Convert the decimal number 5.125. Turn it into a reduced (simplified) improper fraction, into a mixed number and write it as a percentage value. Equivalent fractions calculator

Convert 5.125 into equivalent fractions and write it as a percentage value

1. Write the number as a percentage.

  • Multiply the number by 100/100
  • Note: 100/100 = 1
  • The value of the number does not change when multiplying by 100/100

5.125 =

5.125 × 100/100 =

(5.125 × 100)/100 =

512.5/100 =

512.5%


  • In other words:
  • Multiply the number by 100...
  • ... And then add the percent sign, %
  • 5.125 = 512.5%

» Convert fractions to percentages, online calculator


2. Write the number as an improper fraction.

  • 5.125 can be written as an improper fraction.
  • An improper fraction = the numerator is larger than or equal to the denominator..

Write down the number divided by 1, as a fraction:

5.125 = 5.125/1


Turn the top number into a whole number.

  • Multiply both the top and the bottom by the same number.
  • This number is: 1,000.
  • 1 followed by as many 0-s as the number of digits after the decimal point.

5.125/1 =

(5.125 × 1,000)/(1 × 1,000) =

5,125/1,000


3. Reduce (simplify) the fraction above:
5,125/1,000
to the lowest terms, to its simplest equivalent form, irreducible.

To reduce a fraction to the lowest terms divide the numerator and denominator by their greatest (highest) common factor (divisor), GCF.


Factor the numerator and denominator (prime factorization).

5,125 = 53 × 41

1,000 = 23 × 53


» Prime factorization: break numbers down to prime factors, online calculator


Calculate the greatest (highest) common factor (divisor), GCF.

Multiply all the common prime factors by the lowest exponents.

GCF (53 × 41; 23 × 53) = 53


» Calculate the greatest (highest) common factor (divisor), GCF, online calculator


Divide both the numerator and the denominator by their GCF.

5,125/1,000 =

(53 × 41)/(23 × 53) =

((53 × 41) ÷ 53) / ((23 × 53) ÷ 53) =

41/23 =

41/8


4. The fraction is an improper one, rewrite it as a mixed number (mixed fraction):

  • A mixed number = an integer number and a proper fraction, of the same sign.
  • Example 1: 2 1/5; Example 2: - 1 3/7.
  • A proper fraction = the numerator is smaller than the denominator.

41 ÷ 8 = 5, remainder = 1 ⇒

41 = 5 × 8 + 1 ⇒

41/8 =

(5 × 8 + 1) / 8 =

(5 × 8) / 8 + 1/8 =

5 + 1/8 =

5 1/8


41/8 ~ Equivalent fractions.

  • The above fraction cannot be reduced.
  • That is, it has the smallest possible numerator and denominator.

  • By expanding it we can build up equivalent fractions.

  • Multiply the numerator & the denominator by the same number.


Example 1. By expanding the fraction by 5.

41/8 = (41 × 5)/(8 × 5) = 205/40

Example 2. By expanding the fraction by 6.

41/8 = (41 × 6)/(8 × 6) = 246/48

  • Of course, the above fractions are reducing...
  • ... to the initial fraction: 41/8

» Reduce fractions and write them as decimal numbers and percentages


:: Final answer ::
Written in 4 different ways

As a reduced (simplified) positive improper fraction:
5.125 = 41/8

As a mixed number:
5.125 = 5 1/8

As a percentage:
5.125 = 512.5%

As equivalent fractions:
5.125 = 41/8 = 205/40 = 246/48

More operations of this kind

5.126 = ? Convert the decimal number 5.126. Turn it into a reduced (simplified) improper fraction, into a mixed number and write it as a percentage. Calculate other equivalent fractions to the decimal number, by expanding

Decimal numbers to fractions and percentages, calculator

Learn how to turn a decimal number into a fraction and a percentage. Steps.

1. How to write the number as a percentage:

  • Multiply the number by 100. Then add the percent sign, %.

2. How to write the number as a fraction:

  • Write down the number divided by 1, as a fraction.
  • Turn the top number into a whole number: multiply both the top and the bottom by the same number.
  • Reduce (simplify) the above fraction to the lowest terms, to its simplest equivalent form, irreducible. To reduce a fraction divide the numerator and the denominator by their greatest (highest) common factor (divisor), GCF.
  • If the fraction is an improper one, rewrite it as a mixed number (mixed fraction).
  • Calculate equivalent fractions. By expanding it we can build up equivalent fractions: multiply the numerator & the denominator by the same number.

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