Question

The integral part of $78.027$ is?
$\begin{array}{rl}& \left(a\right)24\\ & \left(b\right)0.27\\ & \left(c\right)78\\ & \left(d\right)38\end{array}$

Answer 1

Hint: To solve the question given above, we will write the given number in the form of sum of an integer and a decimal part (whose value is less than 1). The integral part of the given number will be then equal to the integer which is written in the sum form with a decimal part.

Complete step-by-step answer:
In the above question, the number written as a decimal number. Before solving the question given above, we must know what is a decimal number and what are the parts of a decimal number. A decimal number is a kind of real number which we generally obtain by dividing a natural number with the power of 10.The decimal number generally contains a decimal point (.). The decimal numbers have two parts: a whole number part and a fractional part. The whole number part of a decimal is those digits to the left of the decimal point. The fractional part of decimal is represented by the digits to the right of the decimal point. The decimal point is used to separate these parts. In the question, we have to find the integral part of 78.029. For this, we will write 78.029 as a sum of the whole number and a decimal part (whose value is less than 1). Thus, we can say that: $78.029=78+0.029$. Now, the integral part of the above decimal number which is equal to the whole number part of the above sum. The whole number part of the above sum is 78.
Hence, option (c) is correct.

Note: The above question can also be solved alternatively by changing the decimal form of number into fractional form. For this, we will multiply and divide 78.027 with 1000.
 Thus, we will get: ${\displaystyle \frac{78.027}{1000}}\times 1000={\displaystyle \frac{78027}{1000}}$
The above fraction can also be written as:
$\begin{array}{rl}& {\displaystyle \frac{78027}{1000}}={\displaystyle \frac{78000}{1000}}+{\displaystyle \frac{27}{1000}}\\ & \Rightarrow {\displaystyle \frac{78027}{1000}}=78+{\displaystyle \frac{27}{1000}}\end{array}$
As we can see that 78 as a whole number part and the value of ${\displaystyle \frac{27}{1000}}$ is less than 1. So the integral part is 78.