Answer:
Decimal 0.333 to a fraction in simplest form is: [tex]\frac{333}{1000}[/tex]
Step-by-step explanation:
Given the decimal
[tex]0.333[/tex]
Multiply and divide by 10 for every number after the decimal point.
There are three digits to the right of the decimal point, therefore multiply and divide by 1000.
Thus,
[tex]0.333=\frac{0.333\cdot \:\:1000}{1000}[/tex]
[tex]=\frac{333}{1000}[/tex] ∵ 0.333×1000 = 333
Let us check if we can reduce the fraction [tex]\frac{333}{1000}[/tex]
For this, we need to find a common factor of 333 and 1000 in order to cancel it out.
But, first, we need to find the Greatest Common Divisor (GCD) of 333, 1000
Greatest Common Divisor (GCD) :
The GCD of a, b is the largest positive number that divides both a and b without a remainder.
Prime Factorization of 333: 3 · 3 · 37
Prime Factorization of 1000: 2 · 2 · 2 · 5 · 5 · 5
As there is no common factor for 333 and 1000, therefore, the GCD is 1.
Important Tip:
- As GCD is 1, therefore the fraction can not be simplified.
Therefore, decimal 0.333 to a fraction in simplest form is: [tex]\frac{333}{1000}[/tex]
