Convert the pure repeating (recurring) decimal number 14.9. Turn it into a fraction and also write it as a percentage. Calculate other equivalent fractions to the decimal number, by expanding
Convert 14.9
1. Write the pure repeating (recurring) decimal number as a percentage.
Approximate to the desired number of decimal places:
14.9 ≈ 15
Multiply the number by 100/100.
The value of the number does not change when multiplying by 100/100.
Note: 100/100 = 1
15 =
15 × 100/100 =
(15 × 100)/100 =
1,500/100 =
1,500%
In other words:
Approximate to the desired number of decimal places...
Multiply the number by 100...
... And then add the percent sign, %
14.9 ≈ 1,500%
2. Write the pure repeating (recurring) decimal number as an improper fraction.
14.9 can be written as an improper fraction.
The numerator larger than or equal to the denominator.
Set up the first equation.
Let y equal the decimal number:
y = 14.9
Set up the second equation.
Number of decimal places repeating: 1
Multiply both sides of the first equation by 101 = 10
y = 14.9
10 × y = 10 × 14.9
10 × y = 149.9
Subtract the first equation from the second equation.
Having the same number of decimal places ...
The repeating pattern drops off by subtracting the two equations.
10 × y - y = 149.9 - 14.9 ⇒
(10 - 1) × y = 149.9 - 14.9 ⇒
We now have a new equation:
9 × y = 135
Solve for y in the new equation.
9 × y = 135 ⇒
y = 135/9
Let the result written as a fraction.
Write the number as a fraction.
According to our first equation:
y = 14.9
According to our calculations:
y = 135/9
⇒ 14.9 = 135/9
3. Reduce (simplify) the fraction above: 135/9
(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):
135 = 33 × 5
9 = 32
Calculate the greatest (highest) common factor (divisor), GCF.
Multiply all the common prime factors by the lowest exponents.
GCF (33 × 5; 32) = 32
Divide both the numerator and the denominator by their greatest common factor, GCF.
135/9 =
(33 × 5)/32 =
((33 × 5) ÷ 32) / (32 ÷ 32) =
(3 × 5)/1 =
15/1
Note: 15/1 = 15
15/1: 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 2:
15/1 = (15 × 2)/(1 × 2) = 30/2
Example 2. By expanding the fraction by 3:
15/1 = (15 × 3)/(1 × 3) = 45/3
Of course, the above fractions are reducing...
... to the initial fraction: 15/1
:: Final answer ::
Written in 3 different ways
As a reduced (simplified) positive improper fraction:
14.9 = 15/1
As a percentage:
14.9 = 1,500%
As equivalent fractions:
14.9 = 15/1 = 30/2 = 45/3
More operations of this kind
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