How Do You Change Decimals Into Fractions

Catechumen Decimal to Fraction

Converting decimals to fractions is one of the most frequently carried out steps in arithmetic. However, in club to exercise so, you need to have your division basics in place. Once you lot grasp this, you will exist able to convert decimals to fractions, as well as fractions to decimals.

Cheque out the decimal to fraction table in this lesson to get a better thought of how y'all tin can convert decimals into fractions.

one.	How to Catechumen Decimal to Fraction?
2.	Decimal to Fraction Conversion Tabular array
3.	Convert Decimal to Fraction: Inches
4.	FAQs on Converting Decimal to Fraction

How to Convert Decimal to Fraction?

Here is a simple 4-stride procedure to convert any decimal into a fraction.

Steps for Conversion:

Step 1- Place the place value of the digits after the decimal, in the number.
Stride 2- Use that to determine what the denominator of the fraction would be.
Stride 3- Remove the decimal point. Re-write in the fraction form and simplify information technology.
Step iv- Limited in terms of the lowest Equivalent fraction.

Let us look at an instance to understand these steps.

Case: Convert 0.5 into a fraction.

Solution: Permit's apply the steps that we learned.

Step 1: Identify the place value of the concluding digit.

0.5 <------------ 5 is in the tenths place. (0.v indicates 0.50)

Step 2: The denominator would exist ten

Pace 3: Fraction format: Numerator/Denominator = v/x

Step 4: Simplest Grade: 1/2

Thus, 0.5=5/10=i/2.

Go through the sections below to find more examples on how to convert fractions to decimals. There are three individual cases that you might come across while converting decimal to fraction, and those are listed below:

Converting Repeating Decimal to Fraction
Converting Decimals to Mixed Number Fractions
Convert Negative Decimal to a Fraction

Permit's learn about each case in detail.

Converting Repeating Decimal to Fraction

Repeating decimals are those that do not cease after a finite number of decimal places and some particular digits or a single digit after the decimal point keep on repeating in the number. To catechumen any repeating decimal to a fraction, at that place is a particular method that needs to be applied. Allow'due south consider an example to understand that.

Convert 0.77777... to a fraction.

Let x = recurring number, i.e.

0.77777....

northward= the number of recurring digits, i.e. seven

Multiply the recurring decimal by x, i.e.,

10x=vii.77777...

This implies,

10x - x=7
9x=7
∴ x= seven/9

Converting Decimals to Mixed Number Fractions

Decimals with values greater than 1 can be written equally mixed fractions. Await at the steps to convert such decimal numbers into mixed fraction class:

Step 1- Consider the whole number office and decimal part in the given decimal number separately.
Step 2- Write the decimal part in the fractional course by ignoring the decimal bespeak and dividing it by a power of 10 in which there is the same number of zeros as the decimal places.
Footstep 3- Simplify the fraction obtained.
Step 4- Attach the whole number part of the original number with the fraction obtained in footstep 3. That would be your respond.

Let'southward consider an example.

Convert two.5 into a mixed fraction.

Step 1: Consider 2 and 0.five as separate entities.
Step 2: 0.v can be written equally 5/x (as a fraction).
Footstep iii: 5/x = 1/ii (in the simplified form).
Pace 4: 2+ane/two= \(2\dfrac{one}{2}\)

∴ 2.5 can be wriiten equally \(two\dfrac{i}{2}\) every bit fraction.

Convert Negative Decimal to a Fraction

To convert any negative decimal number to a fraction, nosotros follow the steps given below:

Step ane: Remove the negative sign from the decimal number.
Step ii: Perform the conversion on the positive value.
Pace 3: Apply the negative sign to the fraction answer.

For example, convert -3.2 into a fraction.

Stride ane: Remove the negative sign. Consider it every bit iii.two
Step ii: There is one digit after the fraction, so multiply and divide 3.ii by 10.
Step 3: Convert 32/10 to its lowest form and use a negative sign to the fraction answer.

Thus, the answer is -16/five.

Decimal to Fraction Conversion Table

The decimal to fraction conversion tabular array below shows some unremarkably-used fractions and their decimal equivalents.

Decimal	Fraction Equivalent	Fraction in simplest class
0.one	1/x	1/10
0.two	ii/10	1/5
0.3	3/ten	iii/10
0.4	4/10	2/5
0.5	5/ten	ane/2
0.half-dozen	6/10	3/5
0.75	75/100	three/4
0.125	125/one thousand	1/8
0.625	625/m	5/8
1.25	125/100=\(i\dfrac{25}{100}\)	\(1\dfrac{iii}{four}\)=7/4

This is the tabular way of showing the conversion of decimal to its equivalent fraction. Now, look at the chart given below and understand it visually.

Fraction and Decimal Chart

Convert Decimal to Fraction: Inches

Decimal and Fractions are used to represent inches values. To convert a given inch measurement from decimals to fractions, nosotros take to focus on the partial part of the decimal number. For example, if we have to convert vi.25 inches to its fractional equivalent, it has six in the whole number part and 0.25 in the fractional part. 0.25 has two digits after the decimal point, and so it can exist written as 25/100 as a fraction, which can exist reduced to 1/4. Therefore, we get 6.25= six 1/four inches. This is how we catechumen inches from decimal to fraction.

Decimal Inches	Fraction Inches
36.000	36"
36.125	36 1/8"
36.250	36 i/four"
36.375	36 3/8"
36.500	36 i/2"
36.625	36 5/8"
36.750	36 iii/4"

Procedure to Catechumen Decimal to Fraction Inches

A fractional inch value like 36.125 inches includes 3 anxiety and an additional 0.125 inches. There are three digits after the decimal. Hence, multiply and divide 0.125 past 1000. For 0.125, the all-time option is i/8 of an inch. Therefore, the height volition be \( 3\dfrac{ane}{8} \)" in.

Points to Remember:

Procedure to convert decimal to fraction:

Place the identify value of the final digit in the number.
Use that to make up one's mind what the denominator of the fraction would be.
Remove the decimal signal. Re-write in the fraction form and simplify information technology.
Limited in terms of the everyman Equivalent fraction.

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Fraction to Decimal Chart
Decimal to Fraction Calculator

Examples on Converting Decimal to Fraction

Example 1: On the basis of your understanding of decimal to fraction conversion, catechumen 0.124 to a fraction.

Solution:

Stride 1: Identify the identify value of the terminal digit. 0.124 <------------ 4 is in the thousandths identify.

Pace 2: The denominator would be one thousand.

Step 3 : Fraction format: Numerator/Denominator= 124/yard

Step four : Simplest Form: 31/250.

∴ 0.124= 31/250.
Instance 2: Silvia is fond of reading. She has started reading a new novel. Out of 200 pages, Silvia read 20 pages in a solar day. What fraction of pages did she read in a day? Convert that fraction into decimals.

Solution:

Total number of pages = 200. Pages read past her in a day = 20. The fraction of pages read past her in a day = xx/200 = one/10. ∴ She read 1/ten or 0.1 pages in a mean solar day.

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Practice Questions on Conversion of Decimal to Fraction

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FAQs on Converting Decimal to Fraction

What is Decimal to Fraction Conversion?

Decimal to fraction conversion is a procedure of writing decimal values in the form of fraction value and vice-versa. To catechumen the number from decimal to fraction form we divide the number past the power of 10 such that the number of zeros in that should be equal to the number of decimal places in the given number and simplify the fraction. For example, decimal form = 7.v = 75/10 = 15/ii (fraction course of seven.5).

How to Catechumen Decimal to Fraction?

To convert a decimal to a fraction, we follow three bones steps mentioned below:

Rewrite the number by ignoring the decimal point.
Divide the number by the place value of the terminal digit in the fractional role of the number.
Simplify the fraction.

How to Catechumen Fractions to Decimal?

To convert any fraction to decimal form, we just need to divide its numerator by denominator.

What is the Divergence Between the Fraction and the Decimal?

The main difference between the fraction and decimals is that fraction represents a ratio between ii, while decimals tin can be used for writing space values and for more precision.

How to Catechumen Mixed Fraction to Decimals?

To convert a mixed fraction to a decimal, we first need to convert information technology into an improper fraction. Then we can divide the numerator by denominator to convert it into decimal.

What is the Use of Decimal to Fraction Chart?

When we correspond decimal value into a fraction (p/q) form we use decimal to fraction chart for easy and fast calculations. It as well helps in the contrary conversion that is converting fraction to decimal as well.

☛ Cheque now for more exercise:

Decimal to Fraction Calculator
Fraction to Decimal Calculator
Converting Decimal to Fraction Worksheets

How Practise you Write 0.25 Decimal Value as a Fraction?

Let'southward see how to convert 0.25 into fraction footstep-wise:

Pace ane: Count the numbers after the decimal signal.
Step 2: There are two digits after the decimal bespeak. Hence, multiply and dissever 0.25 by 100.
Stride 3: Simplify 25/100 to its lowest course, that is 1/four.

Thus, 1/4 is the fraction form of 0.25.

What are Repeating and Non-Repeating Decimals?

Repeating Decimals are those in which one or more digits repeat again and again, for example, i/iii=0.333333....., while non-repeating decimals are those that stop after a specific number of digits, for example, 1/2=0.5.

How are Decimal and Fractions Represented?

Fractions are written in the class of p/q, where q≠0, while in decimals, the whole number part and fractional part is connected through a decimal point, for example, 0.5.