Show an example of a rational number that is between 10−−√ and 11−−√.(1 point)
Responses
165
Start Fraction 16 over 5 end fraction
3.1
3.1
3.4
3.4
103
Start Fraction 109 over 10 end fraction
what is it semplefide
The simplified form of the rational number 109/10 is 10.9.
To find a rational number between 10√ and 11√, we can use the following steps:
1. Convert the two numbers to decimal form:
- 10√ ≈ 3.162
- 11√ ≈ 3.317
2. Find the average of the two decimal values:
- Average = (3.162 + 3.317) / 2 = 6.479 / 2 = 3.2395
3. Round the average to an appropriate number of decimal places, depending on the desired precision:
- Rounded to one decimal place, the rational number is 3.2
- Rounded to two decimal places, the rational number is 3.24
- Rounded to three decimal places, the rational number is 3.239
Therefore, a rational number between 10√ and 11√ is approximately 3.2, 3.24, or 3.239.