so then for -4.33333
would be in a fraction
-13/3
IF the 333's are repeating. Yes.
To convert a decimal to a fraction, follow these steps:
Step 1: Let x be the given decimal number.
Step 2: Multiply both sides of the equation x = -4.33333 by 10^n, where n is the number of repeating digits after the decimal point. In this case, there is a repeating 3, so n = 1.
-4.33333 × 10 = -43.33333.
Step 3: Subtract the original equation (x = -4.33333) from the equation obtained in step 2.
-43.33333 - (-4.33333) = -39.
Step 4: Let y be the value obtained in step 3.
Step 5: Find the denominator for the fraction by subtracting 1 from 10^n.
10^1 - 1 = 9.
Step 6: Express y as the numerator over the denominator found in step 5.
y/9 = -39/9.
Step 7: Simplify the fraction if possible. In this case, -39/9 can be simplified by dividing both the numerator and the denominator by their greatest common divisor (gcd), which is 3.
(-39 ÷ 3) / (9 ÷ 3) = -13/3.
Therefore, the decimal -4.33333, with the repeating 3s, can be expressed as the fraction -13/3.