Find the range of allowable values based on a measure of 130 inches if the values can vary by 1.4%.

Steps to Solve

1. Calculate the percentage of the measurement To find the amount by which the measurement can vary, we need to calculate 1.4% of 130 inches.

First, convert the percentage to a decimal: $$ 1.4% = \frac{1.4}{100} = 0.014 $$

Then, multiply this decimal by the measurement: $$ \text{Variation} = 130 \times 0.014 $$

2. Determine the variation amount Now, we compute the variation: $$ \text{Variation} = 130 \times 0.014 = 1.82 \text{ inches} $$

3. Calculate the lower and upper limits Next, we find the lower and upper limits by subtracting and adding the variation from the original measurement, respectively.

• Lower limit: $$ \text{Lower limit} = 130 - 1.82 = 128.18 \text{ inches} $$

• Upper limit: $$ \text{Upper limit} = 130 + 1.82 = 131.82 \text{ inches} $$

4. Summarize the range of allowable values The range of allowable values based on the measurement of 130 inches and a variation of 1.4% is: $$ [128.18, 131.82] \text{ inches} $$