what is 3.83 repeating as a fraction 3 is repeating
.3333... = 1/3
so, .0333... = 1/30
So you have
3.8 + 1/30 = 3 8/10 + 1/30
= 3 24/30 + 1/30 = 3 25/30 = 3 5/6
To convert a decimal into a fraction, follow these steps:
Step 1: Let x = the repeating decimal.
Step 2: Multiply both sides of the equation by a power of 10 that eliminates the repeating part. In this case, multiply both sides by 100 to eliminate the repeating part (since there are two decimal places).
100x = 383.838383...
Step 3: Subtract the equation obtained in step 1 from the equation obtained in step 2.
100x - x = 383.838383... - 3.838383...
99x = 380
Step 4: Solve for x by dividing both sides of the equation by 99.
x = 380 / 99
Therefore, the fraction representation of 3.83 repeating is 380/99.
To convert the repeating decimal 3.83 to a fraction, we can use the algebraic method. Let's denote the repeating part as 'x'.
Step 1: Set up the equation.
Since there are two digits repeating after the decimal point, we multiply the repeating part by 100 (10 raised to the power of 2) to shift the decimal point two places to the right:
100x = 383.83
Step 2: Subtract the original equation.
Now, we subtract the original equation from the equation we obtained in Step 1 to eliminate the decimal part:
100x - x = 383.83 - 3.83
99x = 380
Step 3: Solve for x.
Divide both sides of the equation by 99 to isolate x:
x = 380 / 99
Step 4: Simplify the fraction (if possible).
To check if the fraction is already in simplest form, we can find the greatest common divisor (GCD) of the numerator and the denominator. In this case, 380 and 99 have no common factors other than 1. Therefore, the fraction 380/99 cannot be simplified further.
So, 3.83 (repeating) can be written as the fraction 380/99.