(a) The recommended daily allowance (RDA) of the trace metal...

(a) The recommended daily allowance (RDA) of the trace metal magnesium is $410 \mathrm{mg} /$ day for males. Express this quantity in $\mu \mathrm{g} /$ day. (b) For adults, the RDA of the amino acid lysine is $12 \mathrm{mg}$ per $\mathrm{kg}$ of body weight. How many grams per day should a $77-\mathrm{kg}$ adult receive? (c) A typical multivitamin tablet can contain $2.0 \mathrm{mg}$ of vitamin $\mathrm{B}_{2}$ (riboflavin), and the RDA is $0.0030 \mathrm{~g} /$ day. How many such tablets should a person take each day to get the proper amount of this vitamin, if he gets none from other sources? (d) The RDA for the trace element selenium is $0.000070 \mathrm{~g} /$ day. Express this dose in $\mathrm{mg} /$ day.

(a) The recommended daily allowance (RDA) of the trace metal magnesium is $410 \mathrm{mg} /$ day for males. Express this quantity in $\mu \mathrm{g} /$ day. (b) For adults, the RDA of the amino acid lysine is $12 \mathrm{mg}$ per $\mathrm{kg}$ of body weight. How many grams per day should a $77-\mathrm{kg}$ adult receive? (c) A typical multivitamin tablet can contain $2.0 \mathrm{mg}$ of vitamin $\mathrm{B}_{2}$ (riboflavin), and the RDA is $0.0030 \mathrm{~g} /$ day. How many such tablets should a person take each day to get the proper amount of this vitamin, if he gets none from other sources?
(d) The RDA for the trace element selenium is $0.000070 \mathrm{~g} /$ day. Express this dose in $\mathrm{mg} /$ day.

Key Concepts

Dimensional Analysis

Dimensional analysis is a systematic approach used to convert one set of units to another, ensuring the result remains consistent with the original measurement. It involves multiplying by conversion factors that relate the different units so that unwanted units cancel out, leaving only the desired units in the final answer.

Unit Conversion

Unit conversion refers to the process of changing a measurement from one unit system to another, such as from milligrams to micrograms or from grams to milligrams. This involves applying known relationships between units, such as 1 mg = 1000 ?g or 1 g = 1000 mg, to re-express the same quantity in different terms.

Recommended Daily Allowance (RDA)

The Recommended Daily Allowance (RDA) is a guideline that specifies the daily intake level of a nutrient considered sufficient to meet the requirements of most healthy individuals. It serves as an important nutritional benchmark used in dietary planning and assessing nutrient adequacy.

Proportional Reasoning

Proportional reasoning involves understanding and applying the concept that certain quantities scale in relation to each other. It is crucial when calculating dosages based on body weight or adjusting quantities, allowing one to set up proportional relationships to determine the correct amounts for varied conditions.

Transcript

00:01 In this problem, we're asked to convert from various values of recommended daily allowances for vitamins from one unit to another, and this is essentially a series of conversion factor problems.

00:17 So in the first part, part a, we're told that the recommended daily allowance, or rda, of the trace metal magnesium, is 410 milligrams per day for males.

00:30 And we want to convert that into a quantity expressed in micrograms per day.

00:36 So we're told that the rda is 410 milligrams per day.

00:43 That little m stands for milligrams.

00:45 And we want to convert that into some number of, i'll put it over here on the right hand side of the equal sign, a number of micrograms per day.

00:57 Okay, notice that symbol up there.

00:59 That's a greek letter mu.

01:02 Spelled like that, mu, and that stands for micro or that's times 10 to the minus 6.

01:11 Whereas the milly value that we over here have over here, that's times 10 to the minus 3.

01:20 Okay, so this is just a conversion factor problem, and i'll use the conversion factor to go from milly to micro and what i need to do is put the milligrams in the bottom and i'll put the micrograms in the top and there are 1 ,000 micrograms for every 1 milligram since there are 10 to the minus 3 milligrams and 10 to the minus 6 for micrograms.

01:51 So if i multiply 410 times 1 ,000, that just gives me, i'll write this in scientific notation, it's going to be 40010 ,000, but we'll write that as 4 .10 times 10 to the 5 micrograms per day.

02:10 Okay, in part b, we're asked to calculate how much of the amino acid lysine a adult that weighs 77 kilograms should consume, knowing that the recommended daily allowance is 12 milligrams per kilogram of body.

02:29 Weight.

02:32 So here i'm actually calculating a total mass, so i'll write that the mass of lysine that we want to calculate is going to be given by the recommended daily allowance per kilogram of body weight times the mass of the person.

02:50 So i was told that the recommended daily allowance is 12 milligrams per one kilogram of body weight.

03:00 And then i'm going to multiply that by the mass of the adult person, which is 77 kilograms.

03:09 You can see that my units of kilograms and kilograms will cancel out.

03:13 I'm going to be left with just the total mass of lysine that is needed for this adult.

03:19 And that comes out to be 924 milligrams.

03:26 But we're actually asked to calculate it in terms of grams...

Please give Ace some feedback