Q72E - Chemistry (OpenStax)

Question

Complete the following conversions between SI units.

(a) 612 g = ________ mg

(b) 8.160 m = ________ cm

(c) 3779 μg = ________ g

(d) 781 mL = ________ L

(e) 4.18 kg = ________ g

(f) 27.8 m = ________ km

(g) 0.13 mL = ________ L

(h) 1738 km = ________ m

(i) 1.9 Gg = ________ g

Step-by-Step Solution

Answer

(a) 612 g = 6.12  10⁵  mg

(b) 8.160 m = 8.160   10² cm

(c) 3779 μg = 3.779   10^-3 g

(d) 781 mL = 0.781 L

(e) 4.18 kg = 4.18  10³ g

(f) 27.8 m = 2.78  10^-2 km

(g) 0.13 mL = 1.3   10^-4 L

(h) 1738 km = 1.738  10⁶ m

(i) 1.9 Gg = 1.9   10⁹ g

Step 1: Defining the SI units

The SI units are the international unit system and most widely used units globally. These units are divided into two types known as base units and derived units.

Base units – There are only seven base units. These units are used extensively to create derived units.

Derived units – These units are derived from the base units. The derived units are always indicated in the mathematical operation of base units such as multiplication and division.

 

Step 2: Converting the quantities into required units

a) 612 g

\(612\,\,g\,\, = \,\,612\, \times \,\frac{{{{10}^3}}}{{{{10}^3}}}\,g\,\, = \,\,6.12\,\, \times \,{10^2} \times \,{10^3}\,\,mg\,\, = \,\,6.12\, \times \,{10^5}\,\,kg\)

b) 8.160 m

\(8.160\,\,m\,\, = \,\,8.160\,\, \times \,\,\frac{{{{10}^2}}}{{{{10}^2}}}\,m\,\, = \,\,8.160\,\, \times \,\,{10^2}cm\,\,\)

c) 3779 μg

\(3779\,\mu g\,\, = \,\,3779\,\, \times \,\,{10^{ - 6}}\,g\,\, = \,\,3.779\, \times \,{10^3}\, \times \,{10^{ - 6}}\,g\,\, = \,\,3.779\,\, \times \,\,{10^{ - 3}}\,\,g\)

d) 781 mL

\(781\,\,mL\,\, = \,\,781\,\, \times \,{10^{ - 3}}\,L\,\, = \,\,0.781\,L\,\,\)

e) 4.18 kg

\(4.18\,\,kg\,\, = \,\,4.18\,\, \times \,\,{10^3}\,\,g\,\,\)

f) 27.8 m

\(27.8\,\,m\,\, = \,\,27.8\, \times \,{10^{ - 3}}\, \times \,{10^3}\,m\,\, = \,\,2.78\,\, \times \,\,{10^{ - 2}}\,\,km\,\)

g) 0.13 mL

\(0.13\,mL\,\, = \,\,0.13\,\, \times \,\,{10^{ - 3}}\,L\,\, = \,1.3\,\, \times \,\,{10^{ - 4}}\,\,L\)

h) 1738 km

\(1738\,\,km\,\, = \,\,1738\,\, \times \,\,{10^3}\,m\,\, = \,\,1.738\,\, \times \,\,{10^6}\,m\)

i) 1.9 Gg

\(1.9\,\,Gg\,\, = \,\,1.9\,\, \times \,\,{10^9}\,g\)