Express 811 as a repeating decimal. Mark the cycle of repeating digits with a bar.(1 point)
To express 811 as a repeating decimal, we can divide 811 by 9.
The result is 90 with a remainder of 1.
So 811 ÷ 9 = 90.111111...
Thus, the repeating decimal representation of 811 is 90.1 with a bar over the digit 1.
Express 8/11 as a repeating decimal. Mark the cycle of repeating digits with a bar.(1 point)
To express 8/11 as a repeating decimal, we can divide the numerator 8 by the denominator 11.
8 ÷ 11 = 0.727272...
Thus, the repeating decimal representation of 8/11 is 0.72 with a bar over the digits 72.
Convert 0.72¯¯¯¯¯ to a rational number in simplest form.(1 point)
To convert the repeating decimal 0.72¯¯¯¯¯ to a rational number, we can set it equal to the variable x:
x = 0.72¯¯¯¯¯
We multiply both sides of the equation by 100, to get rid of the repeating decimal:
100x = 72.727272...
We then subtract the left equation from the right equation:
100x - x = 72.727272... - 0.72¯¯¯¯¯
99x = 72
Dividing both sides of the equation by 99:
x = 72/99
We can simplify this fraction by finding the greatest common divisor (GCD) of the numerator and the denominator, which is 9.
Therefore, the fraction 72/99 simplifies to 8/11.
So, the rational number equivalent to the repeating decimal 0.72¯¯¯¯¯ is 8/11.
Which of the following is a rational number between 5 and 514?(1 point)
Responses
525
5 Start Fraction 2 over 5 end fraction
517
5 Start Fraction 1 over 7 end fraction
513
5 Start Fraction 1 over 3 end fraction
26−−√
A rational number is any number that can be expressed as a fraction, where the numerator and denominator are both integers.
Out of the given options, the only one that represents a rational number between 5 and 514 is:
5 Start Fraction 2 over 5 end fraction
So, the correct answer is 5 Start Fraction 2 over 5 end fraction.
What is a rational number with a denominator of 7 that is between 7–√ and 8–√. Write your answer as an improper fraction.(1 point)
To find a rational number with a denominator of 7 that lies between 7–√ and 8–√, we need to express both numbers with a denominator of 7.
7–√ ≈ 7 – 2.646 ≈ 4.354
8–√ ≈ 8 – 2.828 ≈ 5.172
Thus, the rational number with a denominator of 7 that lies between 7–√ and 8–√ is:
5.172 - 4.354 = 0.818.
To write this as an improper fraction, we multiply by 7/7:
0.818 * 7/7 = 5.726/7.
Therefore, the rational number with a denominator of 7 between 7–√ and 8–√ is 5.726/7.