How do you show the group of digits that repeat in a repeating decimal?(1 point)
To show the group of digits that repeat in a repeating decimal, the repeating part is usually enclosed in parentheses. For example, if the decimal representation of a number is 0.36363636..., we can write it as 0.36(36). The digits within the parentheses indicate the repeating pattern in the decimal.
How many digits long could the repeating cycle of a repeating decimal be if the denominator of the rational number is 7?(1 point)
Responses
any finite length
any finite length
up to six digits long
up to six digits long
infinitely long
infinitely long
up to seven digits long
The repeating cycle of a repeating decimal with a denominator of 7 could be up to six digits long. This means that the pattern of digits that repeat can have a maximum length of six digits.
Convert 0.27¯¯¯¯¯
to a rational number in simplest form.(1 point)
Responses
27100
Start Fraction 27 over 100 end fraction
311
Start Fraction 3 over 11 end fraction
2799
Start Fraction 27 over 99 end fraction
127
Start Fraction 1 over 27 end fraction
To convert the repeating decimal 0.27¯¯¯¯¯ to a rational number in simplest form, we can use the formula for repeating decimals:
x = 0.27¯¯¯¯¯
10x = 2.7¯¯¯¯¯
Now, subtract the two equations:
10x - x = 2.7¯¯¯¯¯ - 0.27¯¯¯¯¯
9x = 2.43
Divide both sides by 9:
9x/9 = 2.43/9
x = 0.27
Therefore, the rational number equivalent to 0.27¯¯¯¯¯ is Start Fraction 27 over 100 end fraction.
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
999
999
1,000
1,000
10
10
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.
If a repeating decimal has a repeating cycle of three digits, it will convert to a rational number with what denominator? (1 point)
Responses
999
999
99
99
1,000
1,000
100