Convert 0.72¯¯¯¯¯ to a rational number in simplest form.(1 point)
$$
0.72¯¯¯¯¯ = 0.727272... = 0.\overline{72}
$$
Let x = 0.\overline{72}
100x = 72.\overline{72}
Subtracting the first equation from the second equation, we get:
100x - x = 72.\overline{72} - 0.\overline{72}
99x = 72
x = 72/99
Therefore, 0.72¯¯¯¯¯ as a rational number in simplest form is 72/99.
r u sure
I apologize for the incorrect response. Let's go through the calculation again.
Let's say x = 0.\overline{72}.
Multiplying x by 100 gives 100x = 72.\overline{72}.
Now, let's subtract the original equation from the second equation:
100x - x = 72.\overline{72} - 0.\overline{72}
Simplifying both sides:
99x = 72
Dividing both sides by 99:
x = 72/99
To simplify this fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 9:
x = (8 * 9) / (11 * 9)
x = 8/11
Therefore, 0.72¯¯¯¯¯ as a rational number in simplest form is 8/11.
Which of the following is a rational number between 5 and 514?(1 point)
Responses
26−−√
start root 26 end root
513
5 Start Fraction 1 over 3 end fraction
525
5 Start Fraction 2 over 5 end fraction
517
5 Start Fraction 1 over 7 end fraction
To determine which of the given options is a rational number between 5 and 514, let's examine each option:
1. √26:
This option is irrational since the square root of 26 cannot be expressed as a fraction or a terminating decimal.
2. 513:
This option is an integer, but it is not between 5 and 514. It is less than 5.
3. 5/3:
This option is a fraction and falls between 5 and 514. However, it is not in simplest form. Reducing 5/3, we get 1 2/3.
4. 525:
This option is an integer, but it is not between 5 and 514. It is greater than 514.
5. 517:
This option is an integer between 5 and 514. It is a rational number.
Therefore, the rational number between 5 and 514 is 517.
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 between 7–√ and 8–√, we need to determine the value of each of these radical expressions.
Let's start with 7–√:
To evaluate this, we can represent it as 7–√ = 7 - √(49) = 7 - 7 = 0.
Now, let's consider 8–√:
To evaluate this, we can represent it as 8–√ = 8 - √(64) = 8 - 8 = 0.
Both 7–√ and 8–√ equal 0, so there is no rational number with a denominator of 7 between them.
i need a answer give me an answer
Apologies for the confusion. Let's find a rational number with a denominator of 7 between 7–√ and 8–√.
To start, let's estimate the values of 7–√ and 8–√:
7–√ ≈ 7 - 2.65 ≈ 4.35
8–√ ≈ 8 - 2.82 ≈ 5.18
Now, let's find a rational number with a denominator of 7 that is greater than 4.35 but less than 5.18. One such number is 5.
Therefore, the rational number with a denominator of 7 between 7–√ and 8–√ is 5/7.
To convert 0.72¯¯¯¯¯ to a rational number in simplest form, we need to understand that the overline indicates that the digit 72 repeats indefinitely.
Let's call the number 0.72¯¯¯¯¯ as x. To find x, we can multiply both sides of the equation by 100 to get rid of the decimal point:
100x = 72.7272¯¯¯¯¯
Now, let's subtract x from 100x to eliminate the repeating part:
100x - x = 72.7272¯¯¯¯¯ - 0.7272¯¯¯
99x = 72
Divide both sides of the equation by 99 to solve for x:
x = 72/99
To simplify the fraction 72/99, we can find the greatest common divisor (GCD) of the numerator and the denominator, which is 9.
Dividing both numerator and denominator by 9:
x = (72/9)/(99/9)
x = 8/11
Therefore, 0.72¯¯¯¯¯ as a rational number in simplest form is 8/11.