- Substitute \(z = 9\) into the left-hand side to get \(\frac{9}{100} = 0.09\).
- Compare the result \(0.09\) with the right-hand side \(0.009\).
- Since \(0.09
eq 0.009\), the value is not a solution.
- Final Answer: \(\boxed{\text{No}}\).
Explanation
- Understanding the Problem
The problem asks us to determine whether the value \(z = 9\) is a solution to the equation \(\frac{z}{100} = 0.009\). A value is a solution to an equation if substituting it for the variable makes the left-hand side (LHS) equal to the right-hand side (RHS). The given equation is \(\frac{z}{100} = 0.009\), and we need to check if \(z = 9\) satisfies this equality.
- Substituting and Evaluating the Equation
We substitute \(z = 9\) into the left-hand side of the equation:
\[\text{LHS} = \frac{z}{100} = \frac{9}{100}\]
Performing the division, we find that:
\[\frac{9}{100} = 0.09\]
The right-hand side (RHS) of the equation is given as \(0.009\).
- Comparing Results and Conclusion
Now, we compare the calculated value of the left-hand side to the given right-hand side:
\[0.09 \stackrel{?}{=} 0.009\]
Since \(0.09\) is not equal to \(0.009\), substituting \(z = 9\) does not result in a true statement. Therefore, \(z = 9\) is not a solution to the equation.
Examples
When working with decimal unit conversions, such as converting millimeters to meters, understanding place value is essential. For example, if you are told that 9 millimeters is equal to 0.009 meters, you can verify this by using the formula \(\frac{\text{length in mm}}{1000} = \text{length in m}\). Calculating \(\frac{9}{1000} = 0.009\) shows that 9 mm is indeed 0.009 m, whereas \(\frac{9}{100} = 0.09\) would incorrectly represent 9 cm as 0.09 m. Checking these conversions carefully ensures accuracy in measurements and calculations.