Decimals: Definition, Expanded Form, Place Value, Types & Solved Examples

Decimals are used to depict or express the fraction and whole numbers together. A decimal number is defined as a decimal point separating the whole number and fractional parts in Algebra. The whole number is separated from the fraction by inserting the “.” as a decimal point. The digits which are present after the decimal point represent a value less than one. For instance,43.87 is a decimal number. Here, the whole number is 43, and the decimal half is 87. There are numerous real-life situations where we use decimals without even realizing the same. 

Key Terms: Decimals, Fractions, Whole Number, Decimal Point, Place Value, Face Value, Integers, Expanded Form, Denominator

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What are Decimals?

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Decimals can be defined as a set of numbers lying between integers on a number line. Decimals are just another way of representing fractions in Mathematics. They can be extremely useful in writing precise values of measurable quantities like length, weight, distance, money, etc. 

The numbers that are on the left of the decimal point are whole numbers and the numbers to the right of the decimal point are decimal fractions.

For example, 45.67. Here, 45 is the whole number while 67 is the decimal fraction. 

Decimals

Read More: Addition and Subtraction of Integers

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Decimals Place Value Chart

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The place value of a digit in a number are identified by its position in the given number. The place value of the digit 8 in the number 1873, for example, is 800 because it is in the hundreds place. However, if the numbers 8 and 7 in the number 1873 are swapped, we get the new number 1783. The numeral 8 has an 80 place value in 1783 because it is in the tens place.

In decimals, the place value system for the whole number part is the same as the whole number. However for the decimal fraction part, when we are going towards the left, each place is ten times greater than the previous place value. Hence we can say that, to the right of the ones place, we have tenths (1/10) and to the right of tenths, we have hundredths (1/100), and so on. To find the place values of the digits in a decimal number, we can use a decimal place value chart. 

Decimal Place Value Chart

The face value of a digit is its true value. Unlike the place value of a digit, which is determined by its location in a number, the face value of a digit remains constant regardless of its location.

Read More: Face Value and Place Value

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How to Read Decimal Numbers?

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A decimal number can be read in two ways:

• The first method is to read the complete number followed by "point," then read the fractional part's digits separately. It's a more relaxed approach to reading decimals. For example, 52.36 can be read as fifty-two point three-six. 
• The second method is to read the whole number part first, then the fractional part, which is read in the same way as whole numbers but with the place value of the last digit. We can read 52.36 as fifty-two and thirty-six hundredths.

Reading Decimals

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Expanded Form of Decimal Numbers

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The mathematical statement that shows the sum of the values of each digit in a decimal number is known as expanded form notation.

The decimal or fraction expanded form is written with a base 10-multiple denominator, denoted by the power of 10.

For example, the expanded form of the number 3.482 is

Read More: Difference Between Fraction and Rational Numbers

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Rounding Decimal Numbers to Nearest Tenths

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When rounding a decimal number to the closest tenths, the digit at the hundredth place is considered. There are two possibilities for the digit at the hundredth position. Remove all the digits to the right of the tenth place digit if the number is 4 or less, and the remainder is our desired result. If the digit in the hundredths place is 5 or above, we must first increase the tenths place digit by 1, then eliminate all the digits to its right.

Example: Consider the number 6.914

6.914 rounded to the nearest tenth is 6.9 because 9 is followed by 1 and 1 is less than 5.

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How To Compare Decimals?

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The following are the rules for comparing decimal numbers:

• First, compare the whole number component (i.e., compare the digits before the decimal). If they're not the same, compare the numbers as if they were whole numbers. If they are identical, proceed to the next step.
• Take a look at the tenth place. If they're not the same, compare the numbers as if they were whole numbers. If they have the same value, move to the next digit.
• Compare the tenths position with the hundredth place. If they're not the same, compare the digits as if they were whole numbers. If they have the same value, move to the next digit, and so on.

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Types of Decimal Numbers

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There are two sorts of decimal numbers, each of which is described below:

• Terminating Decimal Numbers
  • After the decimal point, these decimal values have a finite number of digits. These decimal numbers are rational because they can be represented in the form p/q. Example: 2.5674

• Non-Terminating Decimal Numbers 
  • In non-terminating decimals, the digits have an endless number of digits after the decimal point. There are two types of decimal numbers: recurring and non-recurring decimal numbers.

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Things to Remember 

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• Decimals are just another way of representing fractions in Mathematics.Decimals are a way of writing fractions and mixed numbers with denominators of powers of ten, such as 10,100,1000,10000. If a number has a decimal point, the number of tenths is shown by the first digit to the right of the decimal point.
• A tenth is equal to one-tenth of a per cent. It is 0.1 in decimal form. The term "hundredth" refers to one-hundredth of a per cent. It is 0.01 in decimal form.
• Consider one digit at a time from the right of the decimal point to compare the decimal or fractional component of any decimal value.
• Terminating and non-terminating decimal numbers are the two forms of decimal numbers. The digits in non-terminating decimals have infinite digits after the decimal point. The digits after the decimal point have a finite number of digits in terminating decimals.

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