Question

intro q1 calculation review:
name:
period:

1. how many steps apart are nano and micro?
2. how many steps apart are the base units and milli?
3. how many steps apart are the micro and milli?

**knowing that our units are base unit, milli, micro, then nano (largest to smallest) and are all 3 steps apart from the next nearest units is an important thing to know for doing the conversions.

1. how many microliters are in 3.5 ml?
2. how many milliliters are in 3.5 μl?
3. how many micrograms are in 5600 nanograms?
4. how many millimeters are in 18 nanometers?
5. how many meters are in 1,500,000 micrometers?
6. how many nanograms are in 0.65 milligrams?
7. how many liters are in 8500 milliliters?
8. how many nanograms are in 0.0001 milligrams?

*answers for recipes should include the amount of original sample and the amount of water in microliters

1. what is the recipe to make 2000 μl of a 1:10 dilution?
2. what is the recipe to make 5 ml of a 1:20 dilution?

Explanation:

Step1: Recall metric - prefix relationships

The metric - prefixes and their relationships are as follows:
Base unit: no prefix, Milli ($10^{- 3}$), Micro ($10^{-6}$), Nano ($10^{-9}$).

1. The difference between nano ($10^{-9}$) and micro ($10^{-6}$) is 1 step since $10^{-6}\div10^{-9}=10^{3}$.
2. The difference between the base unit (power of 10 is 0) and milli ($10^{-3}$) is 1 step.
3. The difference between micro ($10^{-6}$) and milli ($10^{-3}$) is 1 step since $10^{-3}\div10^{-6}=10^{3}$.
4. To convert from mL to μL, use the conversion factor $1\ mL = 1000\ \mu L$. So, if we have $3.5\ mL$, then $3.5\ mL\times1000\ \frac{\mu L}{mL}=3500\ \mu L$.
5. To convert from μL to mL, use the conversion factor $1\ \mu L = 10^{-3}\ mL$. So, if we have $3.5\ \mu L$, then $3.5\ \mu L\times10^{-3}\ \frac{mL}{\mu L}=0.0035\ mL$.
6. To convert from ng to μg, use the conversion factor $1\ ng = 10^{-3}\ \mu g$. So, if we have $5600\ ng$, then $5600\ ng\times10^{-3}\ \frac{\mu g}{ng}=5.6\ \mu g$.
7. To convert from nm to mm, use the conversion factor $1\ nm = 10^{-6}\ mm$. So, if we have $18\ nm$, then $18\ nm\times10^{-6}\ \frac{mm}{nm}=1.8\times10^{-5}\ mm$.
8. To convert from μm to m, use the conversion factor $1\ \mu m = 10^{-6}\ m$. So, if we have $1500000\ \mu m$, then $1500000\ \mu m\times10^{-6}\ \frac{m}{\mu m}=1.5\ m$.
9. To convert from mg to ng, use the conversion factor $1\ mg = 10^{6}\ ng$. So, if we have $0.65\ mg$, then $0.65\ mg\times10^{6}\ \frac{ng}{mg}=650000\ ng$.
10. To convert from mL to L, use the conversion factor $1\ mL = 10^{-3}\ L$. So, if we have $8500\ mL$, then $8500\ mL\times10^{-3}\ \frac{L}{mL}=8.5\ L$.
11. To convert from mg to ng, use the conversion factor $1\ mg = 10^{6}\ ng$. So, if we have $0.0001\ mg$, then $0.0001\ mg\times10^{6}\ \frac{ng}{mg}=100\ ng$.
12. For a $1:10$ dilution, if the final volume $V_f = 2000\ \mu L$, let the volume of the sample be $V_s$ and the volume of water be $V_w$. We know that the dilution ratio $D=\frac{V_f}{V_s}=10$. So, $V_s=\frac{V_f}{10}=\frac{2000\ \mu L}{10}=200\ \mu L$ and $V_w=V_f - V_s=2000\ \mu L-200\ \mu L = 1800\ \mu L$.
13. For a $1:20$ dilution, if the final volume $V_f = 5\ mL=5000\ \mu L$. Let the volume of the sample be $V_s$ and the volume of water be $V_w$. We know that the dilution ratio $D = 20$. So, $V_s=\frac{V_f}{20}=\frac{5000\ \mu L}{20}=250\ \mu L$ and $V_w=V_f - V_s=5000\ \mu L - 250\ \mu L=4750\ \mu L$.

Answer:

1. 1
2. 1
3. 1
4. 3500 μL
5. 0.0035 mL
6. 5.6 μg
7. $1.8\times10^{-5}$ mm
8. 1.5 m
9. 650000 ng
10. 8.5 L
11. 100 ng
12. Sample: 200 μL, Water: 1800 μL
13. Sample: 250 μL, Water: 4750 μL