College

Select the equivalent unit:

[tex]10^{-6} L =[/tex]

A. 1 mL

B. [tex]1 \mu L[/tex]

C. 1 pL

D. 1 dL

Answer :

Sure! Let's solve the problem step-by-step.

The question asks us to find the equivalent unit for [tex]\( 10^{-6} \)[/tex] liters (L).

To solve this, we need to understand the relationship between liters and the smaller units.

1. Microliters ([tex]\(\mu\)[/tex]L):
- 1 liter (L) is equivalent to [tex]\(10^6\)[/tex] microliters ([tex]\(\mu\)[/tex]L).
- To find the equivalent of [tex]\(10^{-6}\)[/tex] liters, we convert it to microliters ([tex]\(\mu\)[/tex]L).
- Therefore, [tex]\(10^{-6}\)[/tex] liters is equal to 1 microliter ([tex]\(\mu\)[/tex]L), because:
[tex]\[
10^{-6} \text{ L} = \frac{10^{-6} \text{ L}}{10^{-6} \text{ L}/\mu\text{L}} = 1 \mu\text{L}
\][/tex]

2. Other units (to verify):
- Milliliters (mL): 1 liter (L) is [tex]\(10^3\)[/tex] milliliters (mL), so [tex]\(10^{-6} \text{ L} = 10^{-6} \times 10^3 \text{ mL} = 10^{-3} \text{ mL} = 0.001 \text{ mL}\)[/tex].
- Picoliters (pL): 1 liter (L) is [tex]\(10^{12}\)[/tex] picoliters (pL), so [tex]\(10^{-6} \text{ L} = 10^{-6} \times 10^{12} \text{ pL} = 10^6 \text{ pL}\)[/tex].
- Deciliters (dL): 1 liter (L) is [tex]\(10^1\)[/tex] deciliters (dL), so [tex]\(10^{-6} \text{ L} = 10^{-6} \times 10^1 \text{ dL} = 10^{-5} \text{ dL} = 0.00001 \text{ dL}\)[/tex].

After these conversions, it's clear that the equivalent unit for [tex]\(10^{-6}\)[/tex] liters is:

[tex]\[ 1 \mu\text{L} \][/tex]

So, the correct selection is:

[tex]\[
1 \mu\text{L}
\][/tex]