Convert the unit of length. Use $1 m=100 cm$ and $1 m \approx 3.28 ft$. Round the answer to one decimal place if necessary.
$1.1 ft \approx \frac{1.1 ft}{\square} \cdot \frac{\square}{\square} \cdot \frac{\square}{\square} \approx 33.5 cm$
Answer (1)
We are given 1.1 f t and want to convert it to c m using 1 m = 100 c m and 1 m ≈ 3.28 f t .
Convert feet to meters: 1.1 f t ⋅ 3.28 f t 1 m .
Convert meters to centimeters: 1.1 f t ⋅ 3.28 f t 1 m ⋅ 1 m 100 c m .
Calculate the final value and round to one decimal place: 1.1 f t ≈ 1 1.1 f t ⋅ 3.28 f t 1 m ⋅ 1 m 100 c m ≈ 33.5 c m . The answer is 33.5 c m .
Explanation
Understanding the Problem We are given the length 1.1 f t and we want to convert it to c m . We are also given the conversions 1 m = 100 c m and 1 m ≈ 3.28 f t . Our goal is to fill in the blanks in the expression 1.1 f t ≈ □ 1.1 f t ⋅ □ □ ⋅ □ □ ≈ 33.5 c m .
Converting Feet to Meters First, we want to convert feet to meters. We know that 1 m ≈ 3.28 f t . Therefore, to convert 1.1 f t to meters, we multiply by the conversion factor 3.28 f t 1 m . This gives us 1.1 f t ⋅ 3.28 f t 1 m .
Converting Meters to Centimeters Next, we want to convert meters to centimeters. We know that 1 m = 100 c m . Therefore, to convert meters to centimeters, we multiply by the conversion factor 1 m 100 c m . This gives us 1.1 f t ⋅ 3.28 f t 1 m ⋅ 1 m 100 c m .
Calculating the Final Value Combining these conversions, we have 1.1 f t ≈ 1 1.1 f t ⋅ 3.28 f t 1 m ⋅ 1 m 100 c m . Calculating this value, we get 1 ⋅ 3.28 ⋅ 1 1.1 ⋅ 1 ⋅ 100 = 3.28 110 ≈ 33.536585... . Rounding to one decimal place, we get 33.5 c m .
Filling in the Blanks Therefore, the blanks should be filled with 1, 1 m, 3.28 ft, 100 cm, 1 m. The final expression is 1.1 f t ≈ 1 1.1 f t ⋅ 3.28 f t 1 m ⋅ 1 m 100 c m ≈ 33.5 c m .
Examples
Imagine you're building a model airplane and the instructions are in metric units (centimeters), but your ruler is in feet. Converting feet to centimeters, as we did here, helps you accurately measure the parts needed for your model. This type of unit conversion is also essential in many other fields, such as construction, engineering, and even cooking, where recipes might use different units of measurement. Understanding how to convert between units allows for accurate and consistent results in various practical applications.
