Convert 0.82 repeating to a rational number
To convert a repeating decimal to a rational number, we can treat the repeating part as a variable and solve for it.
Let x = 0.82 repeating.
Then, 100x = 82.82 repeating (multiply both sides by 100 to move the decimal point two places to the right)
Subtracting the original equation from the second equation, we get:
100x - x = 82.82 - 0.82
99x = 82
Dividing both sides by 99, we get:
x = 82/99
Therefore, 0.82 repeating can be expressed as the rational number 82/99.
To convert 0.82 repeating to a rational number, we can use the concept of repeating decimals.
Let x = 0.82 repeating.
Multiply both sides of the equation by 100 to move the decimal point two places to the right:
100x = 82.82 repeating.
Now, subtract the original equation from the new equation to eliminate the repeating decimal:
100x - x = 82.82 repeating - 0.82 repeating.
This simplifies to:
99x = 82.
Divide both sides of the equation by 99 to solve for x:
x = 82 / 99.
Therefore, 0.82 repeating can be expressed as the rational number 82/99.