6 Repeated As A Fraction

Decimal to Fraction Figurer

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This estimator converts a decimal number to a fraction or a decimal number to a mixed number. For repeating decimals enter how many decimal places in your decimal number echo.

Inbound Repeating Decimals

For a repeating decimal such as 0.66666... where the half dozen repeats forever, enter 0.6 and since the 6 is the only one trailing decimal identify that repeats, enter 1 for decimal places to repeat. The reply is 2/3
For a repeating decimal such as 0.363636... where the 36 repeats forever, enter 0.36 and since the 36 are the merely 2 trailing decimal places that repeat, enter 2 for decimal places to repeat. The answer is 4/11
For a repeating decimal such as one.8333... where the three repeats forever, enter 1.83 and since the 3 is the only i trailing decimal place that repeats, enter 1 for decimal places to repeat. The answer is 1 5/six
For the repeating decimal 0.857142857142857142..... where the 857142 repeats forever, enter 0.857142 and since the 857142 are the half-dozen abaft decimal places that echo, enter six for decimal places to repeat. The answer is 6/7

How to Convert a Negative Decimal to a Fraction

Remove the negative sign from the decimal number
Perform the conversion on the positive value
Utilise the negative sign to the fraction answer

If a = b and then it is true that -a = -b.

How to Convert a Decimal to a Fraction

Step 1: Make a fraction with the decimal number as the numerator (top number) and a 1 as the denominator (lesser number).
Step ii: Remove the decimal places by multiplication. Commencement, count how many places are to the right of the decimal. Next, given that you take x decimal places, multiply numerator and denominator past 10^ten.
Step 3: Reduce the fraction. Find the Greatest Mutual Factor (GCF) of the numerator and denominator and carve up both numerator and denominator by the GCF.
Step 4: Simplify the remaining fraction to a mixed number fraction if possible.

Example: Convert 2.625 to a fraction

ane. Rewrite the decimal number number every bit a fraction (over ane)

\( 2.625 = \dfrac{ii.625}{1} \)

ii. Multiply numerator and denominator by by 10³ = g to eliminate 3 decimal places

\( \dfrac{two.625}{1}\times \dfrac{1000}{1000}= \dfrac{2625}{thou} \)

3. Find the Greatest Common Factor (GCF) of 2625 and one thousand and reduce the fraction, dividing both numerator and denominator past GCF = 125

\( \dfrac{2625 \div 125}{m \div 125}= \dfrac{21}{8} \)

4. Simplify the improper fraction

\( = 2 \dfrac{five}{8} \)

Therefore,

\( 2.625 = ii \dfrac{v}{8} \)

Decimal to Fraction

For another example, catechumen 0.625 to a fraction.
Multiply 0.625/1 by 1000/1000 to get 625/chiliad.
Reducing we become five/eight.

Convert a Repeating Decimal to a Fraction

Create an equation such that 10 equals the decimal number.
Count the number of decimal places, y. Create a 2nd equation multiplying both sides of the outset equation by 10^y.
Decrease the second equation from the first equation.
Solve for 10
Reduce the fraction.

Example: Convert repeating decimal 2.666 to a fraction

one. Create an equation such that ten equals the decimal number
Equation 1:

\( 10 = ii.\overline{666} \)

2. Count the number of decimal places, y. There are 3 digits in the repeating decimal group, so y = 3. Ceate a second equation by multiplying both sides of the beginning equation past x³ = 1000
Equation 2:

\( 1000 10 = 2666.\overline{666} \)

three. Subtract equation (ane) from equation (2)

\( \eqalign{one thousand x &= &\hfill2666.666...\cr 10 &= &\hfill2.666...\cr \hline 999x &= &2664\cr} \)

We get

\( 999 x = 2664 \)

iv. Solve for ten

\( 10 = \dfrac{2664}{999} \)

v. Reduce the fraction. Find the Greatest Common Factor (GCF) of 2664 and 999 and reduce the fraction, dividing both numerator and denominator by GCF = 333

\( \dfrac{2664 \div 333}{999 \div 333}= \dfrac{viii}{3} \)

Simplify the improper fraction

\( = two \dfrac{two}{3} \)

Therefore,

\( 2.\overline{666} = two \dfrac{2}{3} \)

Repeating Decimal to Fraction

For another case, convert repeating decimal 0.333 to a fraction.
Create the start equation with x equal to the repeating decimal number:
10 = 0.333
There are iii repeating decimals. Create the second equation by multiplying both sides of (1) by ten^three = 1000:
1000X = 333.333 (ii)
Subtract equation (1) from (ii) to get 999x = 333 and solve for x
ten = 333/999
Reducing the fraction we get 10 = one/3
Reply: x = 0.333 = i/3

Related Calculators

To convert a fraction to a decimal see the Fraction to Decimal Estimator.

References

Wikipedia contributors. "Repeating Decimal," Wikipedia, The Free Encyclopedia. Last visited 18 July, 2016.

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