Question

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)
O 1,000
• 999.
O 10
О 100

Answer 1

If a repeating decimal has a repeating cycle of three digits, it will convert to a rational number with what denominator? (1 point)
O 1,000
0 99
• 100
• 999.

Answer 2

To convert the 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.

This is because 0.264 has three decimal places, and multiplying by 1,000 will shift the decimal point three places to the right, resulting in the integer 264.

So the correct answer is:
- **1,000**

Answer 3

If a repeating decimal has a repeating cycle of three digits, it will convert to a rational number with a denominator of **999**.

This is because for a repeating decimal of the form \(0.\overline{abc}\), where \(abc\) are the three repeating digits, the conversion process generally involves creating a fraction with a denominator that is one less than a power of ten corresponding to the number of repeating digits (in this case, \(10^3 - 1 = 999\)).

So the correct answer is:
- **999**.