Convert the mixed repeating (recurring) decimal number 0.37. 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 0.37
1. Write the mixed repeating (recurring) decimal number as a percentage.
Rewrite / normalize the original number.
There is only one repeating decimal place:
0.377 = 0.37
Approximate to the desired number of decimal places (14):
0.37 ≈ 0.37777777777778
Multiply the number by 100/100.
The value of the number does not change when multiplying by 100/100.
Note: 100/100 = 1
0.37777777777778 =
0.37777777777778 × 100/100 =
(0.37777777777778 × 100)/100 =
37.777777777778/100 =
37.777777777778% ≈
37.78%
(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, %
0.37 ≈ 37.78%
2. Write the mixed repeating (recurring) decimal number as a proper fraction.
0.37 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 = 0.37
Set up the second equation.
Number of decimal places repeating: 1
Multiply both sides of the first equation by 101 = 10
y = 0.37
10 × y = 10 × 0.37
10 × y = 3.7
Get the same number of decimal places as for y:
10 × y = 3.77
Note: 3.77 = 3.7
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 = 3.77 - 0.37 ⇒
(10 - 1) × y = 3.77 - 0.37 ⇒
We now have a new equation:
9 × y = 3
Solve for y in the new equation.
9 × y = 3 ⇒
y = 3/9
Let the result written as a fraction.
Write the number as a fraction.
According to our first equation:
y = 0.37
According to our calculations:
y = 3/9
⇒ 0.37 = 3/9
3. Reduce (simplify) the fraction above: 3/9
(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):
3 is a prime number, it cannot be factored into other prime factors
9 = 32
Calculate the greatest (highest) common factor (divisor), GCF.
Multiply all the common prime factors by the lowest exponents.
GCF (3; 32) = 3
Divide both the numerator and the denominator by their greatest common factor, GCF.
3/9 =
3/32 =
(3 ÷ 3) / (32 ÷ 3) =
1/3
1/3: 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:
1/3 = (1 × 4)/(3 × 4) = 4/12
Example 2. By expanding the fraction by 8:
1/3 = (1 × 8)/(3 × 8) = 8/24
Of course, the above fractions are reducing...
... to the initial fraction: 1/3
:: Final answer ::
Written in 3 different ways
As a reduced (simplified) positive proper fraction:
0.37 = 1/3
As a percentage:
0.37 ≈ 37.78%
As equivalent fractions:
0.37 = 1/3 = 4/12 = 8/24
More operations of this kind
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