Step-by-Step Conversion of -0.72222222222222 to a Fraction
To convert the decimal -0.72222222222222 to a fraction, follow these steps:
Step 1: Identify the Decimal
The decimal is -0.72222222222222. The first thing to notice is that the number is negative.
Step 2: Recognize the Repeating Part
The decimal -0.72222222222222 can be recognized as -0.72 with repeating 2s. Thus, we can express this as:
-0.72(2)
Step 3: Let x be the Decimal
Let:
x = -0.72222222222222
Step 4: Multiply to Remove the Decimal
To eliminate the repeating decimal, multiply x by 100:
100x = -72.22222222222222
Step 5: Set Up a Second Equation
Now multiply x by 10:
10x = -7.22222222222222
Step 6: Subtract the Two Equations
Next, subtract the second equation from the first equation:
100x - 10x = -72.222... - (-7.222...)
This simplifies to:
90x = -65
Step 7: Solve for x
Now, solving for x gives us:
x = -65 / 90
Step 8: Simplify the Fraction
Now, we simplify the fraction -65/90. Both the numerator and denominator can be divided by 5:
-65 ÷ 5 = -13
90 ÷ 5 = 18
Thus, we get:
x = -13/18
Step 9: Conclusion
The decimal -0.72222222222222 as a fraction is:
-13/18