Question

36. Dimensional Analysis: A useful way to convert units using multiplication & division *Always start with what you are given! Practice: A. Convert 2.0 x 105 m to inches, given that 1 meter = 39.37 inches. B. Convert 1.004 kg to grams, given that 1 pound (lb) = 453.59 grams (g) and 1 kilogram (kg) = 2.205 pounds (lb). C. Convert 1.2 m/s to inches/minute. D. Convert 120 nm to mm.

Answer 1

A.
`7.9x10^6in`

B.
`1004g`

C.
`2834.64(in)/(min)`

D.
`1.2x10^(-4)mm`

Step-by-step explanation:

Hello,

In this case, we use the proportional factors to obtain the required conversions as shown below:

A. We consider the given data:

`2.0x10^5m*(39.37in)/(1m) =7.9x10^6in`

B. It is not necessary to use the given data referred to pounds:

`1.004kg*(1000g)/(1kg)=1004g`

C. We consider that 1 meter es equivalent to 39.37 inches and 1 min to 60 seconds:

`1.2(m)/(s)*(39.37in)/(1m) *(60s)/(1min)=2834.64(in)/(min)`

D. We consider that 1nm is equivalent to 1x10⁻⁹m and 1mm to 1x10⁻³:

`120nm(1x10^(-9)m)/(1nm)*(1mm)/(1x10^(-3)m) =1.2x10^(-4)mm`

Best regards.

Answer 2

A) 7.9 x 10⁶ inches

B) 1004 g

C) 2.8 x 10³ inches/ min

D) 1.2 x 10⁻⁴ mm

Step-by-step explanation:

A) Since 39.37 inches = 1 m, you can convert meters to inches by multiplying by the conversion factor (39.37 inches / 1 m).

Notice that if 39.37 inches = 1 m then 39.37 inches / 1 m = 1. That means that when you multiply by a conversion factor, you are only changing units since it is the same as multiplying by 1 :

2.0 x 10⁵ m * (39.37 inches / 1 m) = 7.9 x 10⁶ inches

B) Conversion factors : (2.205 pounds / 1 kg) and (453.59 g / 1 pound), because 2.205 pounds = 1 kg and 1 pound = 453.59 g. Then:

1.004 kg * ( 2.205 pounds / 1 kg) * ( 453.59 g / 1 pound) = 1004 g

C) Conversion factor: (39.37 inches / 1 m) and (60 s / 1 min)

1.2 m/s * (39.37 inches / 1 m) * ( 60 s / 1 min) = 2.8 x 10³ inches/ min

D)Converison factor ( 1 mm / 1 x 10⁶ nm):

120 nm (1 mm / 1 x 10⁶ nm) = 1.2 x 10⁻⁴ mm