1. Write the number as a percentage.
Note: 100/100 = 1
3.45 = 3.45 × 100/100 = (3.45 × 100)/100 = 345/100 = 345%
In other words: multiply the number by 100... and then add the percent sign, %: 3.45 = 345%
2. Write the number as an improper fraction.
(The numerator is larger than or equal to the denominator).
Write down the number divided by 1, as a fraction:
3.45 = 3.45/1
Turn the top number into a whole number.
Multiply both the top and the bottom by the same number: 100 (1 followed by as many 0s as the number of digits after the decimal point).
3.45/1 = (3.45 × 100)/(1 × 100) = 345/100
3. Reduce (simplify) the fraction above: 345/100
(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).
345 = 3 × 5 × 23; 100 = 22 × 52;
Calculate the greatest (highest) common factor (divisor), GCF.
Multiply all the common prime factors by the lowest exponents.
GCF (3 × 5 × 23; 22 × 52) = 5
Divide both the numerator and the denominator by their greatest common factor, GCF.
345/100 = (3 × 5 × 23)/(22 × 52) = ((3 × 5 × 23) ÷ 5) / ((22 × 52) ÷ 5) = (3 × 23)/(22 × 5) = 69/20
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.
69 ÷ 20 = 3, remainder = 9 => 69 = 3 × 20 + 9 =>
69/20 = (3 × 20 + 9) / 20 = (3 × 20) / 20 + 9/20 = 3 + 9/20 = 3 9/20
69/20: Equivalent fractions.
By expanding the reduced fraction we can build up equivalent fractions (multiply the numerator & the denominator by the same number).
Example 1. By expanding the fraction by 2:
69/20 = (69 × 2)/(20 × 2) = 138/40
Example 2. By expanding the fraction by 6:
69/20 = (69 × 6)/(20 × 6) = 414/120
Of course, the above fractions are reducing... to the initial fraction: 69/20
:: Final answer ::
Written in 4 different ways
As a reduced (simplified) positive improper fraction:
3.45 = 69/20
As a mixed number:
3.45 = 3 9/20
As a percentage:
3.45 = 345%
As equivalent fractions:
3.45 = 69/20 = 138/40 = 414/120