Convert the pure repeating (recurring) decimal number 0.236. Turn it into a reduced (simplified) proper fraction and write it as a percentage. Calculate other equivalent fractions to the decimal number, by expanding
Convert 0.236
1. Write the pure repeating (recurring) decimal number as a percentage.
Approximate to the desired number of decimal places (14):
0.236 ≈ 0.23623623623624
Multiply the number by 100/100.
The value of the number does not change when multiplying by 100/100.
Note: 100/100 = 1
0.23623623623624 =
0.23623623623624 × 100/100 =
(0.23623623623624 × 100)/100 =
23.623623623624/100 =
23.623623623624% ≈
23.62%
(rounded off to a maximum of 2 decimal places)
In other words:
Approximate to the desired number of decimal places...
Multiply the number by 100...
... And then add the percent sign, %
0.236 ≈ 23.62%
2. Write the pure repeating (recurring) decimal number as a proper fraction.
0.236 can be written as a proper fraction. The numerator is smaller than the denominator.
Set up the first equation.
Let y equal the decimal number:
y = 0.236
Set up the second equation.
Number of decimal places repeating: 3
Multiply both sides of the first equation by 103 = 1,000
y = 0.236
1,000 × y = 1,000 × 0.236
1,000 × y = 236.236
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.
1,000 × y - y = 236.236 - 0.236 ⇒
(1,000 - 1) × y = 236.236 - 0.236 ⇒
We now have a new equation:
999 × y = 236
Solve for y in the new equation.
999 × y = 236 ⇒
y = 236/999
Let the result written as a fraction.
Write the number as a fraction.
According to our first equation:
y = 0.236
According to our calculations:
y = 236/999
⇒ 0.236 = 236/999
3. Reduce (simplify) the fraction above: 236/999
(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):
236 = 22 × 59
999 = 33 × 37
Calculate the greatest (highest) common factor (divisor), GCF.
Multiply all the common prime factors by the lowest exponents.
But, the numerator and the denominator have no common factors.
GCF (22 × 59; 33 × 37) = 1
The numerator and the denominator are coprime numbers (no common prime factors, GCF = 1). So, the fraction cannot be reduced (simplified): irreducible fraction.
236/999: 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:
236/999 = (236 × 4)/(999 × 4) = 944/3,996
Example 2. By expanding the fraction by 6:
236/999 = (236 × 6)/(999 × 6) = 1,416/5,994
Of course, the above fractions are reducing...
... to the initial fraction: 236/999
:: Final answer ::
Written in 3 different ways
As a reduced (simplified) positive proper fraction:
0.236 = 236/999
As a percentage:
0.236 ≈ 23.62%
As equivalent fractions:
0.236 = 236/999 = 944/3,996 = 1,416/5,994
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