Representation Of Decimals On Number Line

Decimal numbers are a form of number in mathematics used in representing a fraction of a number. These numbers lie between two whole numbers. For example, 1.5 will be a decimal number as it lies between two whole numbers 1 and 2.

• For denoting integers and non integers decimal numbers are used.
• In decimal numbers the whole number and the fractional part are separated by a decimal point (.).
• In ancient India Aryabhata and other mathematicians were the first ones to use the decimal system of numbers.

Key Terms: Decimal Numbers Whole Number, Fraction, Number Line.

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What are Decimal Numbers?

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Decimal numbers are a certain type of number where a decimal point is separating two parts of a number; one of them is an integer and the other one is a fractional part. For example, if 3 biscuits are being divided between 2 kids then each of them will get 1.5 biscuits. Here, 1.5 is a decimal number, where 1 is the integer part and the number after the decimal point is the fractional part.

• To check if a number is logical or irrational decimal numbers are used.
• All decimal numbers are fractions.
• Tenths, hundredths, thousandths, and other fractions of a unit are expressed by decimals.

Read More: Polynomial Equation

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How are Decimal Numbers Represented?

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A non-negative real number ‘r’ can be written as a combined form of its whole number and fractional part; the form will look like –

r = \(\sum^k_{i=0} b_i10^i = \sum^{\infty} _{i = 1} \frac{a_i}{10^i}\)

Here, the first part of the equation represents the integer part and the second part of the equation represents the fractional part. Here, ai is a non-negative integer and a₁, a₂, …are the integers satisfying the condition 0≤ a_i≤ 9

Decimal numbers are all rational numbers and there could be two possibilities such as the number might be a terminal decimal number or it can be a repeating decimal number. 

For example, ⅖ = 0.4 is an example of terminating decimal number.

And ⅓ = 0.33333…… is an example of repeating decimal number.

A decimal number 11.256 will sound like “eleven point two five six”.

Coloring in one of the squares in the table, will represent decimal 0.01. This means 0.01 is equal to one hundredth (1/100).

This would be represented by 0.1, as 10 boxes are coloured among the 100 and 10/100 = 0.1

Read More: Real-Valued Function

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Decimal Number Representation on a Number Line

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Considering a line from 0 to 1 it is possible to get a concept about the position of the decimal numbers on that line.

Now, the distance between these two numbers can be divided into ten parts and the middle point of this number line will be 0.5

For example, the position of 0.7 in the number line will be –

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Solved Examples

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Example 1: Represent 4.6 on the number line.

Solution: The number 4.6 = 4 + 0.6

From the number 4.6 on the number line the section between 4 and 5 is divided into 10 equal parts. Now, to represent 4.6 the position should be starting from 4 towards six steps ahead of 5.

Example 2: Represent 0.3 on the number line.

Solution: The number 0.3 = 0 + 0.3

From the number 0.3 on the number line the section between 0 and 1 is divided into 10 equal parts. Now, to represent 0.3 the position should be starting from 0 towards six steps ahead of 1.

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Things to Remember

• Decimal number lies between two whole numbers.
• Decimal numbers consist of two parts: the first part is the whole number and the second part is the fraction.
• Both the whole number and fractional part is separated by a decimal point (.).
• All decimal numbers are fractions.
• Decimals express tenths, hundredths, thousandths, and other fractions of a unit.
• To represent any decimal number the distance between two whole numbers can be divided into ten parts.