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.
Describe the relationship between rational numbers and whole numbers. Are all rational numbers also whole numbers? Are all whole numbers also rational numbers? Give examples to support your answer.(4 points)
Rational numbers and whole numbers are related, but they are not the same.
All whole numbers are rational numbers because they can be expressed as fractions with a denominator of 1. For example, 5 can be written as the fraction 5/1.
But not all rational numbers are whole numbers. Rational numbers include both integers (positive whole numbers, negative whole numbers, and zero) and fractions. For example, 1/4 is a rational number, but it is not a whole number.
In summary, while all whole numbers are rational numbers, not all rational numbers are whole numbers. Whole numbers form a subset of rational numbers that consists of integers and zero.