To express 811 as a repeating decimal, we divide 811 by 9 (because the repeating cycle will be in the tenths place, which is 10^(-1), and 1/9 = 0.1111...), which gives:
811 ÷ 9 = 90.1111...
Since there is a repeating cycle of 1s after the decimal point, we can represent it with a bar over the repeating digits. Therefore, the decimal form of 811 is 90.1¯¯¯¯¯¯¯¯¯¯+.
Express 811 as a repeating decimal. Mark the cycle of repeating digits with a bar
19 answers
Convert 0.72¯¯¯¯¯ to a rational number in simplest form.
Let's call the repeating decimal 0.72¯¯¯¯¯ as x.
To convert this repeating decimal to a rational number, we can subtract it from a number formed by moving the repeating part to the left of the decimal point.
10x - x = 7.2¯¯¯¯¯ - 0.72¯¯¯¯¯
=> 9x = 7.2
Now, we isolate x by dividing both sides by 9:
x = 7.2 / 9
x = 0.8
Therefore, the rational number in simplest form that corresponds to 0.72¯¯¯¯¯ is 0.8.
To convert this repeating decimal to a rational number, we can subtract it from a number formed by moving the repeating part to the left of the decimal point.
10x - x = 7.2¯¯¯¯¯ - 0.72¯¯¯¯¯
=> 9x = 7.2
Now, we isolate x by dividing both sides by 9:
x = 7.2 / 9
x = 0.8
Therefore, the rational number in simplest form that corresponds to 0.72¯¯¯¯¯ is 0.8.
Which of the following is a rational number between 5 and 514?
To find a rational number between 5 and 514, we can start by taking the average of the two numbers:
(5 + 514) / 2 = 519 / 2 = 259.5
Since 259.5 is a decimal, we need to convert it into a rational number. We notice that it can be represented as a fraction where the numerator and denominator are both divisible by 2:
259.5 = 2595 / 10
Simplifying the fraction by dividing both the numerator and denominator by 5:
2595 / 10 = 519 / 2 = 259.5
So, the rational number between 5 and 514 is 259.5.
(5 + 514) / 2 = 519 / 2 = 259.5
Since 259.5 is a decimal, we need to convert it into a rational number. We notice that it can be represented as a fraction where the numerator and denominator are both divisible by 2:
259.5 = 2595 / 10
Simplifying the fraction by dividing both the numerator and denominator by 5:
2595 / 10 = 519 / 2 = 259.5
So, the rational number between 5 and 514 is 259.5.
Which of the following is a rational number between 5 and 5 1/4
To find a rational number between 5 and 5 1/4, we need to convert 5 1/4 into a decimal.
5 1/4 = 5 + 1/4 = 20/4 + 1/4 = 21/4 = 5.25
Now we can find a rational number between 5 and 5.25 by taking their average:
(5 + 5.25)/2 = 10.25/2 = 5.125
Therefore, the rational number between 5 and 5 1/4 is 5.125.
5 1/4 = 5 + 1/4 = 20/4 + 1/4 = 21/4 = 5.25
Now we can find a rational number between 5 and 5.25 by taking their average:
(5 + 5.25)/2 = 10.25/2 = 5.125
Therefore, the rational number between 5 and 5 1/4 is 5.125.
wrong
I apologize for the mistake. Let's correct it.
To find a rational number between 5 and 5 1/4, we can convert 5 1/4 into an improper fraction:
5 1/4 = (4 * 5 + 1)/4 = 21/4
Now, to find a rational number between 5 and 21/4, we can take the average:
(5 + 21/4)/2 = (20/4 + 21/4)/2 = 41/8
Therefore, a rational number between 5 and 5 1/4 is 41/8.
To find a rational number between 5 and 5 1/4, we can convert 5 1/4 into an improper fraction:
5 1/4 = (4 * 5 + 1)/4 = 21/4
Now, to find a rational number between 5 and 21/4, we can take the average:
(5 + 21/4)/2 = (20/4 + 21/4)/2 = 41/8
Therefore, a rational number between 5 and 5 1/4 is 41/8.
ur wrong again
Apologies for the mistake. Let's correct it.
To find a rational number between 5 and 5 1/4, we can convert 5 1/4 to an improper fraction:
5 1/4 = (4 * 5 + 1) / 4 = 21 / 4
Now, to find a rational number between 5 and 5 1/4, we can take the 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.
To find a rational number between 5 and 5 1/4, we can convert 5 1/4 to an improper fraction:
5 1/4 = (4 * 5 + 1) / 4 = 21 / 4
Now, to find a rational number between 5 and 5 1/4, we can take the 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.
ur dumber than me
I apologize if my previous responses were not what you were expecting. If you have any other questions or need further assistance, please let me know, and I will be glad to help you.
What is a rational number with a denominator of 7 that is between √7 and √8 write your answer as an improper fraction.
To find a rational number between √7 and √8 with a denominator of 7, we need to calculate the value of √7 and √8 and then find a fraction with a denominator of 7 that falls in between them.
√7 ≈ 2.645751311
√8 ≈ 2.828427125
Now, we can find the fraction with a denominator of 7 that lies between these two values:
2.645751311 < 2.646 < 2.828427125
By observation, we can select 2.646 as the decimal representation for the rational number between √7 and √8. To express it as an improper fraction, we multiply both the numerator and denominator by 7:
2.646 * 7 = 18.522
Therefore, the rational number between √7 and √8, with a denominator of 7, is 18/7 or 18.522 as an improper fraction.
√7 ≈ 2.645751311
√8 ≈ 2.828427125
Now, we can find the fraction with a denominator of 7 that lies between these two values:
2.645751311 < 2.646 < 2.828427125
By observation, we can select 2.646 as the decimal representation for the rational number between √7 and √8. To express it as an improper fraction, we multiply both the numerator and denominator by 7:
2.646 * 7 = 18.522
Therefore, the rational number between √7 and √8, with a denominator of 7, is 18/7 or 18.522 as an improper fraction.
so this is the answer?
I apologize for the incorrect response in my previous message. Let's correct it.
To find a rational number between √7 and √8 with a denominator of 7, we need to determine the fractions equivalent to these radicals.
√7 can be written as 7/√7, and √8 can be written as 8/√8.
To rationalize the denominators, we multiply the numerators and denominators of each fraction by the conjugate of the denominator:
√7 = (7/√7) * (√7/√7) = 7√7 / (√7)^2 = 7√7/7 = √7
√8 = (8/√8) * (√8/√8) = 8√8 / (√8)^2 = 8√8/8 = √8
We now have √7 = 7√7/7 and √8 = 8√8/8.
To find a rational number between √7 and √8 with a denominator of 7, we can choose the average:
(7√7/7 + 8√8/8) / 2 = (7√7 + 8√8) / 14
Therefore, the rational number between √7 and √8 with a denominator of 7 is (7√7 + 8√8) / 14.
To find a rational number between √7 and √8 with a denominator of 7, we need to determine the fractions equivalent to these radicals.
√7 can be written as 7/√7, and √8 can be written as 8/√8.
To rationalize the denominators, we multiply the numerators and denominators of each fraction by the conjugate of the denominator:
√7 = (7/√7) * (√7/√7) = 7√7 / (√7)^2 = 7√7/7 = √7
√8 = (8/√8) * (√8/√8) = 8√8 / (√8)^2 = 8√8/8 = √8
We now have √7 = 7√7/7 and √8 = 8√8/8.
To find a rational number between √7 and √8 with a denominator of 7, we can choose the average:
(7√7/7 + 8√8/8) / 2 = (7√7 + 8√8) / 14
Therefore, the rational number between √7 and √8 with a denominator of 7 is (7√7 + 8√8) / 14.
Express 7/11
as a repeating decimal. Mark the cycle of repeating digits with a bar.
Note: You will find the option to add a bar above text in the Geometry (∠
) keyboard.
(1 point)
as a repeating decimal. Mark the cycle of repeating digits with a bar.
Note: You will find the option to add a bar above text in the Geometry (∠
) keyboard.
(1 point)
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.
12 answers