Question

I just need someone to check my work.. emphasis on checking significant figures and if there is a better conversion method to use and show please.

1. How many centimeters are there in 403.9 inches? Round your answer to the correct number of significant figures. (1 in = 2.54cm)

(2.54 cm) * (403.9 in) = 1030 cm

2. Suppose that an artillery piece has a range R=1.302×10⁴ yards. Find its range in miles. Round your answer to the correct number of significant figures. (1 yd = 0.000568182 mi)

(1.302X10^4 yd) * (0.00056818 mi) = 7.398 mi

3. What is the weight measurement, 827 lb, in kilonewtons? Express your answer in kilonewtons. Round your answer to the correct number of significant figures. (1 lb = 0.00444822 kN)

(827 lb) * (0.004448 kN) = 3.68 kN

4. What is the speed measurement, 89.0 mi/h, in meters per second? Express your answer in meters per second. Round your answer to the correct number of significant figures. (1 m/h = 0.44704 m/s)

(89 mi/h) * (0.447 m/s) = 4.0*10^1 m/s

5. What is the area measurement, 753*(10⁶) ft², in SI units? Express your answer in kilometers squared. Round your answer to the correct number of significant figures. (1 ft² = 9.29*10^-8 km²)

753 * 10⁶ ft² = (753*10⁶ ft²) * (9.29*10^-8 km²) = 70.0 km²

6. Convert 450 lb⋅ft to N⋅m. Express your answer using three significant figures. (1 lb⋅ft = 1.35582 N⋅m)

(450 lb⋅ft) * (1.3558 N⋅m) = 610 N⋅m

7. Convert 600 lb/ft³ to kN/m³. Express your answer using three significant figures. (1 Ib/ft³ = 0.1570865731 kN/m³)

(600 Ib/ft³) * (0.1571 kN/m³) = 94.3 kN/m³

8. Convert 5 ft/h to mm/s. Express your answer using three significant figures. (1 ft/h = 0.0846667 mm/s)

(5 ft/h) * (0.0846667) = 0.42 mm/s

9. What is the weight in newtons of an object that has a mass of 9 kg? Express your answer using three significant figures. (1 kg = 9.81 N)

(9 kg) * (9.81 N) = 88.3 N

10. What is the weight in newtons of an object that has a mass of 860 Mg? Express your answer using three significant figures. (1 Mg = 9806.65 N)

(860 Mg) * (9806.65 N) = 84.0*10^5 N

Answer 1

1 inch = 2.54 cm

So, 403.9 inch = 403.9 x 2.54 = 1025.906 cm = 1025.91 cm

As 1 yd = 0.000568182 mi

So, 1.302 x 10 ⁴ yard = 1.302 x 10⁴ x 0.000568182 = 7.3977296 mi = 7.398 mi

As  1 lb = 0.00444822 kN

So, 827 lb = 827 x 0.00444822 = 3.67867794 kN = 3.68 kN = 3.7 kN

As 1 mi/h = 0.44704 m/s

So, 89.0 mi/h = 89.0 x 0.44704 = 39.78656 m/s = 39.79 m/s

As 1 ft² = 9.29 x 10^-8 km²

^So,  753 x 10⁶ ft² = 753 x 10⁶ x 9.29 x 10^-8 = 69.957 km² = 70.0 km²

As 1 lb⋅ft = 1.35582 N⋅m

So, 450 lb .ft = 450 x 1.35582 = 610.119 N.m ~ 610 N.m

As 1 Ib/ft³ = 0.1570865731 kN/m³

So, 600 lb/ft³ = 600 x 0.1570865731 = 94.25194386 kN/m³ = 94.3 kN/m³

As 1 ft/h = 0.0846667 mm/s

So, 5 ft/h = 5 x 0.0846667 = 0.4233335 mm/s = 0.42 mm/s

As 1 kg = 9.81 N

So, 9 kg = 9 x 9.81 = 88.29 N = 88.3 N

As 1 Mg = 9806.65 N

So, 860 Mg = 860 x 9806.65 = 8433719 N = 84.3 x 10⁵ N

You can compare your answers with these calculated values.

NOTE : We approximate values as per our need and our situation . viz you can write 39.79 as 39.8 or 40 if this will not effect our final result too much .

For any doubt please comment and please give an up vote. Thank you.