How to Convert -0.72222222222222 to a Fraction: A Step-By-Step Guide

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