0.5 3 As A Fraction

Decimal to Fraction Calculator

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Calculator Employ

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 echo.

Entering Repeating Decimals

• For a repeating decimal such as 0.66666... where the vi repeats forever, enter 0.half dozen and since the half dozen is the only one trailing decimal place that repeats, enter 1 for decimal places to repeat. The respond is 2/3
• For a repeating decimal such every bit 0.363636... where the 36 repeats forever, enter 0.36 and since the 36 are the merely two abaft decimal places that repeat, enter 2 for decimal places to repeat. The respond is 4/xi
• For a repeating decimal such as 1.8333... where the 3 repeats forever, enter 1.83 and since the 3 is the only ane trailing decimal identify that repeats, enter 1 for decimal places to repeat. The answer is i 5/6
• For the repeating decimal 0.857142857142857142..... where the 857142 repeats forever, enter 0.857142 and since the 857142 are the 6 trailing decimal places that repeat, enter 6 for decimal places to echo. The answer is 6/7

How to Convert a Negative Decimal to a Fraction

1. Remove the negative sign from the decimal number
2. Perform the conversion on the positive value
3. Use the negative sign to the fraction respond

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

How to Convert a Decimal to a Fraction

1. Pace one: Make a fraction with the decimal number equally the numerator (tiptop number) and a 1 every bit the denominator (bottom number).
2. Step 2: Remove the decimal places by multiplication. First, count how many places are to the right of the decimal. Adjacent, given that you have x decimal places, multiply numerator and denominator past x^x.
3. Step 3: Reduce the fraction. Notice the Greatest Common Factor (GCF) of the numerator and denominator and divide both numerator and denominator by the GCF.
4. Step four: Simplify the remaining fraction to a mixed number fraction if possible.

Case: Convert ii.625 to a fraction

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

\( 2.625 = \dfrac{2.625}{one} \)

2. Multiply numerator and denominator by past xⁱⁱⁱ = g to eliminate 3 decimal places

\( \dfrac{2.625}{i}\times \dfrac{1000}{1000}= \dfrac{2625}{grand} \)

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

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

four. Simplify the improper fraction

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

Therefore,

\( ii.625 = two \dfrac{5}{viii} \)

Decimal to Fraction

• For some other example, convert 0.625 to a fraction.
• Multiply 0.625/1 by thousand/1000 to go 625/thou.
• Reducing we get 5/8.

Convert a Repeating Decimal to a Fraction

1. Create an equation such that x equals the decimal number.
2. Count the number of decimal places, y. Create a second equation multiplying both sides of the first equation by ten^y.
3. Decrease the 2nd equation from the starting time equation.
4. Solve for ten
5. Reduce the fraction.

Example: Catechumen repeating decimal 2.666 to a fraction

1. Create an equation such that 10 equals the decimal number
Equation ane:

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

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 kickoff equation past ten³ = 1000
Equation ii:

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

3. Decrease equation (one) from equation (2)

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

We get

\( 999 x = 2664 \)

4. Solve for 10

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

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

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

Simplify the improper fraction

\( = 2 \dfrac{ii}{iii} \)

Therefore,

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

Repeating Decimal to Fraction

• For another example, 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 10^three = thou:
  1000X = 333.333 (2)
• Subtract equation (one) from (2) to become 999x = 333 and solve for 10
• 10 = 333/999
• Reducing the fraction we get x = 1/three
• Answer: x = 0.333 = ane/3

Related Calculators

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

References

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

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0.5 3 As A Fraction,

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