Question

chem introduction 4 assignment

1. write in the number corresponding to the unit prefix.

a. 1 kg = 1000 g (or 1x10³ g)
b. 1 mm = m
c. 1 μg = g
d. 1 gb = b (b mean byte a unit of computer memory)
e. 1 ml = l

1. write two conversion factors from each equality above.

a. \\(\frac{1kg}{1000g}\\) \\(\frac{1000g}{1kg}\\)
b.
c.
d.
e.

1. use the conversion factors you wrote to convert:

a. convert 1.41 kg to g.
b. convert 5.74 l to ml.
c. convert 120 m to mm.
d. convert 123 mm to m.
e. convert 3.45x10⁻³ g to μg.
f. convert 5.85x10⁴ μg to kg.

Explanation:

Part 1

Step1: Identify metric prefix values

Use standard SI prefix definitions.

Step2: Assign values to each equality

Substitute prefix equivalents.

Step1: Flip each equality to get factors

For $A=B$, factors are $\frac{A}{B}$ and $\frac{B}{A}$.

Step1: Select appropriate conversion factor

Choose factor to cancel unwanted units.

Step2: Multiply value by conversion factor

Cancel units and compute result.
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a. Convert $1.41\ \text{kg}$ to $\text{g}$

Step1: Use kg to g conversion factor

$\frac{1000\ \text{g}}{1\ \text{kg}}$

Step2: Multiply value by factor

$1.41\ \text{kg} \times \frac{1000\ \text{g}}{1\ \text{kg}} = 1410\ \text{g}$

b. Convert $5.74\ \text{L}$ to $\text{mL}$

Step1: Use L to mL conversion factor

$\frac{1000\ \text{mL}}{1\ \text{L}}$

Step2: Multiply value by factor

$5.74\ \text{L} \times \frac{1000\ \text{mL}}{1\ \text{L}} = 5740\ \text{mL}$

c. Convert $120\ \text{m}$ to $\text{mm}$

Step1: Use m to mm conversion factor

$\frac{1000\ \text{mm}}{1\ \text{m}}$

Step2: Multiply value by factor

$120\ \text{m} \times \frac{1000\ \text{mm}}{1\ \text{m}} = 120000\ \text{mm}$

d. Convert $123\ \text{mm}$ to $\text{m}$

Step1: Use mm to m conversion factor

$\frac{1\times10^{-3}\ \text{m}}{1\ \text{mm}}$

Step2: Multiply value by factor

$123\ \text{mm} \times \frac{1\times10^{-3}\ \text{m}}{1\ \text{mm}} = 0.123\ \text{m}$

e. Convert $3.45\times10^{-3}\ \text{g}$ to $\mu\text{g}$

Step1: Use g to $\mu\text{g}$ conversion factor

$\frac{1\times10^{6}\ \mu\text{g}}{1\ \text{g}}$

Step2: Multiply value by factor

$3.45\times10^{-3}\ \text{g} \times \frac{1\times10^{6}\ \mu\text{g}}{1\ \text{g}} = 3450\ \mu\text{g}$

f. Convert $5.85\times10^4\ \mu\text{g}$ to $\text{kg}$

Step1: Use $\mu\text{g}$ to g, then g to kg

$\frac{1\times10^{-6}\ \text{g}}{1\ \mu\text{g}}$ and $\frac{1\ \text{kg}}{1000\ \text{g}}$

Step2: Multiply by both factors

$5.85\times10^4\ \mu\text{g} \times \frac{1\times10^{-6}\ \text{g}}{1\ \mu\text{g}} \times \frac{1\ \text{kg}}{1000\ \text{g}} = 5.85\times10^{-5}\ \text{kg}$

Answer:

a. $1\ \text{kg} = 1000\ \text{g}$ (or $1\times10^3\ \text{g}$)
b. $1\ \text{mm} = 0.001\ \text{m}$ (or $1\times10^{-3}\ \text{m}$)
c. $1\ \mu\text{g} = 0.000001\ \text{g}$ (or $1\times10^{-6}\ \text{g}$)
d. $1\ \text{GB} = 1000000000\ \text{B}$ (or $1\times10^9\ \text{B}$)
e. $1\ \text{mL} = 0.001\ \text{L}$ (or $1\times10^{-3}\ \text{L}$)

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Part 2