Perform the following conversions. (a) 32.0 dm / s to km / hr (d) 137.5 mL to L (b) 8.2 mg / mL

step 1 We're going to perform the following conversions. So for A we start with 32 decimeters per secon

Perform the following conversions. (a) 32.0 dm / s to km /...

Perform the following conversions. (a) $32.0 \mathrm{dm} / \mathrm{s}$ to $\mathrm{km} / \mathrm{hr}$ (d) $137.5 \mathrm{~mL}$ to $\mathrm{L}$ (b) $8.2 \mathrm{mg} / \mathrm{mL}$ to $\mu \mathrm{g} / \mathrm{L}$ (e) $0.025 \mathrm{~L}$ to $\mathrm{mL}$ (c) $75.3 \mathrm{mg}$ to $\mathrm{kg}$ (f) $342 \mathrm{pm}^{2}$ to $\mathrm{dm}^{2}$

Perform the following conversions.
(a) $32.0 \mathrm{dm} / \mathrm{s}$ to $\mathrm{km} / \mathrm{hr}$
(d) $137.5 \mathrm{~mL}$ to $\mathrm{L}$
(b) $8.2 \mathrm{mg} / \mathrm{mL}$ to $\mu \mathrm{g} / \mathrm{L}$
(e) $0.025 \mathrm{~L}$ to $\mathrm{mL}$
(c) $75.3 \mathrm{mg}$ to $\mathrm{kg}$
(f) $342 \mathrm{pm}^{2}$ to $\mathrm{dm}^{2}$

Key Concepts

Conversion Factors

Conversion factors are the numerical relationships between different units of measurement. They are used in multiplication to ensure that desired units appear while the original units cancel out. This concept is fundamental in solving problems that require the transformation of quantities, such as converting mg/mL to µg/L or L to mL.

Handling Units with Exponents

When converting measurements involving squared or cubed units, such as area or volume, special care must be taken to square or cube the conversion factor as well. This ensures that the conversion respects the dimensional power. For example, converting pm² to dm² requires applying the conversion factor to each dimension, reflecting the squared nature of the area.

Dimensional Analysis

Dimensional analysis is a systematic method used to convert from one set of units to another. This technique involves multiplying the original measurement by conversion factors that cancel out the original units and introduce the desired units, ensuring that the calculation remains consistent and accurate.

Metric System and Prefixes

The metric system relies on prefixes that represent powers of ten, which makes it especially convenient for unit conversions. Understanding metric prefixes such as kilo-, deci-, milli-, micro-, and pico- is crucial because they allow for straightforward scaling up or down when converting between units like dm/s to km/hr, mL to L, or mg to kg.

Transcript

00:01 We're going to perform the following conversions.

00:03 So for a we start with 32 decimeters per second and we're going to change those to kilometers per hour.

00:10 So i'm going to start by changing the decimeters.

00:13 We know there are 10 decimeters in one meter and we know there's a thousand meters in one kilometer.

00:22 So the unit that i'm trying to cancel out needs to be in the opposite corner kind of.

00:30 So if i start with decimeters on top i want to cancel decimeters on the bottom.

00:34 I have meters on top i want to cancel meters on the bottom.

00:37 Now we get to kilometers which is what we want for that first part of the unit.

00:42 I also need to change my seconds into hours.

00:45 I know there's 60 seconds in one minute and there's 60 minutes in one hour.

00:56 And so again we're going to make sure our units cancel.

00:59 The seconds on the bottom cancel with seconds on the top.

01:03 Minutes on the bottom cancel minutes on the top.

01:08 And we're left with hours in the denominator which is what we want.

01:11 So we're going to multiply all across the top and divide by everything on the bottom and we get 11 .5 kilometers per hour.

01:22 And i did round that for significant digits.

01:25 So if you're concerned about significant digits our number started with three significant digits so i rounded my answer to three significant digits.

01:34 All right for b we have 8 .2 milligrams per milliliter.

01:39 So again we're going to change one unit at a time.

01:43 I know there's a thousand milligrams in one gram.

01:49 And in every one gram there are 10 to the sixth micrograms.

01:55 I'm going to change my milliliters so we have a thousand milliliters in one liter.

02:01 Again making sure our units cancel.

02:03 Milligrams cancel.

02:05 Grams cancel.

02:06 Milliliters cancel.

02:08 We're left with micrograms per liter which gives us 8 .2 times 10 to the sixth micrograms per liter.

02:22 For c we have 75 .3 milligrams.

02:27 We know there's a thousand milligrams in one gram.