4.16666 as a Fraction

Answer

The answer for 4.16666 as a fraction is 25/6.

Explanation

Converting a repeating decimal to a fraction can be straightforward if you follow certain steps. Here are the steps to find the answer:

Step 1: Let x = 4.16666... (with 6 repeating). This can be expressed as x = 4.1̅6.

Step 2: Multiply both sides of the equation by 10 to move the decimal point one place to the right for the repeating part: 10x = 41.6666...

Step 3: Multiply both sides by 10 again to move the decimal point to the end of the repeating sequence: 100x = 416.6666...

Step 4: Subtract the equation from step 2 from the equation in step 3 to eliminate the repeating part: 100x - 10x = 416.6666... - 41.6666... 90x = 375

Step 5: Solve for x by dividing both sides by 90: x = 375/90

Step 6: Simplify the fraction by finding the greatest common divisor (GCD) of 375 and 90, which is 15: 375 ÷ 15 = 25 90 ÷ 15 = 6

Thus, 4.16666 can be written as the fraction 25/6.

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

• Decimal: A number that uses 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.