Convert the decimal number 8.4. Turn it into a reduced (simplified) improper fraction, into a mixed number and write it as a percentage value. Equivalent fractions calculator

Convert 8.4 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

8.4 =

8.4 × 100/100 =

(8.4 × 100)/100 =

840/100 =

840%


  • In other words:
  • Multiply the number by 100...
  • ... And then add the percent sign, %
  • 8.4 = 840%

» Convert fractions to percentages, online calculator


2. Write the number as an improper fraction.

  • 8.4 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:

8.4 = 8.4/1


Turn the top number into a whole number.

  • Multiply both the top and the bottom by the same number.
  • This number is: 10.
  • 1 followed by as many 0-s as the number of digits after the decimal point.

8.4/1 =

(8.4 × 10)/(1 × 10) =

84/10


3. Reduce (simplify) the fraction above:
84/10
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).

84 = 22 × 3 × 7

10 = 2 × 5


» 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 (22 × 3 × 7; 2 × 5) = 2


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


Divide both the numerator and the denominator by their GCF.

84/10 =

(22 × 3 × 7)/(2 × 5) =

((22 × 3 × 7) ÷ 2) / ((2 × 5) ÷ 2) =

(2 × 3 × 7)/5 =

42/5


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.

42 ÷ 5 = 8, remainder = 2 ⇒

42 = 8 × 5 + 2 ⇒

42/5 =

(8 × 5 + 2) / 5 =

(8 × 5) / 5 + 2/5 =

8 + 2/5 =

8 2/5


42/5 ~ 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 3.

42/5 = (42 × 3)/(5 × 3) = 126/15

Example 2. By expanding the fraction by 7.

42/5 = (42 × 7)/(5 × 7) = 294/35

  • Of course, the above fractions are reducing...
  • ... to the initial fraction: 42/5

» Reduce fractions and write them as decimal numbers and percentages


:: Final answer ::
Written in 4 different ways

As a reduced (simplified) positive improper fraction:
8.4 = 42/5

As a mixed number:
8.4 = 8 2/5

As a percentage:
8.4 = 840%

As equivalent fractions:
8.4 = 42/5 = 126/15 = 294/35

More operations of this kind

8.5 = ? Convert the decimal number 8.5. 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.

More on ordinary (common) fractions / theory: