Convert the mixed repeating (recurring) decimal number 0.94. 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 0.94
1. Write the mixed repeating (recurring) decimal number as a percentage.
Approximate to the desired number of decimal places (14):
0.94 ≈ 0.94444444444444
Multiply the number by 100/100.
The value of the number does not change when multiplying by 100/100.
Note: 100/100 = 1
0.94444444444444 =
0.94444444444444 × 100/100 =
(0.94444444444444 × 100)/100 =
94.444444444444/100 =
94.444444444444% ≈
94.44%
(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, %
0.94 ≈ 94.44%
2. Write the mixed repeating (recurring) decimal number as a proper fraction.
0.94 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 = 0.94
Set up the second equation.
Number of decimal places repeating: 1
Multiply both sides of the first equation by 101 = 10
y = 0.94
10 × y = 10 × 0.94
10 × y = 9.4
Get the same number of decimal places as for y:
10 × y = 9.44
Note: 9.44 = 9.4
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 = 9.44 - 0.94 ⇒
(10 - 1) × y = 9.44 - 0.94 ⇒
We now have a new equation:
9 × y = 8
Solve for y in the new equation.
9 × y = 8 ⇒
y = 8/9
Let the result written as a fraction.
Write the number as a fraction.
According to our first equation:
y = 0.94
According to our calculations:
y = 8/9
⇒ 0.94 = 8/9
3. Reduce (simplify) the fraction above: 8/9
(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):
8 = 23
9 = 32
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 (23; 32) = 1
The numerator and the denominator are coprime numbers (no common prime factors, GCF = 1). So, the fraction cannot be reduced (simplified): irreducible fraction.
8/9: 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:
8/9 = (8 × 4)/(9 × 4) = 32/36
Example 2. By expanding the fraction by 7:
8/9 = (8 × 7)/(9 × 7) = 56/63
Of course, the above fractions are reducing...
... to the initial fraction: 8/9
:: Final answer ::
Written in 3 different ways
As a reduced (simplified) positive proper fraction:
0.94 = 8/9
As a percentage:
0.94 ≈ 94.44%
As equivalent fractions:
0.94 = 8/9 = 32/36 = 56/63
More operations of this kind
Decimal numbers to fractions and percentages, calculator