Hey bot i need help with this answer
how many digits are in the repeating cycle of 17/27
To find the length of the repeating cycle of the fraction 17/27, we can perform long division:
0.629629...
First, we divide 17 by 27, which equals 0.6296. The remainder is 17.
Then, we multiply the remainder 17 by 10 (moving the decimal point one place to the right) to get 170.
We divide 170 by 27, which gives us 6.2963. The remainder is 14.
Repeating the process, we multiply the remainder 14 by 10, resulting in 140.
We divide 140 by 27, obtaining the quotient 5.1851 repeating. The remainder is 5.
Continuing, we multiply the remainder 5 by 10 to obtain 50.
We divide 50 by 27, resulting in the quotient 1.851 repeating. The remainder is 23.
We multiply the remainder 23 by 10, which gives us 230.
Finally, we divide 230 by 27, obtaining the quotient 8.5185 repeating. The remainder is 2.
At this point, we have reached a remainder of 2 again, indicating that the decimal representation of 17/27 will start repeating from this point onwards. Therefore, the repeating cycle has a length of 4 digits: 6296.
Hence, there are 4 digits in the repeating cycle of 17/27.
Which of the following rational numbers can be expressed as a repeating decimal: 7:8, 5/12, 17/25, or 31/40?
To determine which of the given rational numbers can be expressed as a repeating decimal, we can convert them into decimal form.
1. 7/8: When dividing 7 by 8, we get 0.875. It does not repeat, so 7/8 cannot be expressed as a repeating decimal.
2. 5/12: When dividing 5 by 12, we get 0.4166... with a repeating 6. Therefore, 5/12 can be expressed as a repeating decimal.
3. 17/25: When dividing 17 by 25, we get 0.68. It does not repeat, so 17/25 cannot be expressed as a repeating decimal.
4. 31/40: When dividing 31 by 40, we get 0.775. It does not repeat, so 31/40 cannot be expressed as a repeating decimal.
Therefore, out of the given options, only 5/12 can be expressed as a repeating decimal.
Express 7/13 as a repeating decimal. Mark the repeating digits with a bar.
To express 7/13 as a repeating decimal, we need to perform long division. Here is the division process:
0.538461538...
First, we divide 7 by 13, which gives the quotient 0.538 (rounded to three decimal places). The remainder is 7.
Next, we multiply the remainder 7 by 10 (moving the decimal point one place to the right) to get 70. We then divide 70 by 13, which gives the quotient 5. The remainder is 5.
Repeating the process, we multiply the remainder 5 by 10 to obtain 50. Dividing 50 by 13 results in the quotient 3. The remainder is 11.
Continuing, we multiply the remainder 11 by 10, which gives us 110. Dividing 110 by 13, we obtain the quotient 8. The remainder is 6.
Then, we multiply the remainder 6 by 10, which gives 60. Dividing 60 by 13, we get the quotient 4. The remainder is 8.
Finally, we multiply the remainder 8 by 10, resulting in 80. Dividing 80 by 13, we get the quotient 6. The remainder is 2.
Since the remainder 2 repeats after this point, we can mark it as a bar over the digit 2: 0.538461538...
Therefore, the repeating decimal representation of 7/13 is 0.538461538 with the digit 2 marked as repeating.
Express 7/13 as a repeating decimal. Mark the repeating digits with a bar.
Note: You will find the option to add a bar above text in the Geometry (<) keyboard
To express 7/13 as a repeating decimal, we need to perform long division. Here is the division process:
0.538461538...
First, we divide 7 by 13, which gives the quotient 0.538 (rounded to three decimal places). The remainder is 7.
Next, we multiply the remainder 7 by 10 (moving the decimal point one place to the right) to get 70. We then divide 70 by 13, which gives the quotient 5. The remainder is 5.
Repeating the process, we multiply the remainder 5 by 10 to obtain 50. Dividing 50 by 13 results in the quotient 3. The remainder is 11.
Continuing, we multiply the remainder 11 by 10, which gives us 110. Dividing 110 by 13, we obtain the quotient 8. The remainder is 6.
Then, we multiply the remainder 6 by 10, which gives 60. Dividing 60 by 13, we get the quotient 4. The remainder is 8.
Finally, we multiply the remainder 8 by 10, resulting in 80. Dividing 80 by 13, we get the quotient 6. The remainder is 2.
Since the remainder 2 repeats after this point, we can mark it as a bar above the digit 2: 0.5384615(3846)...
Therefore, the repeating decimal representation of 7/13 is 0.5384615 with the digits 3846 repeating, marked with a bar.
Convert 0.8 to a rational number
To convert 0.8 to a rational number, we need to express it as a fraction in the form of ๐/๐, where ๐ and ๐ are integers.
We can start by representing 0.8 as ๐ฅ/10, where ๐ฅ is an unknown integer. This is because 0.8 is equivalent to 8/10, and we express it as ๐ฅ/10 for clarity.
To get rid of the decimal point, we can multiply the numerator and denominator by 10:
(๐ฅ/10) * (10/10) = (๐ฅ * 10) / (10 * 10) = ๐ฅ/100
Therefore, we have ๐ฅ/100 = 0.8.
To solve for ๐ฅ, we can cross-multiply:
๐ฅ = 0.8 * 100
๐ฅ = 80
So, 0.8 can be expressed as the rational number 80/100.
However, we can simplify this fraction further by dividing both the numerator and denominator by their greatest common factor, which is 20:
80/100 = (80 รท 20) / (100 รท 20) = 4/5
Hence, 0.8 can be expressed as the rational number 4/5.