What is comparing decimals

• Written By Priya_Singh
• Last Modified 20-07-2022

Comparing Decimals: The word decimal comes from the Latin word “Decem”, which means \(10.\) Decimal numbers are the standard form of representing integers and non-integer numbers. 

When you compare the decimals, you need to check the digits before the decimal point and check if they are smaller than or greater than the other number. Second, if the digits before the decimal point are identical, you have to compare the first digit after the decimal point, which is the tenth digit and identify which is greater or smaller. Let’s learn in detail how to compare decimals with solved examples.

What are Decimals?

Decimals are the extension of the number system. They can also be considered as fractions only when the denominators are \(10, 100, 1000\) etc. The numbers expressed in decimal forms are known as decimals.

Example: \(17.235, 0.149, 125.005, 2534.0\) etc. are the decimal numbers or decimals.

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So, each decimal number or decimal has two parts, namely

1. Whole number part
2. Decimal part

These two parts are separated by a dot \((.),\) which is known as the decimal point.In the decimal number \(27.54,\) the whole number part is \(27,\) and the decimal part is \(54.\)

Decimal Places: The number of digits accommodated in the decimal part of a decimal number is known as the number of decimal places.

Examples: \(3.75\) has two decimal places, and \(85.325\) has three decimal places.

Types of Decimals Numbers

There are two types of decimals which are mentioned below, along with the examples:

1. Terminating decimals
2. Non-terminating decimals

Practice Exam Questions

Terminating Decimals

These decimals have a finite number of digits after the decimal point. These are also called exact decimal numbers, as the digits after the point is countable.

Example: \(89.9856, 2.32, -1.89546, 3.37543\) etc., are examples of the terminating decimal numbers. They can also be written in the form of  \(\frac{p}{q},\) and hence, they are rational numbers.

Non-Terminating Decimals

These decimals have an infinite number of digits after the decimal point. They are non-terminating decimals that repeat endlessly. These are further divided into two more numbers, and they are:

1. Recurring decimal numbers
2. Non-recurring decimal numbers

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Recurring Decimal Numbers

These decimals have an infinite number of digits after the decimal point, but these digits (single-digit or a group of digits) are repeated.

Examples: \(5.313131…., 7.89898989…., 9.1111111….,\) etc. these are recurring decimals as one or a group of digits at the decimal places are repeated. The recurring decimal numbers can also be expressed by putting a bar over the digit or the group of digits that are repeating.

Example: \(120.\overline {35} = 120.3535353535 \ldots \ldots ,\)\(5.\overline {13} = 5.1313131313 \ldots \ldots ,\) 

\(7.\overline {809} = 7.809809809809 \ldots \ldots \ldots \)