What are Whole Numbers?
The set of whole numbers (denoted using the letter W) consists of zero and the set of natural numbers (N: 1, 2, 3, 4…). In simple words, the set of whole numbers includes all positive integers and zero. So, the only difference between the set of natural numbers and the set of whole numbers is that the latter set has zero as a part of the set. We use whole numbers to associate whole parts with numbers. We cannot use whole numbers to represent shares or fractions.
What are Decimal Numbers?
Decimal numbers are numbers that belong to the decimal number system, and this is an extension of the Hindu-Arabic numeral system. We can represent all whole numbers, fractions, and mixed numbers as decimal numbers. The whole number part and the fractional part of a decimal number are separated using a decimal point ‘.’. The whole number part is written on the left of the decimal point, and the fractional part is written on the right of the decimal point. For example, the whole number part of ‘1.2’ is ‘1’, and the fractional part is ‘.2’. We get 1.2 by combining both parts.
How to divide a Decimal Number by a Whole Number?
A decimal number can be divided by a whole number using the normal long division method. Here, the dividend and the quotient will be decimal numbers, and the divisor will be a whole number. The division operation may or may not result in a remainder. This depends on whether the divisor completely divides the dividend or not.
Let us consider the division operation of 18.93. We start the long division operation by placing a decimal point in the quotient’s field right above the decimal point present in the dividend’s field.
Now, we will divide the whole number part of the dividend by the divisor, that is, 18 ones divided by 3.
The next step is to divide the decimal part of the dividend by the divisor, that is, 9 tenths divided by 3.
So, we obtain a decimal number as the quotient, and the remainder is zero.
Hence, 18.9 \(\div\) 3 = 6.3.
Solved Examples
Example 1: Evaluate 40.2 \(\div\) 2.
Solution:
We can use the long division method to find the value of 40.2 \(\div\) 2.
Hence, 40.2 \(\div\) 2 = 20.1
Example 2: Evaluate 8.64 \(\div\) 6.
Solution:
We can use the long division method to find the value of 8.64 \(\div\) 6.
Hence, 8.64 \(\div\) 6 = 1.44
Example 3: Suppose the price of eight grams of gold is $52.8. Calculate the price of gold per gram.
Solution:
Price of 8 grams of gold = $52.8
Price of 1 gram of gold = $52.8 \(\div\) 8
We can evaluate this using the long division method.
So, 52.8 \(\div\) 8 = 6.6
Hence, the price of gold per gram is $6.6.
Yes, the result of dividing a decimal number by a whole number will result in a decimal number.
The presence of a remainder after the division operation of a decimal number by a whole number depends on the value of dividend and the divisor. A remainder is observed only if the divisor does not completely divide the dividend.
Yes, a whole number can completely divide a decimal number. In such cases, the division operation will not result in a remainder.