dry marble floor, newspaper, and towel. The force of friction depends on the nature of the surface in... View Article

Four children were asked to arrange forces due to rolling, static and sliding frictions in a decreasing order. Their arrangements are given below. Choose the correct arrangement. (a) rolling, static, sliding (b) rolling, sliding, static (c) static, sliding, rolling (d) sliding, static, rolling

The answer is option (c) Static, sliding, rolling. Sliding friction is the force of friction, below two objects, when one of them is sliding... View Article

Fill in the blanks. (a) Friction opposes the _______ between the surfaces in contact with each other. (b) Friction depends on the _ of surfaces. (c) Friction produces . (d) Sprinkling of powder on the carrom board friction. (e) Sliding friction is _______ than the static friction.

(a) Friction opposes the motion between the surfaces in contact with each other. (b) Friction depends on the irregularities of surfaces. (c)... View Article

Lightning and thunder take place in the sky at the same time and at the same distance from us. Lightning is seen earlier and thunder is heard later. Can you explain why?

Lightning is seen earlier than the thunder because speed of light is more than the speed of sound. Therefore, even though both occurs as same... View Article

The sound from a mosquito is produced when it vibrates its wings at an average rate of 500 vibrations per second. What is the time period of the vibration?

Frequency equals the number of waves that passes a given point per second or the number of oscillations of a vibrating body per second or number... View Article