$CATEGORY: Maths - TicTacLearn/1. Real Numbers/1. Real Numbers--Euclid's Division Lemma

//Multiple Choice

The decimal expansion of 13÷3125 is  {
= 0.00416
~ 0.000416
~ 0.0316
~ None of the above
}

The decimal expansion of 17÷8 {
~ 2.125125125
~ 0.2125
= 2.125
~ None of the above
}

The decimal expansion of 15÷1600 {
~ 0.0009375
= 0.009375
~ 0.09375
~ None of the above
}

The decimal expansion of 23÷2352 {
= 0.115
~ 0.0115
~ 1.115
~ None of the above
}

The decimal expansion of 6÷15 {
~ 0.40404
= 0.4
~ 0.040
~ None of the above
}

The decimal expansion of 35÷50 {
~ 0.70770
~ 0.07
= 0.7
~ None of the above
}

If p÷q is a rational number with terminating decimal expansion where p and q are coprimes, then q can be represented as\: (Here, n and m are non-negative integers 
{
= 2 or 5 or both
~ 2 or 3 or both
~ 3 or 5 or both
~ 2, 3 or 4
}

//True or False

If any rational number whose decimal expansion is terminating in nature, then the rational number can be expressed in form of p/q, where p and q are co-primes and the prime factorization of q is of the form \(2^n×5^m\) where n and m are non-negative integers. {T}

If a rational number, which can be represented as the ratio of two integers i.e. p/q and the prime factorization of q takes the form \(2^n×5^m\) where n and m are non-negative integers then, then it can be said that the rational number has a decimal expansion which is terminating. {T}

If a rational number, which can be represented as the ratio of two integers i.e. p/q and the prime factorization of q does not take the form \(2^n×5^m\), where n and m are non-negative integers. Then, it can be said that the rational number has a decimal expansion which is non-terminating (recurring). {T}

A rational number gives either terminating or non-terminating recurring decimal expansion. Thus, we can say that a number whose decimal expansion is terminating or non-terminating is rational. {T}

The decimal expansion of a rational number cannot be non- terribly and non- repeating. {T}

Any number that can be written in fraction form is a rational number. This includes integers, terminating decimals, and repeating decimals as well as fractions. {T}

//Numericals

Determine whether the decimal expansion of 7/16 is terminating or non-terminating. {
= Terminating
~ Non-terminating
}

Determine whether the decimal expansion of 23/30 is terminating or non-terminating? {
~ Terminating
= Non-terminating
}

Determine whether the decimal expansion of 5/8 is terminating or non-terminating. {
= Terminating
~ Non-terminating
}

Determine whether the decimal expansion of 19/45 is terminating or non-terminating. {
~ Terminating
= Non-terminating
}

Determine whether the decimal expansion of 77/250 is terminating or non-terminating. {
= Terminating
~ Non-terminating
}

//Fill in the blanks

___ is a number where the digits after the decimal point end. {
= Terminating decimal
~ Non-terminating decimal
~ Both
~ None of the above
}

29÷9261 has a   _____ decimal expansion. {
~ Terminating and repeating
= Non-terminating and non- repeating
~ Non-terminating and repeating
~ Terminating and non- repeating
}

_____ is the decimal expansion of 3÷13 {
~ 0.2300
~ 0.23
= 0.2307692
~ None of the above
}

_____ is the decimal expansion of 3÷7 {
= 0.428
~ 0.399
~ 0.41
~ None of the above
}

//Match the following

Match the following items from Column A with their correct corresponding options from Column B\:
{
=Non- terminating decimal expansion means -> non-terminating and non-repeating
=Terminating decimal expansion of a rational number  means -> while using the long division method we will get a fixed number of digits in the quotient
=The decimal expansion of a rational number can never be -> non-terminating and non-repeating
=The decimal expansion of  an irrational number is always -> non-terminating and non-repeating
}



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