Convert the mixed repeating (recurring) decimal number 10.49. Turn it into a reduced (simplified) improper fraction, into a mixed number and write it as a percentage. Equivalent fractions calculator
Convert 10.49 into equivalent fractions and write it as a percentage value
1. Write the mixed repeating (recurring) decimal number as a percentage.
Rewrite / normalize the original number.
- There is only one repeating decimal place:
10.499 = 10.49
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
10.5 =
10.5 × 100/100 =
(10.5 × 100)/100 =
1,050/100 =
1,050%
- In other words:
- Approximate to the desired number of decimal places...
- Multiply the number by 100...
- ... And then add the percent sign, %
- 10.49 ≈ 1,050%
2. Write the mixed repeating (recurring) decimal number as an improper fraction.
10.49 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 = 10.49
Set up the second equation.
- Number of decimal places repeating: 1
Multiply both sides of the first equation by 101 = 10
y = 10.49
10 × y = 10 × 10.49
10 × y = 104.9
Get the same number of decimal places as for y:
10 × y = 104.99
Note: 104.99 = 104.9
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 = 104.99 - 10.49 ⇒
(10 - 1) × y = 104.99 - 10.49 ⇒
We now have a new equation:
9 × y = 94.5
Solve for y in the new equation.
9 × y = 94.5 ⇒
y = 94.5/9
Let the result written as a fraction.
Now we can write the number as a fraction.
According to our first equation:
y = 10.49
According to our calculations:
y = 94.5/9
⇒ 10.49 = 94.5/9
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.
10.49 = (94.5 × 10)/(9 × 10)
10.49 = 945/90
3. Reduce (simplify) the fraction above:
945/90
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).
945 = 33 × 5 × 7
90 = 2 × 32 × 5
Calculate the greatest (highest) common factor (divisor), GCF.
Multiply all the common prime factors by the lowest exponents.
GCF (33 × 5 × 7; 2 × 32 × 5) = 32 × 5
Divide both the numerator and the denominator by their GCF.
945/90 =
(33 × 5 × 7)/(2 × 32 × 5) =
((33 × 5 × 7) ÷ (32 × 5)) / ((2 × 32 × 5) ÷ (32 × 5)) =
(3 × 7)/2 =
21/2
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.
21 ÷ 2 = 10, remainder = 1 ⇒
21 = 10 × 2 + 1 ⇒
21/2 =
(10 × 2 + 1) / 2 =
(10 × 2) / 2 + 1/2 =
10 + 1/2 =
10 1/2
21/2 ~ 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.
21/2 = (21 × 2)/(2 × 2) = 42/4
Example 2. By expanding the fraction by 3.
21/2 = (21 × 3)/(2 × 3) = 63/6
- Of course, the above fractions are reducing...
- ... to the initial fraction: 21/2
:: Final answer ::
Written in 4 different ways
As a reduced (simplified) positive improper fraction:
10.49 = 21/2
As a mixed number:
10.49 = 10 1/2
As a percentage:
10.49 = 1,050%
As equivalent fractions:
10.49 = 21/2 = 42/4 = 63/6
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