To convert 0.264¯¯¯¯¯¯¯¯ to a rational number, you would set x equal to 0.264¯¯¯¯¯¯¯¯ and then multiply both sides of the equation by what number?(1 point)
10
999
1,000
100
To convert 0.264¯¯¯¯¯¯¯¯ to a rational number, you would set x equal to 0.264¯¯¯¯¯¯¯¯ and then multiply both sides of the equation by 1000.
Can you explain?
To convert the repeating decimal 0.264¯¯¯¯¯¯¯¯ to a rational number, you would set x equal to 0.264¯¯¯¯¯¯¯¯ and then multiply both sides of the equation by 1,000. So the answer is 1,000.
To convert a repeating decimal to a rational number, we can use the property of repeating decimals to represent them as fractions.
Let's set x equal to the repeating decimal 0.264¯¯¯¯¯¯¯¯ and try to find an equivalent fraction for it.
Step 1: Multiply both sides of the equation by a power of 10 to eliminate the repeating decimal. Since there are 3 repeating digits (264), we will multiply by 1000.
Multiplying both sides by 1000 gives us:
1000x = 264.264264...
Step 2: Subtract the original equation from this equation to eliminate the repeating part.
1000x - x = 264.264264... - 0.264264...
This simplifies to:
999x = 264
Step 3: Solve for x by dividing both sides of the equation by 999.
x = 264/999
Simplifying the fraction, we have:
x = 88/333
Therefore, to convert 0.264¯¯¯¯¯¯¯¯ to a rational number, you would multiply both sides of the equation by 999 (option 2).