Convert the decimal number 4.002. Turn it into a reduced (simplified) improper fraction, into a mixed number and write it as a percentage value. Equivalent fractions calculator

Convert 4.002 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

4.002 =

4.002 × 100/100 =

(4.002 × 100)/100 =

400.2/100 =

400.2%


  • In other words:
  • Multiply the number by 100...
  • ... And then add the percent sign, %
  • 4.002 = 400.2%

» Convert fractions to percentages, online calculator


2. Write the number as an improper fraction.

  • 4.002 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:

4.002 = 4.002/1


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.

4.002/1 =

(4.002 × 1,000)/(1 × 1,000) =

4,002/1,000


3. Reduce (simplify) the fraction above:
4,002/1,000
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).

4,002 = 2 × 3 × 23 × 29

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 (2 × 3 × 23 × 29; 23 × 53) = 2


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


Divide both the numerator and the denominator by their GCF.

4,002/1,000 =

(2 × 3 × 23 × 29)/(23 × 53) =

((2 × 3 × 23 × 29) ÷ 2) / ((23 × 53) ÷ 2) =

(3 × 23 × 29)/(22 × 53) =

2,001/500


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.

2,001 ÷ 500 = 4, remainder = 1 ⇒

2,001 = 4 × 500 + 1 ⇒

2,001/500 =

(4 × 500 + 1) / 500 =

(4 × 500) / 500 + 1/500 =

4 + 1/500 =

4 1/500


2,001/500 ~ 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.

2,001/500 = (2,001 × 3)/(500 × 3) = 6,003/1,500

Example 2. By expanding the fraction by 4.

2,001/500 = (2,001 × 4)/(500 × 4) = 8,004/2,000

  • Of course, the above fractions are reducing...
  • ... to the initial fraction: 2,001/500

» Reduce fractions and write them as decimal numbers and percentages


:: Final answer ::
Written in 4 different ways

As a reduced (simplified) positive improper fraction:
4.002 = 2,001/500

As a mixed number:
4.002 = 4 1/500

As a percentage:
4.002 = 400.2%

As equivalent fractions:
4.002 = 2,001/500 = 6,003/1,500 = 8,004/2,000

More operations of this kind

4.003 = ? Convert the decimal number 4.003. 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: