Convert the mixed repeating (recurring) decimal number 8.29. Turn it into a reduced (simplified) improper fraction, into a mixed number and write it as a percentage. Equivalent fractions calculator
Convert 8.29 into equivalent fractions and write it as a percentage value
1. Write the mixed repeating (recurring) decimal number as a percentage.
Approximate to the desired number of decimal places.
Multiply the number by 100/100.
- The value of the number does not change when multiplying by 100/100.
- Note: 100/100 = 1
8.3 =
8.3 × 100/100 =
(8.3 × 100)/100 =
830/100 =
830%
- In other words:
- Approximate to the desired number of decimal places...
- Multiply the number by 100...
- ... And then add the percent sign, %
- 8.29 ≈ 830%
2. Write the mixed repeating (recurring) decimal number as an improper fraction.
8.29 can be written as an improper fraction.
- The numerator is larger than or equal to the denominator.
Set up the first equation.
- Let y equal the decimal number:
y = 8.29
Set up the second equation.
- Number of decimal places repeating: 1
Multiply both sides of the first equation by 101 = 10
y = 8.29
10 × y = 10 × 8.29
10 × y = 82.9
Get the same number of decimal places as for y:
10 × y = 82.99
Note: 82.99 = 82.9
Subtract the first equation from the second one.
- Having the same number of decimal places ...
- The repeating pattern drops off by subtracting the two equations.
10 × y - y = 82.99 - 8.29 ⇒
(10 - 1) × y = 82.99 - 8.29 ⇒
We now have a new equation:
9 × y = 74.7
Solve for y in the new equation.
9 × y = 74.7 ⇒
y = 74.7/9
Let the result written as a fraction.
Now we can write the number as a fraction.
According to our first equation:
y = 8.29
According to our calculations:
y = 74.7/9
⇒ 8.29 = 74.7/9
Get rid of the decimal places in the fraction above.
- Multiply the top and the bottom number by 10.
- 1 followed by as many 0-s as the number of digits after the decimal point.
8.29 = (74.7 × 10)/(9 × 10)
8.29 = 747/90
3. Reduce (simplify) the fraction above:
747/90
to the lowest terms, to its simplest equivalent form, irreducible.
To reduce a fraction to the lowest terms divide the numerator and denominator by their greatest (highest) common factor (divisor), GCF.
Factor the numerator and denominator (prime factorization).
747 = 32 × 83
90 = 2 × 32 × 5
Calculate the greatest (highest) common factor (divisor), GCF.
Multiply all the common prime factors by the lowest exponents.
GCF (32 × 83; 2 × 32 × 5) = 32
Divide both the numerator and the denominator by their GCF.
747/90 =
(32 × 83)/(2 × 32 × 5) =
((32 × 83) ÷ 32) / ((2 × 32 × 5) ÷ 32) =
83/(2 × 5) =
83/10
4. The fraction is an improper one, rewrite it as a mixed number (mixed fraction):
- A mixed number = an integer number and a proper fraction, of the same sign.
- Example 1: 2 1/5; Example 2: - 1 3/7.
- A proper fraction = the numerator is smaller than the denominator.
83 ÷ 10 = 8, remainder = 3 ⇒
83 = 8 × 10 + 3 ⇒
83/10 =
(8 × 10 + 3) / 10 =
(8 × 10) / 10 + 3/10 =
8 + 3/10 =
8 3/10
83/10 ~ 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.
83/10 = (83 × 2)/(10 × 2) = 166/20
Example 2. By expanding the fraction by 4.
83/10 = (83 × 4)/(10 × 4) = 332/40
- Of course, the above fractions are reducing...
- ... to the initial fraction: 83/10
:: Final answer ::
Written in 4 different ways
As a reduced (simplified) positive improper fraction:
8.29 = 83/10
As a mixed number:
8.29 = 8 3/10
As a percentage:
8.29 = 830%
As equivalent fractions:
8.29 = 83/10 = 166/20 = 332/40
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