Convert the decimal number - 6.38. 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
Convert - 6.38
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
- 6.38 =
- 6.38 × 100/100 =
- (6.38 × 100)/100 =
- 638/100 =
- 638%
In other words:
Multiply the number by 100...
... And then add the percent sign, %
- 6.38 = - 638%
2. Write the number as an improper fraction.
- 6.38 can be written as an improper fraction.
The numerator is larger than or equal to the denominator.
Write down the number divided by 1, as a fraction:
- 6.38 = - 6.38/1
Turn the top number into a whole number.
Multiply both the top and the bottom by the same number.
This number is: 100.
1 followed by as many 0-s as the number of digits after the decimal point.
- 6.38/1 =
- (6.38 × 100)/(1 × 100) =
- 638/100
3. Reduce (simplify) the fraction above: - 638/100
(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.
Factor both the numerator and the denominator (prime factorization).
In exponential notation (an):
638 = 2 × 11 × 29
100 = 22 × 52
Calculate the greatest (highest) common factor (divisor), GCF.
Multiply all the common prime factors by the lowest exponents.
GCF (2 × 11 × 29; 22 × 52) = 2
Divide both the numerator and the denominator by their greatest common factor, GCF.
- 638/100 =
- (2 × 11 × 29)/(22 × 52) =
- ((2 × 11 × 29) ÷ 2) / ((22 × 52) ÷ 2) =
- (11 × 29)/(2 × 52) =
- 319/50
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.
- 319 ÷ 50 = - 6, remainder = - 19 ⇒
- 319 = - 6 × 50 - 19 ⇒
- 319/50 =
(- 6 × 50 - 19) / 50 =
(- 6 × 50) / 50 - 19/50 =
- 6 - 19/50 =
- 6 19/50
- 319/50: 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 4:
- 319/50 = - (319 × 4)/(50 × 4) = - 1,276/200
Example 2. By expanding the fraction by 8:
- 319/50 = - (319 × 8)/(50 × 8) = - 2,552/400
Of course, the above fractions are reducing...
... to the initial fraction: - 319/50
:: Final answer ::
Written in 4 different ways
As a reduced (simplified) negative improper fraction:
- 6.38 = - 319/50
As a mixed number:
- 6.38 = - 6 19/50
As a percentage:
- 6.38 = - 638%
As equivalent fractions:
- 6.38 = - 319/50 = - 1,276/200 = - 2,552/400
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