0.86666 as a Fraction

Answer

The answer for 0.86666 as a fraction will be 13/15.

Explanation

Converting a decimal to a fraction is a task for students that can be done easily. You can follow the steps mentioned below to find the answer.

Step 1: Firstly, any decimal number should be converted to fraction for easy calculation. Here, 0.86666 is the number on the numerator and the base number 1 will be the denominator. Then, 0.86666 becomes 0.86666/1.

Step 2: To remove the repeating decimal from a fraction, express it as a repeating decimal 0.86666... = 0.86 + 0.00666...

Step 3: Express 0.00666... as a fraction. Let x = 0.00666..., then 1000x = 6.666..., so 1000x - x = 6.66 - 0.00666... = 6.66. Thus, 999x = 6.66. Therefore, x = 6.66/999 = 2/300.

Step 4: Add the fractions: 0.86 = 86/100 and 0.00666... = 2/300. Step 5: Combine the fractions: 86/100 + 2/300 = 258/300 + 2/300 = 260/300. Simplify this by dividing the numerator and denominator by 20: 260/300 = 13/15.

Thus, 0.86666 can be written as a fraction 13/15.

• 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.

• 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.

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