Question

A terminating decimal is a rational number. (T/F). The mean of the first four even numbers is 5. (T/F). A point has no dimension. (T/F).

Answer 1

Hint: Section 1: Rational numbers are the real numbers which can be expressed in the form of $\dfrac{P}{Q}$ where P and Q are integers, Q is not equal to ‘0’ and P and Q have only 1 as their common factor. Terminating decimals are those numbers which come to an end after a few repetitions after the decimal point. For example: 0.5, 2.456, 123.456 are terminating decimal numbers. You can express 0.5 as $\dfrac{1}{2}$and similarly other such decimal numbers too.
Section 2: The mean of a set of finite number of data’s is calculated by adding all the data’s and dividing the sum so obtained by the number of data’s in the set. Even numbers are those natural numbers which are divisible by 2. Clearly, the smallest even number is 2.
Section 3: Dimension of a point means characteristics of the point which includes the information like length, width, and height of the point. A point does not have any length, width, and height.

Complete step by step solution:Step 2: Clearly, 2, 4, 6, 8 are the first four even numbers.
\[Sum\text{ }of\text{ }the\text{ }numbers=\text{ }2+4+6+8=\text{ }20\]
\[Number\text{ }of\text{ }datas\text{ }=\text{ }4\]
\[Mean\text{ }of\text{ }the\text{ }first\text{ }four\text{ }even\text{ }numbers\text{ }=\dfrac{Sum\text{ }of\text{ }the\text{ }datas}{Number\text{ }of\text{ }datas}\text{ }\]
$\Rightarrow \dfrac{20}{4}=5$
Hence the statement is TRUE.
Step 3: Clearly, a point has no length, width, and height. So we can say that it has no size. Hence it has no dimension. Therefore, the statement is TRUE.

Note: Rational numbers when expressed in the decimal form can be terminating or non-terminating. Consider the rational number $\dfrac{1}{3}$, When expressed in decimal form, it results in 0.333333 and the digits never stop. So, the student must keep in mind that every terminating decimal number is a rational number but every rational number is not terminating.
The student often thinks that all those numbers which are divisible by 2 are even numbers. For example, one may think that \[-4\]is also an even number but it is not so. An even number has to be a natural number. A point has no size so it has no dimension. A line has one dimension which is its length, a rectangle has two dimensions, its length and width and a cube has three dimensions, its length, width and height.