Convert 5 meters into a measurement in feet and inches, rounded to the nearest 16th of an inch. If the answer were 2ft,31/16in, type in: 2′ 3-1/16″ (notice the unit marks, one space between ft and inches, and one dash to separate whole inches from the fraction part-simplify if possible. If there are no feet or inches in a. conversion, do not type anything for that unit. Recall 1in=2.54 cm ). 5m=A
The Correct Answer and Explanation is:
To convert 5 meters into feet and inches, we first need to understand the relationship between meters, centimeters, inches, and feet:
- 1 inch = 2.54 cm
- 1 foot = 12 inches
- 1 meter = 100 cm
Step 1: Convert 5 meters to centimeters
5 m×100=500 cm5 \, \text{m} \times 100 = 500 \, \text{cm}
Step 2: Convert centimeters to inches
500 cm÷2.54≈196.8504 inches500 \, \text{cm} \div 2.54 \approx 196.8504 \, \text{inches}
Step 3: Convert total inches to feet and inches
196.8504÷12≈16 feet with a remainder196.8504 \div 12 \approx 16 \, \text{feet} \text{ with a remainder}
Let’s calculate the exact remainder in inches: 16×12=192 inches16 \times 12 = 192 \, \text{inches} 196.8504−192=4.8504 inches196.8504 – 192 = 4.8504 \, \text{inches}
So, we now have:
16 feet and 4.8504 inches
Step 4: Convert decimal inches to the nearest 16th of an inch
0.8504×16≈13.6064⇒round to 140.8504 \times 16 \approx 13.6064 \Rightarrow \text{round to } 14
So the inches part is: 4+1416=4+784 + \frac{14}{16} = 4 + \frac{7}{8}
Final Answer:
16′4−7/8″\boxed{16′ 4-7/8″}
Explanation
Converting metric units to imperial units requires careful step-by-step conversion, especially when expressing the result in both feet and inches. This is particularly important in fields such as engineering, construction, and design, where precise measurements are crucial.
We began by recognizing that 1 meter equals 100 centimeters and that 1 inch equals 2.54 centimeters. So, 5 meters converts to 500 centimeters. Dividing 500 by 2.54 gives approximately 196.8504 inches. Since 1 foot equals 12 inches, we divided this total inch value by 12 to separate out the number of whole feet. That gives us 16 full feet, with the remaining inches calculated by subtracting the feet portion (192 inches) from the total.
This remainder, 4.8504 inches, includes a decimal which must be converted into a fraction of an inch for practical use, particularly when tools and tape measures are marked in sixteenths. To convert the decimal portion to the nearest 1/16 inch, we multiplied the decimal by 16, getting approximately 13.6, which we then rounded to the nearest whole number — 14. Thus, the fraction part becomes 14/16, which simplifies to 7/8.
The final answer of 16′ 4-7/8″ represents a very accurate and practical way to express 5 meters in imperial units.
