Subscribe to our YouTube channel for the latest videos, updates, and tips.


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.



Decimal.

Decimal Place Value Chart.

Expanded form of Decimal Fractions.

Like Decimal Fractions.

Unlike Decimal Fraction.

Equivalent Decimal Fractions.

Changing Unlike to Like Decimal Fractions.

Ordering Decimals

Comparison of Decimal Fractions.

Conversion of a Decimal Fraction into a Fractional Number.

Conversion of Fractions to Decimals Numbers.

Addition of Decimal Fractions.

Problems on Addition of Decimal Fractions

Subtraction of Decimal Fractions.

Problems on Subtraction of Decimal Fractions

Multiplication of a Decimal Numbers.

Multiplication of a Decimal by a Decimal.

Properties of Multiplication of Decimal Numbers.

Problems on Multiplication of Decimal Fractions

Division of a Decimal by a Whole Number.

Division of Decimal Fractions

Division of Decimal Fractions by Multiples.

Division of a Decimal by a Decimal.

Division of a whole number by a Decimal.

Properties of Division of Decimal Numbers

Problems on Division of Decimal Fractions

Conversion of fraction to Decimal Fraction.

Simplification in Decimals.

Word Problems on Decimal.



5th Grade Numbers Page

5th Grade Math Problems

From Equivalent Decimal Fractions to HOME PAGE




Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.




Share this page: What’s this?

Recent Articles

  1. Worksheet on Simple Interest | Word problem on Simple Interest | Free

    Jun 19, 25 01:53 AM

    Worksheet on Simple Interest 2
    In worksheet on simple interest we will get different types of question on calculating the simple interest, the principal amount, the rate of interest and the word problems on simple interest.

    Read More

  2. Terms Related to Simple Interest | Simple Interest Formula | Principal

    Jun 19, 25 12:20 AM

    Terms Related to Simple Interest
    In terms related to simple interest we will learn all the terms related to simple interest. The terms related to simple interest are Interest, Principal, Amount, Simple Interest, Time or period of tim…

    Read More

  3. Introduction to Simple Interest | Definition | Formula | Examples

    Jun 18, 25 01:50 AM

    Simple Interest
    In simple interest we will learn and identify about the terms like Principal, Time, Rate, Amount, etc. PRINCIPAL (P): The money you deposit or put in the bank is called the PRINCIPAL.

    Read More

  4. 5th Grade Profit and Loss Percentage Worksheet | Profit and Loss | Ans

    Jun 18, 25 01:33 AM

    5th Grade Profit and Loss Percentage Worksheet
    In 5th grade profit and loss percentage worksheet you will get different types of problems on finding the profit or loss percentage when cost price and selling price are given, finding the selling pri…

    Read More

  5. Worksheet on Profit and Loss | Word Problem on Profit and Loss | Math

    Jun 18, 25 01:29 AM

    Worksheet on Profit and Loss
    In worksheet on profit and loss, we can see below there are some different types of questions which we can practice in our homework.

    Read More