Change each repeating decimal to fraction form.0.1515 . . .5.246246 . . .,0.21313 . . .,3.98777 . . .

You are wrong Ms.Sue - he said repeating as in 0.15151515151515151515151515151515..............

To change a repeating decimal to fraction form, we can follow these steps:

Step 1: Identify the repeating part of the decimal.

Step 2: Set up an equation where the repeating part is equal to x.

Step 3: Multiply both sides of the equation by the appropriate power of 10 to eliminate the decimal places from the repeating part.

Step 4: Subtract the original equation from the one obtained in step 3 to eliminate the repeating part.

Step 5: Solve the resulting equation to find the value of x.

Step 6: Express x as a fraction in its simplest form.

Let's apply these steps to the given decimals:

1) 0.1515 . . .

Step 1: The repeating part is 15.

Step 2: Let x = 0.1515 . . .

Step 3: Multiply both sides by 100 to eliminate the decimal places from the repeating part:
100x = 15.1515 . . .

Step 4: Subtract the original equation from the one obtained in step 3:
100x − x = 15.1515 . . . − 0.1515 . . .

99x = 15

Step 5: Solve for x:
x = 15/99

Step 6: Simplify the fraction, if possible:
x = 5/33

Therefore, 0.1515 . . . as a fraction is 5/33.

2) 5.246246 . . .

Step 1: The repeating part is 246.

Step 2: Let x = 5.246246 . . .

Step 3: Multiply both sides by 1000 to eliminate the decimal places from the repeating part:
1000x = 5246.246246 . . .

Step 4: Subtract the original equation from the one obtained in step 3:
1000x − x = 5246.246246 . . . − 5.246246 . . .

999x = 5241

Step 5: Solve for x:
x = 5241/999

Step 6: Simplify the fraction, if possible:
x = 5241/999 = 521/111

Therefore, 5.246246 . . . as a fraction is 521/111.

3) 0.21313 . . .

Step 1: The repeating part is 213.

Step 2: Let x = 0.21313 . . .

Step 3: Multiply both sides by 1000 to eliminate the decimal places from the repeating part:
1000x = 213.1313 . . .

Step 4: Subtract the original equation from the one obtained in step 3:
1000x − x = 213.1313 . . . − 0.21313 . . .

999x = 213

Step 5: Solve for x:
x = 213/999

Step 6: Simplify the fraction, if possible:
x = 213/999 = 71/333

Therefore, 0.21313 . . . as a fraction is 71/333.

4) 3.98777 . . .

Step 1: The repeating part is 777.

Step 2: Let x = 3.98777 . . .

Step 3: Multiply both sides by 1000 to eliminate the decimal places from the repeating part:
1000x = 3987.777 . . .

Step 4: Subtract the original equation from the one obtained in step 3:
1000x − x = 3987.777 . . . − 3.98777 . . .

999x = 3983.79

Step 5: Solve for x:
x = 3983.79/999

Step 6: Simplify the fraction, if possible:
x = 3983.79/999 = 4387/111

Therefore, 3.98777 . . . as a fraction is 4387/111.

0.1515 = 1515/10,000

Reduce it to its lowest terms.