Find a rational number with one decimal place that is between √ 17 and √ 18
To find a rational number with one decimal place that is between √17 and √18, we need to find the square roots of these numbers.
√17 ≈ 4.123
√18 ≈ 4.243
We can see that 4.2 lies between these two values. Thus, a rational number with one decimal place that is between √17 and √18 is 4.2.
To find a rational number with one decimal place between √17 and √18, we can start by calculating the decimal approximations of √17 and √18.
Using a calculator or any mathematical software, we can find the following approximate values:
√17 ≈ 4.123105625617661
√18 ≈ 4.242640687119285
Next, we can look for a rational number between these two decimal approximations. A rational number can be written as a fraction of two integers.
To make it simple, we will only consider fractions with a denominator of 10. So, the fractions will have one decimal place.
To find a rational number between the two decimal approximations, we can try different fractions with a denominator of 10 and see which one falls between the two values. Let's start with fractions with a numerator of 4, as it is the integer part of both square roots.
Trying out different fractions, we find:
4.1 = 41/10
4.2 = 42/10
41/10 ≈ 4.1 is less than √17 ≈ 4.123105625617661.
42/10 ≈ 4.2 is greater than √17 ≈ 4.123105625617661 but less than √18 ≈ 4.242640687119285.
Therefore, the rational number with one decimal place that is between √17 and √18 is 4.2.