In Mathematics, we have learnt different types of numbers, such as real numbers, rational numbers, natural numbers, complex numbers, and so on. Similarly, decimals are one among the types of real numbers. The decimal values may be either terminating or non-terminating. Generally, the decimal values are used in the scenarios, where we need more precise value than the whole value.
As we know, decimal numbers are the numbers that have two different parts, such as the integer part and the fractional part. The integer value and the fractional value are separated by a point called the decimal point. The digit which is present on the left side of the decimal point is called the whole number part, and the digit which is present on the right of the decimal point is called the fractional part. The integer part may be either positive or negative. For instance, 5.467 is a decimal number. Here, 5 is an integer part, and 467 is a decimal part.
Now, let’s learn the place values chart, which helps to determine the place value of the digits in a given decimal number. For example, the place value of a decimal number 9674.356 is,
“9” – Thousands
“6” – Hundreds
“7” – Tens
“4” – Ones
“.” – Decimal Point
“3” – Tenths
“5” – Hundredths
“6” – Thousandths
Thus, the decimal number 9674.356 can be read as Nine thousand six hundred seventy-four and three hundred fifty-six thousandths. Or else, it can also be read as nine thousand six hundred seventy-four point three five six.
Depending on the number of digits to the right side of the decimal point, the decimal number can be classified into different types. They are:
In terminating decimals, the number of digits on the right side of the decimal point are countable. It means that there should be a finite number of digits after the decimal point. For example, 6.223 has three digits after the decimal point, and hence it is called terminating decimals.
In non-terminating decimals, the number of digits after the decimal points are infinite, and it cannot be countable. The non-terminating decimals are further classified into two types, namely:
In recurring decimals, the digits after the decimal point are repeated at regular intervals. For example, 4. 17171717…. is a non-terminating recurring decimal number, as the digits 17 is repeated at regular intervals.
In non-repeating decimals numbers, the digits present on the right side of the decimal point are infinite, and at the same time, it does not follow any specific order. The non-terminating and non-repeating decimals are known as irrational numbers, as it cannot be written in the p/q form.
The non-terminating decimal numbers can be converted into the terminating decimals by rounding off to the specific number of decimal places. The rounding off method is given as follows:
- First, identify the number of digits which you want to round off.
- After finding the place value of the digit, now look at the right side of the digit.
- If that digit is greater than or equal to 5, then add 1 to the previous digit.
- If the digit is less than 5, then leave the number as it is.
For example, 7.1457286… is a non-terminating decimal. The rounding of this number up to three decimal places is 7.146, as the fourth digit of the number after the decimal point is 7, which is greater than 5.
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