Equivalent Decimal Fractions

Equivalent decimal fractions are unlike fractions which are equal in value.

Let us take a plane sheet which represents one whole. Now, we divide the sheet into 10 equal parts.

$Equivalent Decimals$

The colored part in the above figure represents two-tenths of the whole or 0.2.

We now further divide the part into 10 equal parts. There are now 100 equal parts.

$Equivalent Decimal Fractions$

The colored part in figure B represents the fraction $\frac{20}{100}$ or 0.02. Same way, if we divide further there will be 1000 equal parts and the colored part will represent $\frac{200}{1000}$ or 0.200. The decimals 0.2, 0.20 and 0.200 are equivalent decimals. So, placing any number of zeroes to the right of the decimal part does not change its value.

Look at the figures:

$Zero Point One$	$Zero Point One Zero$
Shaded portion indicates $\frac{1}{10}$ = 0.1	Shaded portion indicates $\frac{10}{100}$ = 0.10

Both the fractions indicate the same shaded portions.

Therefore, we have 0.10 = 0.1

Similarly 0.20 = 0.2; 0.30 = 0.3

Let us consider the following examples:

(i) 0.4, 0.40, 0.400, 0.4000

Each of the above is equal to 0.4 or 4/10.

(ii) 1.9, 1.90, 1.900, 1.9000

Each of the above is equal to 1.9 or 19/10.

(iii) 10.14, 10.140, 10.1400, 10.14000

Each of the above is equal to 10.14 or 1014/100.

(iv) 0.94, 0.940, 0.9400, 0.94000

Each of the above is equal to 0.94 or 94/100.

(v) 9.1, 9.10, 9.100, 9.1000

Each of the above is equal to 9.1 or 91/10.

(vi) 60.49, 60.4900, 60.490

Each of the above is equal to 60.49 or 6049/100.

Similarly, we have

0.300 = 0.30 = 0.3

0.700 = 0.70 = 0.7

0.200 = 0.20 = 0.2

Thus, by adding any number of zeros after the extreme right digit in the decimal part of a decimal number does not change the value of the number.

Numbers obtained by inserting zeros after the extreme right digit in the decimal part of a decimal number are known as equivalent decimals.

Hence, 0.75, 0.750, 0.7500 etc are equivalent decimals.

More Examples on Equivalent Decimal Fractions:

1. Is 0.90 = 0.9?

0.90 = $\frac{90}{100}$ 0.9 = $\frac{9}{10}$

$\frac{90}{100}$ = $\frac{9 × 10}{10 × 10}$

That is, $\frac{90}{100}$ and $\frac{9}{10}$ are equivalent fractions.

Therefore, $\frac{90}{100}$ = $\frac{9}{10}$

Hence 0.90 = 0.9

2. Is 0.900 = 0.9?

0.900 = $\frac{900}{1000}$ 0.9 = $\frac{9}{10}$

$\frac{900}{1000}$ = $\frac{9 × 100}{10 × 100}$

That is, $\frac{900}{1000}$ and $\frac{9}{10}$ are equivalent fractions.

Therefore, $\frac{900}{1000}$ = $\frac{9}{10}$

Hence 0.900 = 0.9

Similarly, 0.8 = 0.80 = 0.800 = 0.8000 and so on

0.7 = 0.70 = 0.700 = 0.7000 and so on

Adding one, two or three zeroes after the extreme right digit in the decimal part does not change the value of the fractional number.

For example:

0.25 = 0.250

0.46 = 0.4600

0.19 = 0.1900 and so on.

You might like these

$Like Decimal Fractions are discussed here. Two or more decimal fractions are called like decimals if they have equal number of decimal places. However the number of digits in the integral part does not matter. 0.43, 10.41, 183.42, 1.81, 0.31 are all like fractions$

Like Decimal Fractions | Decimal Places | Decimal Fractions|Definition
Like Decimal Fractions are discussed here. Two or more decimal fractions are called like decimals if they have equal number of decimal places. However the number of digits in the integral part does not matter. 0.43, 10.41, 183.42, 1.81, 0.31 are all like fractions
$Decimal numbers can be expressed in expanded form using the place-value chart. In expanded form of decimal fractions we will learn how to read and write the decimal numbers. Note: When a decimal is missing either in the integral part or decimal part, substitute with 0.$

Expanded form of Decimal Fractions |How to Write a Decimal in Expanded
Decimal numbers can be expressed in expanded form using the place-value chart. In expanded form of decimal fractions we will learn how to read and write the decimal numbers. Note: When a decimal is missing either in the integral part or decimal part, substitute with 0.
Multiplication of Decimal Numbers | Multiplying Decimals | Decimals
The rules of multiplying decimals are: (i) Take the two numbers as whole numbers (remove the decimal) and multiply. (ii) In the product, place the decimal point after leaving digits equal to the total number of decimal places in both numbers.
Division of a Decimal by a Whole Number | Rules of Dividing Decimals
To divide a decimal number by a whole number the division is performed in the same way as in the whole numbers. We first divide the two numbers ignoring the decimal point and then place the decimal point in the quotient in the same position as in the dividend.
Multiplication of a Decimal by a Decimal |Multiplying Decimals Example
To multiply a decimal number by a decimal number, we first multiply the two numbers ignoring the decimal points and then place the decimal point in the product in such a way that decimal places in the product is equal to the sum of the decimal places in the given numbers.
$Unlike decimal fractions are discussed here. Two or more decimal fractions are called unlike decimals if they have unequal numbers of decimal places. Let us consider some of the unlike decimals; (i) 8.4, 8.41, 8.412 In 8.4, 8.41, 8.412 the number of decimal places are 1, 2$

Unlike Decimal Fractions | Unlike Decimals | Number of Decimal Places
Unlike decimal fractions are discussed here. Two or more decimal fractions are called unlike decimals if they have unequal numbers of decimal places. Let us consider some of the unlike decimals; (i) 8.4, 8.41, 8.412 In 8.4, 8.41, 8.412 the number of decimal places are 1, 2
Comparison of Decimal Fractions | Comparing Decimals Numbers | Decimal
While comparing natural numbers we first compare total number of digits in both the numbers and if they are equal then we compare the digit at the extreme left. If they also equal then we compare the next digit and so on. We follow the same pattern while comparing the
Addition of Decimal Fractions | Adding with Decimal Fractions|Decimals
Addition of decimal numbers are similar to addition of whole numbers. We convert them to like decimals and place the numbers vertically one below the other in such a way that the decimal point lies exactly on the vertical line. Add as usual as we learnt in the case of whole
Subtraction of Decimal Fractions |Rules of Subtracting Decimal Numbers
The rules of subtracting decimal numbers are: (i) Write the digits of the given numbers one below the other such that the decimal points are in the same vertical line. (ii) Subtract as we subtract whole numbers. Let us consider some of the examples on subtraction
$Division of a decimal number by 10, 100 or 1000 can be performed by moving the decimal point to the left by as many places as the number of zeroes in the divisor. The rules of division of decimal fractions by 10, 100, 1000 etc. are discussed here.$

Division of Decimal Fractions | Decimal Point | Division of Decimal
Division of a decimal number by 10, 100 or 1000 can be performed by moving the decimal point to the left by as many places as the number of zeroes in the divisor. The rules of division of decimal fractions by 10, 100, 1000 etc. are discussed here.