0.17777 as a Fraction

Answer

The answer for 0.17777 as a fraction will be 16/90.

Explanation

Converting a repeating decimal to a fraction involves a few more steps but can still be done systematically. Here's how you can convert 0.17777 to a fraction.

Step 1: Let x equal the repeating decimal: x = 0.17777...

Step 2: Multiply both sides of the equation by 100 to shift the decimal point two places to the right: 100x = 17.777...

Step 3: Subtract the original equation from this new equation to eliminate the repeating part: 100x - x = 17.777... - 0.17777... 99x = 17.6

Step 4: Solve for x by dividing both sides by 99: x = 17.6/99

Step 5: Since 17.6 is not a whole number, multiply numerator and denominator by 10 to eliminate the decimal: x = 176/990

Step 6: Simplify the fraction by finding the GCD of 176 and 990, which is 11: x = 16/90

Thus, 0.17777 can be written as a fraction 16/90.

• 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 one or more digits repeat 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.