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

Answer:

A. $7.9x10^6in$

B. $1004g$

C. $2834.64\frac{in}{min}$

D. $1.2x10^{-4}mm$

Explanation:

Hello,

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

A. We consider the given data:

$2.0x10^5m*\frac{39.37in}{1m} =7.9x10^6in$

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

$1.004kg*\frac{1000g}{1kg}=1004g$

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

$1.2\frac{m}{s}*\frac{39.37in}{1m} *\frac{60s}{1min}=2834.64\frac{in}{min}$

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

$120nm\frac{1x10^{-9}m}{1nm}*\frac{1mm}{1x10^{-3}m} =1.2x10^{-4}mm$

Best regards.

Answer 2

Answer:

A) 7.9 x 10⁶ inches

B) 1004 g

C) 2.8 x 10³ inches/ min

D) 1.2 x 10⁻⁴ mm

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