Certainly! Let's solve the expression [tex]\(\frac{5}{3} - \pi + 0.97 - \sqrt{7}\)[/tex] step-by-step.
1. Convert the fraction to a decimal:
[tex]\[
\frac{5}{3} = 1.6666666666666667
\][/tex]
2. Locate the value of [tex]\(\pi\)[/tex]:
The value of [tex]\(\pi\)[/tex] is approximately:
[tex]\[
\pi = 3.141592653589793
\][/tex]
3. Take the given decimal value:
The given decimal value is:
[tex]\[
0.97
\][/tex]
4. Calculate the square root of 7:
The square root of 7 is approximately:
[tex]\[
\sqrt{7} = 2.6457513110645907
\][/tex]
5. Substitute these values into the expression and simplify:
[tex]\[
1.6666666666666667 - 3.141592653589793 + 0.97 - 2.6457513110645907
\][/tex]
6. Perform the arithmetic step-by-step:
First, combine [tex]\(\frac{5}{3}\)[/tex] and [tex]\(\pi\)[/tex]:
[tex]\[
1.6666666666666667 - 3.141592653589793 = -1.4749259869231263
\][/tex]
Next, include the 0.97:
[tex]\[
-1.4749259869231263 + 0.97 = -0.5049259869231263
\][/tex]
Finally, subtract [tex]\(\sqrt{7}\)[/tex]:
[tex]\[
-0.5049259869231263 - 2.6457513110645907 = -3.150677297987717
\][/tex]
7. Conclusion:
The result of the expression [tex]\(\frac{5}{3} - \pi + 0.97 - \sqrt{7}\)[/tex] is:
[tex]\[
-3.150677297987717
\][/tex]
So, the step-by-step simplified value of the given expression is [tex]\(-3.150677297987717\)[/tex].
