Convert 0.72¯¯¯¯¯ to a rational number in simplest form
To convert the repeating decimal 0.72¯¯¯¯¯ to a rational number in simplest form, we can follow these steps:
Step 1: Assign a variable to the original repeating decimal:
Let x = 0.72¯¯¯¯¯
Step 2: Multiply both sides of the equation by 100 (to move the decimal point two places to the right):
100x = 72.72¯¯¯¯¯
Step 3: Subtract the original equation from the newly multiplied equation to eliminate the repeating part:
100x - x = 72.72¯¯¯¯¯ - 0.72¯¯¯¯¯
99x = 72
Step 4: Divide both sides of the equation by 99 to solve for x:
x = 72/99
Step 5: Simplify the resulting fraction if possible:
The fraction 72/99 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 9:
x = 8/11
Therefore, the repeating decimal 0.72¯¯¯¯¯ is equivalent to the rational number 8/11 in simplest form.
To convert the recurring decimal 0.72¯¯¯¯¯ to a rational number in simplest form, we can follow these steps:
Step 1: Let's represent the recurring decimal 0.72¯¯¯¯¯ as x.
x = 0.72¯¯¯¯¯
Step 2: Multiply both sides of the equation by 100 to remove the recurring part.
100x = 72.72¯¯¯¯¯
Step 3: Subtract the original equation from the equation in Step 2 to eliminate the recurring part.
100x - x = 72.72¯¯¯¯¯ - 0.72¯¯¯¯¯
99x = 72
Step 4: Simplify the equation by dividing both sides by 99.
99x / 99 = 72 / 99
x = 8/11
So, the recurring decimal 0.72¯¯¯¯¯ can be represented as the rational number 8/11 in simplest form.
To convert a repeating decimal to a rational number in simplest form, we can follow these steps:
Step 1: Assign a variable for the repeating decimal. Let's call it x.
x = 0.72¯¯¯¯¯
Step 2: Multiply both sides of the equation by a power of 10 that will remove the repeating part. Since there is only one digit repeating after the decimal point, we need to multiply by 10.
10x = 7.2¯¯¯¯¯
Step 3: Subtract the original equation from this new equation to eliminate the repeating part.
10x - x = 7.2¯¯¯¯¯ - 0.72¯¯¯¯¯
9x = 7.2
Step 4: Solve for x by dividing both sides of the equation by 9.
9x / 9 = 7.2 / 9
x = 0.8
Therefore, the repeating decimal 0.72¯¯¯¯¯ is equal to the rational number 0.8 in its simplest form.