Convert 0.8¯¯¯ to a rational number.
To convert the recurring decimal 0.8¯¯¯ to a rational number, we need to express it as a fraction.
Let x = 0.8¯¯¯
To remove the recurring decimal, we can multiply both sides of the equation by a power of 10 that is equal to the number of decimal places in the recurring part. In this case, there is 1 decimal place in the recurring part, so we can multiply both sides by 10:
10x = 8.8¯¯¯
Next, subtract the original equation from the new equation to eliminate the recurring part:
10x - x = 8.8¯¯¯ - 0.8¯¯¯
9x = 8
Divide both sides of the equation by 9 to solve for x:
x = 8/9
Therefore, 0.8¯¯¯ can be expressed as the rational number 8/9.
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To convert 0.8¯¯¯ to a rational number, we need to express it as a fraction.
Let x = 0.8¯¯¯
To remove the repeating decimal, we can multiply both sides of the equation by a power of 10 equal to the number of repeating digits. In this case, the repeating digit is 8, so we multiply both sides by 10:
10x = 8.8¯¯¯
Next, we subtract the original equation from the equation obtained by multiplying by 10:
10x - x = 8.8¯¯¯ - 0.8¯¯¯
This simplifies to:
9x = 8
Finally, we divide both sides of the equation by 9 to solve for x:
x = 8/9
Therefore, 0.8¯¯¯ is equal to the rational number 8/9.
To convert the recurring decimal 0.8¯¯¯ to a rational number, we need to determine its fractional form.
Let's represent 0.8¯¯¯ as x:
x = 0.8¯¯¯
Now, to get rid of the recurring decimal, we can multiply both sides of the equation by a power of 10. We need to multiply by 10 enough times to shift the recurring part to the left side of the decimal point.
By multiplying x by 10, we get:
10x = 8.8¯¯¯
Now, to eliminate the recurring part, we can subtract the original equation from the multiplied equation. This will give us the difference between them without the recurring part:
10x - x = 8.8¯¯¯ - 0.8¯¯¯
9x = 8
Dividing both sides of the equation by 9, we find:
x = 8/9
Therefore, the rational number representation of 0.8¯¯¯ is 8/9.