How many digits are in the repeating cycle of 1727?(1 point)
To determine the repeating cycle of a fraction, we can use a long division method. When we divide 17 by 27, we get a repeating decimal representation of 0.629629629... The repeating cycle is 629, which consists of 3 digits. Therefore, the repeating cycle of 17/27 contains 3 digits.
To determine if a rational number can be expressed as a repeating decimal, we need to check if the denominator has any prime factors other than 2 or 5.
- The fraction 7/8 has a denominator of 8, which is divisible only by 2. Therefore, it can be expressed as a terminating decimal.
- The fraction 5/12 has a denominator of 12, which is divisible by both 2 and 3. Therefore, it can be expressed as a repeating decimal.
- The fraction 17/25 has a denominator of 25, which is divisible only by 5. Therefore, it can be expressed as a terminating decimal.
- The fraction 31/40 has a denominator of 40, which is divisible by both 2 and 5. Therefore, it can be expressed as a terminating decimal.
From the given options, the only fraction that can be expressed as a repeating decimal is 5/12.
Since the denominator of the rational number is 7, the repeating cycle of the decimal can be up to six digits long.
The repeating cycle of 1727 is 1 digit long.
How many digits are in the repeating cycle of 17/27?(1 point)
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Which of the following rational numbers can be expressed as a repeating decimal: 7/8, 5/12, 17/25, or 31/40?(1 point)
Express 713 as a repeating decimal. Mark the repeating digits with a bar.
Note: You will find the option to add a bar above text in the Geometry (∠
) keyboard.
(1 point)
To express 713 as a repeating decimal, we need to perform division.
First, divide 713 by the denominator, which is 1, to get the quotient 713.
Next, we need to find the repeating part. To do this, we note that the remainder is 1, and it repeats every time. Thus, the repeating part is 1.
Therefore, 713 as a repeating decimal can be expressed as 713.1 with the bar over the digit 1.
How do you show the group of digits that repeat in a repeating decimal?(1 point)
Responses
by underlining them
by underlining them
by printing them in italics
by printing them in italics
by putting them in parentheses
by putting them in parentheses
by putting a bar over them
The correct answer is:
by putting a bar over them
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 seven digits long
up to seven digits long
up to six digits long
up to six digits long
infinitely long
infinitely long
Convert 0.27¯¯¯¯¯
to a rational number in simplest form.(1 point)
Responses
127
Start Fraction 1 over 27 end fraction
2799
Start Fraction 27 over 99 end fraction
27100
Start Fraction 27 over 100 end fraction
311
To convert 0.27¯¯¯¯¯ to a rational number in simplest form, we need to express the repeating decimal as a fraction.
Let x = 0.27¯¯¯¯¯.
Multiplying both sides of the equation by 100 (to move the decimal point two places to the right) gives us:
100x = 27.¯¯¯¯¯.
Next, we subtract x from 100x:
100x - x = 27.¯¯¯¯¯ - 0.27¯¯¯¯¯.
Simplifying the right side gives us:
99x = 27.
Finally, we solve for x by dividing both sides by 99:
x = 27/99.
To express it as a fraction in simplest form, we can simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 9:
x = (27/9) / (99/9) = 3/11.
Therefore, 0.27¯¯¯¯¯ as a rational number in simplest form is 3/11.
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
100
100
999
999
1,000
1,000
10
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
100
100
99
99
999
999
1,000
If a repeating decimal has a repeating cycle of three digits, it will convert to a rational number with a denominator of 999.
Show an example of an irrational number between 9 and 11.(1 point)
Responses
20−−√
start root 20 end root
10−−√
start root 10 end root
99−−√
start root 99 end root
100−−−√
start root 100 end root
An example of an irrational number between 9 and 11 is $\sqrt{10}$.
What is the least integer whose square root is an irrational number between 5 and 7?(1 point)
Responses
6
6
13
13
25
25
26
The least integer whose square root is an irrational number between 5 and 7 is 26.
Show an example of a rational number that is between 10−−√ and 11−−√.(1 point)
Responses
103
Start Fraction 10 over 3 end fraction
3.4
3.4
165
Start Fraction 16 over 5 end fraction
3.1
An example of a rational number that is between $\sqrt{10}$ and $\sqrt{11}$ is $\frac{103}{10}$.
Which irrational number is between 14−−√ and 18−−√?(1 point)
Responses
10−−√
start root 10 end root
15−−√
start root 15 end root
19−−√
start root 19 end root
13−−√
An example of an irrational number that is between $\sqrt{14}$ and $\sqrt{18}$ is $\sqrt{15}$.
How many irrational numbers are there between 11−−√ and 17−−√?(1 point)
Responses
four numbers
four numbers
six numbers
six numbers
an infinite number
an infinite number
twenty-eight numbers
There are an infinite number of irrational numbers between $\sqrt{11}$ and $\sqrt{17}$.
Express 7/13 as a repeating decimal. Mark the repeating digits with a bar.
Express 7/13 as a repeating decimal. Mark the repeating digits with a bar.
Note: You will find the option to add a bar above text in the Geometry (∠) keyboard.
(1 point)