Convert 0.72¯¯¯¯¯ to a rational number in simplest form.(1 point)
To convert 0.72¯¯¯¯¯ to a rational number in simplest form, we need to understand that the bar over the 2 indicates that the digit 2 repeats infinitely.
We can represent 0.72¯¯¯¯¯ as follows:
Let x = 0.72¯¯¯¯¯
Then, 100x = 72.72¯¯¯¯¯
Now, we can subtract the equations:
100x - x = 72.72¯¯¯¯¯ - 0.72¯¯¯¯¯
99x = 72
Dividing both sides by 99:
x = 72/99
To simplify this fraction, we can find the greatest common divisor (GCD) of 72 and 99, which is 9.
Dividing both numerator and denominator by 9:
x = 8/11
Therefore, the rational representation of 0.72¯¯¯¯¯ in simplest form is 8/11.
Which of the following is a rational number between 5 and 5 1/4?(1 point)
Responses
26−−√
start root 26 end root
517
5 Start Fraction 1 over 7 end fraction
513
5 Start Fraction 1 over 3 end fraction
525
To find a rational number between 5 and 5 1/4, we first need to convert 5 1/4 to an improper fraction.
5 1/4 = 5 + 1/4 = 20/4 + 1/4 = 21/4
Now we can find a rational number between 5 and 21/4 by taking their average:
(5 + 21/4) / 2 = (20/4 + 21/4) / 2 = 41/8
Therefore, the rational number between 5 and 5 1/4 is 41/8.
None of the given options (26−−√, 517, 513, 525) are equal to 41/8.
Which of the following is a rational number between 5 and 514?(1 point)
Responses
26−−√
5 1/7
5 1/3
5 2/5
To find a rational number between 5 and 514, we can take their average:
(5 + 514) / 2 = 519 / 2 = 259.5
However, none of the given options (26−−√, 5 1/7, 5 1/3, 5 2/5) are equal to 259.5.
Therefore, there is no rational number between 5 and 514 among the given options.
Which of the following is a rational number between 5 and 5 1/4?(1 point)
26−−√
5 1/7
5 1/3
5 2/5
To find a rational number between 5 and 5 1/4, we can take their average:
(5 + 5 1/4) / 2 = (20/4 + 21/4) / 2 = 41/8
Therefore, the rational number between 5 and 5 1/4 is 41/8.
Among the given options, the rational number 5 1/7 is the closest to 41/8. Therefore, the correct answer is 5 1/7.
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 is between 7–√ and 8–√, we need to find the decimal approximation of the given numbers and then convert it into a fraction with a denominator of 7.
Approximating the square roots:
√7 ≈ 2.65
√8 ≈ 2.83
So, we are looking for a rational number between 2.65 and 2.83.
To convert the decimal approximation to a fraction with a denominator of 7, we can multiply both the numerator and denominator by 100 (to clear the decimal):
2.65 = 265/100 = 53/20
2.83 = 283/100 = 283/100
Now, we can find a rational number between 53/20 and 283/100. Let's take their average:
(53/20 + 283/100) / 2 = (5300/200 + 566/200) / 2 = 5866/200
Therefore, a rational number with a denominator of 7 between 7–√ and 8–√ is 5866/200, or simplifying the fraction, 2933/100.