convert 0.72 ̅ to a rational number in simplest form
To convert the recurring decimal 0.72 ̅ to a rational number in simplest form, we need to express it as a fraction.
Let x = 0.72 ̅
To remove the recurring decimal, let's multiply both sides of the equation by 10:
10x = 7.2 ̅
Now, we can subtract the original equation from this new equation:
10x - x = 7.2 ̅ - 0.72 ̅
Simplifying the right side:
9x = 7.2
Now, divide both sides by 9:
9x/9 = 7.2/9
x = 0.8
Therefore, 0.72 ̅ as a rational number in simplest form is 0.8.
To convert the repeating decimal 0.72̅ to a rational number in simplest form, we need to set up an equation.
Let x = 0.72̅.
To get rid of the repeating decimal, we can multiply x by a power of 10 equal to the number of digits in the repeating part, which is 2.
10x = 7.2̅.
Now, we subtract the original equation from this new equation to eliminate the repeating decimal:
10x - x = 7.2̅ - 0.72̅
9x = 7.2 - 0.72
9x = 6.48
Dividing both sides of the equation by 9, we can solve for x:
x = 6.48 / 9
x = 0.72
So, 0.72̅ can be represented as the rational number 72/99 or as the simplest form 8/11.
To convert the repeating decimal 0.72̅ to a rational number in simplest form, we can follow these steps:
Step 1: Assign a variable to the repeating part of the decimal, in this case, x = 72̅.
Step 2: Subtract x from the entire decimal to eliminate the repeating part. In this case, 0.72̅ - 0.72 = 0.
Step 3: Multiply both sides of the equation by a power of 10 to eliminate the repeating decimal. Since there are two digits in the repeating part of the decimal, we will multiply both sides by 100.
0.72̅ × 100 = 72̅
0 × 100 = 0
Step 4: Subtract the equation from Step 2 from the equation in Step 3 to solve for x.
72̅ - 0 = x
x = 72̅
Step 5: Express the value of x as a fraction over the number of 9s based on the number of repeating digits. Since there are two repeating digits (72̅), put x over 99.
x = 72̅ / 99
Step 6: Simplify the fraction if possible by dividing the numerator and denominator by their greatest common divisor (GCD). In this case, the GCD of 72 and 99 is 9.
x = (72 ÷ 9) / (99 ÷ 9)
x = 8 / 11
Therefore, 0.72̅ can be expressed as the rational number 8/11 in simplest form.