1.57142857143 as a Fraction

Answer

The answer for 1.57142857143 as a fraction will be 11/7.

Explanation

Converting a decimal to a fraction can be done by identifying repeating patterns. You can follow the steps mentioned below to find the answer.

Step 1: Recognize the repeating decimal pattern. Here, 1.57142857143 has a repeating part of 571428. Thus, we express it as 1.571428... which is 1 + 0.571428...

Step 2: Assign x to the repeating decimal: x = 0.571428...

Step 3: Multiply by 10^6 (because the repeating part has 6 digits) to shift the decimal point: 1000000x = 571428.571428...

Step 4: Subtract the original x from this equation: 1000000x - x = 571428.571428... - 0.571428... which simplifies to 999999x = 571428

Step 5: Solve for x: x = 571428/999999

Step 6: Simplify the fraction: The GCD of 571428 and 999999 is 142857. Dividing both by their GCD gives 4/7. Therefore, 1.571428... = 1 + 4/7 = 11/7.

Thus, 1.57142857143 can be written as a fraction 11/7.

• Fraction: A numerical quantity that is not a whole number, representing a part of a whole.

• Decimal: A number that uses the base ten and includes a decimal point to separate the whole part from the fractional part.

• Repeating Decimal: A decimal in which a digit or group of digits repeats infinitely.

• Numerator: The top part of a fraction, indicating how many parts of the whole are being considered.

• Denominator: The bottom part of a fraction, showing how many parts make up a whole.