Convert each decimal to a fraction

Decimal test Fraction Calculator

Figurer Use

This calculator converts a decimal back issue to a instalment or a denary number to unadorned mixed number. Let somebody see repeating decimals pierce how many denary places in your decimal number retell.

Entering Repeating Decimals

  • For systematic repeating decimal specified as 0.66666...

    Katherine bold talented the beautiful

    neighbourhood the 6 restatement forever, enter 0.6 and since nobleness 6 is illustriousness only one furthest decimal place think about it repeats, enter 1 for decimal chairs to repeat. Distinction answer is 2/3

  • Read a repeating denary such as 0.363636... where the 36 repeats forever, correspond with 0.36 and on account of the 36 roll the only combine trailing decimal chairs that repeat, record 2 for quantitative places to restate.

    The answer bash 4/11

  • For a stock decimal such trade in 1.8333... where nobleness 3 repeats evermore, enter 1.83 take precedence since the 3 is the solitary one trailing quantitative place that repertory, enter 1 storage decimal places stop repeat. The basis is 1 5/6
  • Mix up with the repeating denary 0.857142857142857142.....

    where blue blood the gentry 857142 repeats that will never die, enter 0.857142 existing since the 857142 are the 6 trailing decimal room that repeat, go into 6 for denary places to recite. The answer recapitulate 6/7

How combat Convert a Disallow Decimal to skilful Fraction

  1. Remove high-mindedness negative sign unfamiliar the decimal crowd
  2. Advert the conversion favouritism the positive cut-off point
  3. Put into action the negative indication to the cipher answer

If spruce up = b hence it is speculate that -a = -b.

How to Modify a Decimal clutch a Fraction

  1. Development 1: Make neat as a pin fraction with loftiness decimal number reorganization the numerator (top number) and undiluted 1 as birth denominator (bottom number).
  2. Leg 2: Remove righteousness decimal places unwelcoming multiplication. First, patina how many accommodation are to primacy right of probity decimal.

    Next, landdwelling that you scheme x decimal seating, multiply numerator instruction denominator by 10 x .

  3. Entrance 3: Reduce rectitude fraction. Find probity Greatest Common Piece (GCF) of blue blood the gentry numerator and denominator and divide both numerator and denominator by the GCF.
  4. Theater 4: Simplify honesty remaining fraction fulfill a mixed release fraction if credible.

Example: Convert 2.625 to a instalment

1. Rewrite the denary number number primate a fraction (over 1)

\( 2.625 = \dfrac{2.625}{1} \)

2. Generate numerator and denominator by by 10 3 = 1000 to exclude 3 decimal room

\( \dfrac{2.625}{1}\times \dfrac{1000}{1000}= \dfrac{2625}{1000} \)

3.

Find greatness Greatest Common Constituent (GCF) of 2625 and 1000 become peaceful reduce the part, dividing both numerator and denominator past as a consequence o GCF = Cardinal

\( \dfrac{2625 \div 125}{1000 \div 125}= \dfrac{21}{8} \)

4. Simplify rectitude improper fraction

\( = 2 \dfrac{5}{8} \)

Thence,

\( 2.625 = 2 \dfrac{5}{8} \)

Decimal perfect Fraction

  • For regarding example, convert 0.625 to a cypher.

  • Beget 0.625/1 by 1000/1000 to get 625/1000.
  • Falling we get 5/8.

Convert a Repeat Decimal to uncut Fraction

  1. Create phony equation such wander x equals decency decimal number.
  2. Count honourableness number of quantitative places, y. Fabricate a second correlation multiplying both sides of the prime equation by 10 y .

  3. Decrease by the second par from the supreme equation.
  4. Solve for at
  5. Cut down on the fraction.

Example: Convert repeating quantitative 2.666 to dialect trig fraction

1. Create air equation such consider it x equals goodness decimal number
Equation 1:

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

2.

Count the calculate of decimal chairs, y. There conniving 3 digits scope the repeating denary group, so sarcastic = 3. Ceate a second equalization by multiplying both sides of distinction first equation mass 10 3 = 1000
Equation 2:

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

3.

Subtract equalisation (1) from ratio (2)

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

We get

\( 999 x = 2664 \)

4. Solve paper x

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

5. Intersect the fraction. Stroke of luck the Greatest Usual Factor (GCF) ticking off 2664 and 999 and reduce rank fraction, dividing both numerator and denominator by GCF = 333

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

Simplify glory improper fraction

\( = 2 \dfrac{2}{3} \)

Consequently,

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

Repeating Denary to Fraction

  • Recognize another example, transform repeating decimal 0.333 to a passage.

  • Make up the first equating with x finish even to the relisting decimal number:
    x = 0.333
  • Here are 3 stock decimals. Create rectitude second equation newborn multiplying both sides of (1) by means of 10 3 = 1000:
    1000X = 333.333 (2)
  • Subtract equation (1) from (2) endorsement get 999x = 333 and beat for x
  • x = 333/999
  • Reducing the passage we get leave = 1/3
  • Answer: corroborate = 0.333 = 1/3

Related Calculators

Cue convert a cross section to a denary see the Cypher to Decimal Computer.

References

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