Convert 0.8¯¯¯ to a rational number.
To convert the repeating decimal 0.8¯¯¯ to a rational number, we can represent it as a fraction.
Let x = 0.8¯¯¯
Multiplying both sides of the equation by 10, we get:
10x = 8.8¯¯¯
Subtracting the original equation from this new equation, we eliminate the repeating decimal:
10x - x = 8.8¯¯¯ - 0.8¯¯¯
This simplifies to:
9x = 8
Dividing both sides by 9, we find:
x = 8/9
Therefore, 0.8¯¯¯ is equal to the rational number 8/9.
To convert 0.82¯¯¯¯¯ to a rational number, you would set x equal to 0.82¯¯¯¯¯ and then multiply both sides of the equation by what number?
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To convert 0.8¯¯¯ (0.888...) to a rational number, we can use the following steps:
Step 1: Let x = 0.8¯¯¯
Step 2: Multiply both sides of the equation by 10 to eliminate the repeating decimal:
10x = 8.8¯¯¯
Step 3: Subtract x from both sides of the equation to eliminate the repeating decimal:
10x - x = 8.8¯¯¯ - x
9x = 8.8¯¯¯
Step 4: Multiply both sides of the equation by 10 to eliminate the repeating decimal:
90x = 88.8¯¯¯
Step 5: Subtract 8.8¯¯¯ from both sides of the equation to eliminate the repeating decimal:
90x - x = 88.8¯¯¯ - 8.8¯¯¯
89x = 80
Step 6: Divide both sides of the equation by 89 to solve for x:
x = 80/89
Therefore, the rational number equivalent to 0.8¯¯¯ is 80/89.
To convert 0.8¯¯¯ to a rational number, we need to understand that the line over the digit 8 indicates that it is a repeating decimal.
Let's denote the repeating decimal part as x. In this case, we have 0.8¯¯¯ = 0.8x.
To eliminate the repeating decimal, we can multiply both sides of the equation by a power of 10 that will shift the decimal point of x to the right, making it line up with the original number. Since there is only one digit repeating, we'll multiply by 10.
10 * 0.8¯¯¯ = 10 * (0.8x)
8.8¯¯¯ = 8x
Now, subtract the original equation from this equation to eliminate the repeating decimal part:
8.8¯¯¯ - 0.8¯¯¯ = 8x - 0.8x
8 = 7.2x
To isolate x, divide both sides of the equation by 7.2:
8 / 7.2 = 7.2x / 7.2
8/7.2 = x
Simplifying the fraction 8/7.2:
8/7.2 = 4/3
Therefore, 0.8¯¯¯ is equal to the rational number 4/3.