How to convert recurring decimal to fraction?

We need to deal with recurring or repeating decimals in school, in our competitive exams and even later.  Today we’ll discuss a shortcut trick to convert recurring decimals to fractions. However, to understand it’s effectiveness, we need to first understand the method taught in schools.

Just follow the steps below carefully. Say you need to find the value of 0.44444……

Step 1: Let x be the value of the repeating decimal which you are converting to fraction
x = 0.44444444… 

We know the repeating digit is 4

Step 2: Multiply x by a power of 10, such that the resultant has same repeating digits on the right side of decimal. In this case if we multiply 10 both side, we get – Read More

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How to express fractions as decimals

In the past few days I didn’t enough time to think and write about a any topic on QuickerMaths.com. Today the suggestion of this topic came from one of you, so half the work was done. Friends I will request you to keep suggesting new topics on which I can write for everyone’s benefit on QuickerMaths.com

How to express fractions as decimals or percentage

This post will help you to learn:

  1. Express a given percent as a decimal or fraction.
  2. Solve a given problem that involves finding a percent.
  3. Determine the answer to a given percent problem where the answer requires rounding, and explain why an approximate answer is needed (e.g., total cost including taxes).
  4. Work problems involving pie charts and percents.
  5. Work problems involving tables and percents.

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Comparison of Fractions

In this post you will learn about comparing fractions and arranging them in ascending or descending order of magnitude.  All of us must have learned this during our school days. However, here we are going to discuss this in more detail and will discover the most suitable way of doing it.

Fractions can be compared in many ways. Here we’ll discuss 4 different ways of doing it.

If Denominators are same and Numerators are different

Like

56              57

—    and  —

98              98

Just compare the numerators,

So the rule is:

a         b

— > —,       if  a > b

n         n

 

Since 56 < 57,

56        57

—    < —

98         98

They are in the same order as their numerators.

If Numerators are same and Denominators are different

Compare 5/9 and 5/6

This works the opposite way: The bigger the denominator, the smaller the fraction. So the rule

is:

n        n

— > —  if  a < b

a         b

Since 9 > 6, 5/9 < 5/6. They are in the reverse order of their denominators.

General Cases

You simply convert the fractions to the first case, by giving them a common denominator.

You do not really have to worry about finding the least common denominator, though sometimes that will save a lot of work.

Let us compare 5/9 and 4/7. Since we do not see any common factors immediately (and in fact there are not any), we can just multiply the denominators to get a common denominator, 63. To convert 5/9 to 63rds, we multiply by 7; to convert 4/7 to 63rds, we multiply by 9:

5              4

— ,       —

9             7

5*7          4*9

—         ?     —

9*7           7*9

 

35 < 36,

so

5            4

— <     —

9             7

You may not calculate the value of denominator because it will be same in both cases.

5*7=35          4*9=36; since this is bigger, 4/7 is bigger

If there is a common multiple in denominators, for instance, which is bigger, 5/9 or 44/81? I see that

81 is a multiple of 9, so I do not have to go to the trouble of multiplying 5 by 81 and 44 by 9; I just multiply 5 by 9 and compare to 44:

 

5         44

— ,     —

9          81

5*9       44

—     ,   —

9*9       81

45 > 44 so

5           44

— >       —

9            81

Converting Fractions into Decimal Form

Here we need to convert each one of the given fractions in the decimal form. Thereafter, arrange them in ascending or descending order

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Decimal Fraction Rules

Multiplication of a decimal Fraction by a Power of 10: Rule: Shift the decimal point to the right by as many places of decimal as   is the power of 10.

Multiplication of Decimal fractions:- Rule :- Multiply the given numbers considering them without the  decimal  point. Now, in the product, the decimal point is marked off to obtain as many places of decimal as is the sum of the number of decimal in the given numbers.

Dividing a Decimal fraction By a Counting Number

Rule: – Divide the given number without considering the decimal point  by the given counting   number. Now, in the quotient, put the decimal point to give as many places of decimal as are there in  the dividend.

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