Find the range of allowable values based on a measure of 130 inches if the values can vary by 1.4%.
Understand the Problem
The question is asking to find the range of allowable values around a measure of 130 inches, where the values can vary by 1.4%. This requires calculating the allowable range based on the given percentage.
Answer
The allowable range of values is $[128.18, 131.82]$ inches.
Answer for screen readers
The range of allowable values is from $128.18$ to $131.82$ inches.
Steps to Solve
- Calculate the percentage value
Find 1.4% of 130 inches. To calculate this, use the formula: $$ \text{Percentage Value} = \text{Total Measure} \times \left(\frac{\text{Percentage}}{100}\right) $$
Substituting the values: $$ \text{Percentage Value} = 130 \times \left(\frac{1.4}{100}\right) = 130 \times 0.014 = 1.82 \text{ inches} $$
- Determine the minimum allowable value
Subtract the percentage value from the original measure. $$ \text{Minimum Value} = \text{Total Measure} - \text{Percentage Value} $$ Substituting the values: $$ \text{Minimum Value} = 130 - 1.82 = 128.18 \text{ inches} $$
- Determine the maximum allowable value
Add the percentage value to the original measure. $$ \text{Maximum Value} = \text{Total Measure} + \text{Percentage Value} $$ Substituting the values: $$ \text{Maximum Value} = 130 + 1.82 = 131.82 \text{ inches} $$
- State the allowable range
The allowable range of values is from the minimum to the maximum value calculated. $$ \text{Range} = [128.18, 131.82] \text{ inches} $$
The range of allowable values is from $128.18$ to $131.82$ inches.
More Information
This calculation shows how to determine the permissible range of measurements by applying a percentage. This approach is useful in various fields, including construction and manufacturing, where precision is crucial.
Tips
- Forgetting to convert the percentage from a whole number to a decimal form before calculation (e.g., using 1.4 instead of 0.014).
- Confusing the addition and subtraction steps, leading to incorrect minimum and maximum values.
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