Decimal To Fraction

Type de fraction Représentation des fractions
Sur 100
Simplifié
Nombre entier + fraction
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Decimal to Fraction step by step

 Example-1

Step 1: Write the Decimal Divided by 1

Write down the decimal number as a fraction with the decimal as the numerator and 1 as the denominator.

0.75=0.7510.75=10.75​

Step 2: Eliminate the Decimal Point

Multiply both the numerator and the denominator by a power of 10 that makes the numerator a whole number. For 0.75, since there are two digits after the decimal, we multiply by 102102 or 100.

0.751×100100=7510010.75​×100100​=10075​

Step 3: Simplify the Fraction

Find the Greatest Common Divisor (GCD) of the numerator and the denominator to simplify the fraction. The GCD of 75 and 100 is 25.

Divide both the numerator and the denominator by their GCD (25).

75100=75÷25100÷25=3410075​=100÷2575÷25​=43​

Therefore, the decimal 0.75 converted to a fraction is 3443​, in its simplest form.

This example demonstrates a straightforward process for converting a terminating decimal into a fraction. For repeating decimals, the method involves a bit more algebra, but the principle of expressing the value as a ratio of two integers remains the same.

 

Example-2

Converting the Repeating Decimal 0.333... to a Fraction

Step 1: Let's represent the repeating decimal 0.333... by a variable, say x.

Let x=0.333...x=0.333...

Step 2: To deal with the repeating nature, we multiply x by 10 to shift the decimal point, aligning the repeating section with itself. This action helps us set up an equation that can be manipulated algebraically.

Multiply by 10 to shift the repeating digits: 10x=3.333...10x=3.333...

Step 3: We then create an equation to eliminate the repeating part by subtracting the original equation from the multiplied one.

Original equation: x=0.333...x=0.333...

Multiplied equation: 10x=3.333...10x=3.333...

Subtracting the original from the multiplied equation: 10x−x=3.333...−0.333...10x−x=3.333...−0.333...

Step 4: Solve the resulting equation.

The subtraction results in 9x=39x=3, because 3.333...−0.333...=33.333...−0.333...=3.

To find x, divide both sides by 9: x=39x=93​

Step 5: Simplify the fraction.

The fraction 3993​ can be simplified by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 3 in this case.

Simplification: 3÷39÷3=139÷33÷3​=31​

Therefore, the repeating decimal 0.333... is equivalent to the fraction 1331​ in its simplest form.Formun Üstü

FAQ: Decimal to Fraction Conversion

What is a decimal to fraction conversion?

Decimal to fraction conversion involves changing a decimal number, which has a base of 10, into a fraction, which is expressed as one integer over another. This process helps in representing the same value in two different forms, making it easier to perform certain mathematical operations or understand the value in a different context.

How do I convert a simple decimal to a fraction?

To convert a simple decimal to a fraction:

1.Write down the decimal divided by 1 (e.g., 0.75/1).

2.Multiply both the numerator (top number) and the denominator (bottom number) by a power of 10 that makes the numerator a whole number (for 0.75, multiply by 100 to get 75/100).

3.Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD).

Can repeating decimals be converted to fractions?

Yes, repeating decimals can be converted to fractions through a method that involves algebraic manipulation:

1.Let x equal the repeating decimal.

2.Multiply x by a power of 10 that shifts the decimal point to the right, so the repeating digits align.

3.Subtract the original number (x) from this new number to eliminate the repeating part.

4.Solve for x, which now represents the fraction form.

What is the difference between terminating and repeating decimals?

Terminating decimals are those that have a finite number of digits after the decimal point, such as 0.5 or 0.125. They can be easily converted to fractions. Repeating decimals have one or more digits that infinitely repeat, such as 0.333... or 0.666..., and require a specific method for conversion to fractions.

How do I simplify a fraction after converting from a decimal?

After converting a decimal to a fraction, simplify it by dividing the numerator and the denominator by their greatest common divisor (GCD). This will give you the simplest form of the fraction.

Is there a way to convert decimals to fractions automatically?

Yes, many calculators and online tools can automatically convert decimals to fractions. These tools often provide the simplified form of the fraction, making the process quick and accurate.

Why is it important to convert decimals to fractions?

Converting decimals to fractions is important for several reasons:

-It allows for easier comparison of values.

-Some mathematical operations, like addition and subtraction, are simpler with fractions.

-It provides a different perspective on proportions and ratios, which can be useful in various fields like cooking, construction, and science.

Can all decimals be converted to fractions?

All rational numbers, which include terminating and repeating decimals, can be converted to fractions. However, irrational numbers, which have non-repeating, non-terminating decimals, cannot be precisely converted into a fraction.

What are the limitations of converting decimals to fractions?

The main limitation is with irrational numbers, as their decimal representation cannot be accurately converted into a fraction. Additionally, for very long repeating decimals, finding the exact fraction form can be complex and might require approximation.

How do I deal with decimals that have a lot of digits after the decimal point?

For decimals with many digits:

1.Determine if the decimal is repeating or non-repeating.

2.For non-repeating decimals, you may round the number to a certain decimal place before converting to simplify the process.

3.For repeating decimals, identify the repeating pattern and use the algebraic method for conversion.

 

 

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