Question

Convert the decimal to a fraction in simplest form:

Answer 1

Answer:

Decimal 0.333 to a fraction in simplest form is:   $\frac{333}{1000}$

Step-by-step explanation:

Given the decimal

$0.333$

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,

$0.333=\frac{0.333\cdot \:\:1000}{1000}$

         $=\frac{333}{1000}$         ∵ 0.333×1000 = 333

Let us check if we can reduce the fraction $\frac{333}{1000}$

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:   $\frac{333}{1000}$