Rational Numbers in Different Forms Quick Check
Math 8 Q1 (Pre-Algebra) / The Number System
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)
Responses
10
100
999
1,000
Rational Numbers in Different Forms Quick Check
Math 8 Q1 (Pre-Algebra) / The Number System
If a repeating decimal has a repeating cycle of three digits, it will convert to a rational number with what denominator? (1 point)
Responses
1,000
999
100
99
The correct answer is 999.
To convert a repeating decimal like 0.264¯¯¯¯¯¯¯¯ to a rational number, you would set x equal to 0.264¯¯¯¯¯¯¯¯ and multiply both sides of the equation by 1000. Therefore, the correct answer would be 1,000.
To convert a repeating decimal like 0.264¯¯¯¯¯¯¯¯ to a rational number, we can use the following steps:
Step 1: Let x be equal to the repeating decimal. In this case, x = 0.264¯¯¯¯¯¯¯¯.
Step 2: Multiply both sides of the equation by a power of 10 that will shift the decimal point to the right of the repeating part. Since there are three digits in the repeating part (264), we can multiply both sides by 1000. This will eliminate the repeating decimal.
x = 0.264¯¯¯¯¯¯¯¯
1000x = 264.264¯¯¯¯¯¯¯¯
Step 3: Subtract the original equation from the expanded equation to eliminate the repeating part.
1000x - x = 264.264¯¯¯¯¯¯¯¯ - 0.264¯¯¯¯¯¯¯¯
999x = 264
Step 4: Solve for x by dividing both sides of the equation by 999.
x = 264/999
So, the rational number equivalent to 0.264¯¯¯¯¯¯¯¯ is x = 264/999.
Looking at the given options, the correct answer is 999.