Question

show work please

2. Convert the following units. Make sure that your answer has the proper number of significant figures a. 4.8 g/cma to kg/m b. 941 μm to km. Use scientific notation for your answer. (μ is the prefix "micro" and 1 μm 1 x 10-6 m) c. The speed of light is 2.9989 x 108 m/s. Convert to miles/hour. Use scientific notation in your answer. d. 782 kg to ug. Use scientific notion for your answer.

Answer 1

2.

(a) 941 g/cm³ to kg/m³

We know that , 1kg = 1000 g , so 1 g = (1/1000) kg

And 1 m = 100 cm , so cm = (1/100) m

Now,

1 g/cm³ =[ (1/1000)÷(1/100)³] kg/m³ = 1000 kg/m³

Hence 4.8 g/cm³ = 4.8×1000 kg/m³ = 4800 kg/m³

Answer : 4800 kg/m³

(b) 941 $\mu$m to km

We know that , 1 $\mu$m = 1×10^-6 m

Or we can say , 1 m = 10⁶$\mu$m

And 1 km = 1×10³ m

Or we can say , 1 m = 10^-3 km

So , 1 $\mu$m =( 1×10^-6×10^-3)km = 1×10^-9 km

Hence , 941 $\mu$m = 941×10^-9 km = 9.41×10^-7 km

Answer : 9.41 ×10^-7 km

(c) 2.9989×10⁸ m/s to miles/hour

We know that , 1 m = 6.2137 ×10^-4 miles

And 1 s = (1/3600) hour

So 1 m/s = (6.2137×10^-4)÷(1/3600) miles/hour

1 m/s = 2.2369 miles/hour

Hence 2.9989×10⁸ m/s = (2.9989×10⁸×2.2369) miles per hour

= 6.7082 × 10⁸ miles/hour

Answer : 6.7082 ×10⁸ miles/hour

(d) 782 kg to $\mu$g

We know that, 1 $\mu$g = 1×10^-6 g

And 1 kg = 1×10³ g

Or we can say , 1 g = 1×10^-3 kg

So 1 kg = 1×10⁹$\mu$g

Hence 782 kg = 782×10⁹$\mu$g = 7.82×10¹¹$\mu$g

Answer: 7.82×10¹¹$\mu$g