Express 811 as a repeating decimal. Mark the cycle of repeating digits with a bar
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¯¯¯¯¯¯¯¯¯¯+.
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.
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.
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.
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.