What's 2 As A Fraction

Decimal to Fraction Figurer

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Reckoner Use

This calculator 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 repeat.

Entering Repeating Decimals

For a repeating decimal such as 0.66666... where the 6 repeats forever, enter 0.vi and since the half dozen is the only one abaft decimal place that repeats, enter ane for decimal places to repeat. The reply is 2/3
For a repeating decimal such equally 0.363636... where the 36 repeats forever, enter 0.36 and since the 36 are the only two trailing decimal places that repeat, enter ii for decimal places to repeat. The respond is 4/11
For a repeating decimal such every bit i.8333... where the 3 repeats forever, enter i.83 and since the iii is the only one trailing decimal identify that repeats, enter 1 for decimal places to echo. The reply is 1 5/6
For the repeating decimal 0.857142857142857142..... where the 857142 repeats forever, enter 0.857142 and since the 857142 are the six trailing decimal places that echo, enter 6 for decimal places to repeat. The reply is 6/seven

How to Convert a Negative Decimal to a Fraction

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

If a = b then information technology is true that -a = -b.

How to Convert a Decimal to a Fraction

Step 1: Brand a fraction with the decimal number as the numerator (summit number) and a 1 as the denominator (bottom number).
Step 2: Remove the decimal places by multiplication. First, count how many places are to the correct of the decimal. Next, given that you have x decimal places, multiply numerator and denominator by 10¹⁰.
Footstep three: Reduce the fraction. Observe the Greatest Common Gene (GCF) of the numerator and denominator and divide both numerator and denominator by the GCF.
Step 4: Simplify the remaining fraction to a mixed number fraction if possible.

Example: Convert two.625 to a fraction

1. Rewrite the decimal number number as a fraction (over 1)

\( 2.625 = \dfrac{two.625}{one} \)

two. Multiply numerator and denominator past by 10^three = m to eliminate three decimal places

\( \dfrac{2.625}{ane}\times \dfrac{m}{1000}= \dfrac{2625}{1000} \)

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

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

4. Simplify the improper fraction

\( = 2 \dfrac{5}{viii} \)

Therefore,

\( two.625 = two \dfrac{5}{8} \)

Decimal to Fraction

For another case, convert 0.625 to a fraction.
Multiply 0.625/one past one thousand/1000 to get 625/thousand.
Reducing we get 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 second equation multiplying both sides of the kickoff equation by 10^y.
Subtract the second equation from the first equation.
Solve for 10
Reduce the fraction.

Case: Catechumen repeating decimal two.666 to a fraction

i. Create an equation such that x equals the decimal number
Equation 1:

\( x = 2.\overline{666} \)

two. Count the number of decimal places, y. There are three digits in the repeating decimal group, then y = iii. Ceate a 2nd equation by multiplying both sides of the first equation past ten^three = 1000
Equation two:

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

iii. Subtract equation (i) from equation (two)

\( \eqalign{1000 ten &= &\hfill2666.666...\cr 10 &= &\hfill2.666...\cr \hline 999x &= &2664\cr} \)

Nosotros get

\( 999 x = 2664 \)

4. Solve for 10

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

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

\( \dfrac{2664 \div 333}{999 \div 333}= \dfrac{8}{3} \)

Simplify the improper fraction

\( = 2 \dfrac{2}{three} \)

Therefore,

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

Repeating Decimal to Fraction

For some other case, convert repeating decimal 0.333 to a fraction.
Create the kickoff equation with x equal to the repeating decimal number:
x = 0.333
There are iii repeating decimals. Create the second equation by multiplying both sides of (1) by tenⁱⁱⁱ = thou:
1000X = 333.333 (2)
Subtract equation (1) from (2) to become 999x = 333 and solve for 10
x = 333/999
Reducing the fraction nosotros go ten = ane/3
Answer: 10 = 0.333 = 1/3

Related Calculators

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

References

Wikipedia contributors. "Repeating Decimal," Wikipedia, The Gratis Encyclopedia. Last visited eighteen July, 2016.

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