Convert the mixed repeating (recurring) decimal number 0.376. 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 0.376
1. Write the mixed repeating (recurring) decimal number as a percentage.
Approximate to the desired number of decimal places (14):
0.376 ≈ 0.37676767676768
Multiply the number by 100/100.
The value of the number does not change when multiplying by 100/100.
Note: 100/100 = 1
0.37676767676768 =
0.37676767676768 × 100/100 =
(0.37676767676768 × 100)/100 =
37.676767676768/100 =
37.676767676768% ≈
37.68%
(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, %
0.376 ≈ 37.68%
2. Write the mixed repeating (recurring) decimal number as a proper fraction.
0.376 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 = 0.376
Set up the second equation.
Number of decimal places repeating: 2
Multiply both sides of the first equation by 102 = 100
y = 0.376
100 × y = 100 × 0.376
100 × y = 37.676
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.
100 × y - y = 37.676 - 0.376 ⇒
(100 - 1) × y = 37.676 - 0.376 ⇒
We now have a new equation:
99 × y = 37
Solve for y in the new equation.
99 × y = 37 ⇒
y = 37/99
Let the result written as a fraction.
Write the number as a fraction.
According to our first equation:
y = 0.376
According to our calculations:
y = 37/99
⇒ 0.376 = 37/99
3. Reduce (simplify) the fraction above: 37/99
(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):
37 is a prime number, it cannot be factored into other prime factors
99 = 32 × 11
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 (37; 32 × 11) = 1
The numerator and the denominator are coprime numbers (no common prime factors, GCF = 1). So, the fraction cannot be reduced (simplified): irreducible fraction.
37/99: 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:
37/99 = (37 × 2)/(99 × 2) = 74/198
Example 2. By expanding the fraction by 5:
37/99 = (37 × 5)/(99 × 5) = 185/495
Of course, the above fractions are reducing...
... to the initial fraction: 37/99
:: Final answer ::
Written in 3 different ways
As a reduced (simplified) positive proper fraction:
0.376 = 37/99
As a percentage:
0.376 ≈ 37.68%
As equivalent fractions:
0.376 = 37/99 = 74/198 = 185/495
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