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Chapter 1: Problem 64

Medical The concentration of PSA (prostate-specific antigen) in the blood is sometimes used as a screening test for possible prostate cancer in men. The value is normally reported as the number of nanograms of PSA per milliliter of blood. A PSA of \(1.7(\mathrm{ng} / \mathrm{mL})\) is considered low. Express that value in (a) \(\mathrm{g} / \mathrm{L}\), (b) standard SI units of \(\mathrm{kg} / \mathrm{m}^{3}\), and (c) \(\mu \mathrm{g} / \mathrm{L}\).

Short Answer

Expert verified
So, a PSA of 1.7 ng/mL can be expressed as (a) 1.7 * \(10^{-6}\) g/L (b) 1.7 kg/m鲁 and (c) 1.7 碌g/L.

Step by step solution

01

Convert ng/mL to g/L

To convert from nanograms (ng) to grams (g), the conversion factor is \(1 g = 10^{9} ng\). To convert from milliliters (mL) to liters (L), the conversion factor is \(1 L = 10^{3} mL\). Thus, \( 1.7 ng/mL = 1.7 * \frac{1}{10^{9}} g/ \frac{1}{10^{3}} L = 1.7 * 10^{-6} g/L.\)
02

Convert g/L to kg/m鲁

To convert from grams (g) to kilograms (kg), the conversion factor is \(1 kg = 10^{3} g\). To convert from liters (L) to cubic meters (m鲁), the conversion factor is \(1 m鲁 = 10^{3} L\). Thus, \(1.7 * 10^{-6} g/L = 1.7 * 10^{-6} * \frac{1}{10^{3}}kg / \frac{1}{10^{3}}m鲁 = 1.7 kg/m鲁.\)
03

Convert g/L to 碌g/L

To convert from grams (g) to micrograms (碌g), the conversion factor is \(1 g = 10^{6} 碌g\). Thus, \(1.7 * 10^{-6} g/L = 1.7 * 10^{-6} * 10^{6} 碌g/L = 1.7 碌g/L.\)

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Unit Conversion
Unit conversion is a fundamental mathematical process used to express a quantity in different units of measurement. It plays a critical role in scientific and medical fields, where precision is crucial.
When converting units, it's essential to maintain the same quantity value. For example, converting the concentration of PSA from nanograms per milliliter (ng/mL) to grams per liter (g/L) involves changing both the mass and volume units.
To convert from nanograms (ng) to grams (g), use the factor:
  • 1 g = 109 ng
Similarly, to convert from milliliters (mL) to liters (L), remember:
  • 1 L = 103 mL
By applying these conversions, you ensure the measurement remains consistent and accurate across different units.
Prostate Cancer Screening and PSA
Prostate cancer screening is an essential process for detecting prostate abnormalities early. The prostate-specific antigen (PSA) test is a standard screening method used to identify potential prostate cancer.
PSA is a protein produced by cells of the prostate gland. Elevated levels in blood tests can indicate prostate cancer, although high PSA levels might also result from non-cancerous conditions.
Interpreting PSA test results requires understanding the concentration units. Typically, PSA levels are expressed in nanograms per milliliter (ng/mL). In medical diagnostics, "normal" or "low" values, such as 1.7 ng/mL as described, are used to assess the need for further investigation or intervention. The comparison of these values to standardized units ensures the medical community maintains consistent benchmarks.
Introduction to SI Units
The International System of Units (SI units) is the globally accepted metric system of measurement. It standardizes scientific communication and measurement accuracy.
In the context of PSA tests, converting concentrations to SI units, such as kilograms per cubic meter (kg/m鲁), enhances clarity and uniformity in scientific communication. This system is vital for ensuring that quantities expressed in different studies and reports are comparable and consistent.
SI units form the basis of all measurements. For PSA concentration, conversions like:
  • 1 kilogram (kg) = 103 grams (g)
  • 1 cubic meter (m鲁) = 103 liters (L)
are fundamental for ensuring that the values can be translated universally into different scales or units without losing meaning or accuracy.

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Most popular questions from this chapter

The body mass index (BMI) estimates the amount of fat in a person's body. It is defined as the person's mass \(m\) in kg divided by the square of the person's height \(h\) in m. (a) Write the formula for BMI in terms of \(m\) and \(h\). (b) In the United States, most people measure weight in pounds and height in feet and inches. Show that with weight \(W\) in pounds and height \(h\) in inches, the BMI formula is BMI \(=703 \mathrm{~W} / h^{2}\). (c) A person with a BMI between \(25.0\) and \(30.0\) is considered overweight. If a person is \(5^{\prime} 11^{\prime \prime}\) tall, for what range of mass will he be considered overweight?

How many significant figures should be associated with measurements made using a thermometer that is subdivided into \(0.1^{\circ} \mathrm{C}\) increments and can be used for temperatures between 0 and \(10^{\circ} \mathrm{C}\) ?

\(\$ Medical Express each quantity in the standard SI units requested. (a) An adult should have no more than \)2500 \mathrm{mg}\( of sodium per day. What is the limit in \)\mathrm{kg}\( ? (b) A \)240-\mathrm{mL}\( cup of whole milk contains \)35 \mathrm{mg}\( of cholesterol. Express the cholesterol concentration in the milk in \)\mathrm{kg} / \mathrm{m}^{3}\( and in \)\mathrm{mg} / \mathrm{mL}\(. (c) A typical human cell is about \)10 \mu \mathrm{m}\( in diameter, modeled as a sphere. Express its volume in cubic meters. (d) A low-strength aspirin tablet (sometimes called a "baby aspirin") contains \)81 \mathrm{mg}\( of the active ingredient. How many kg of the active ingredient does a 100 -tablet bottle of baby aspirin contain? (e) The average flow rate of urine out of the kidneys is typically \)1.2 \mathrm{~mL} / \mathrm{min}\(. Express the rate in \)\mathrm{m}^{3} / \mathrm{s}\(. (f) The density of blood proteins is about \)1.4 \mathrm{~g} / \mathrm{cm}^{3}\(. Express the density in \)\mathrm{kg} / \mathrm{m}^{3}$.

Which of the following could be correct based on a dimensional analysis? A. The volume flow rate is \(64 \mathrm{~m}^{3} / \mathrm{s}\). B. The height of the Transamerica building is \(332 \mathrm{~m}^{2}\). C. The duration of a fortnight is \(66 \mathrm{~m} / \mathrm{s}\). D. The speed of the train is \(9.8 \mathrm{~m} / \mathrm{s}^{2}\). E. The weight of a standard kilogram mass is \(2.2 \mathrm{lb}\). F. The density of gold is \(19.3 \mathrm{~kg} / \mathrm{m}^{2}\). SSM

Calculate \(1.4+15+7.15+8.003\) using the proper number of significant figures. A. \(31.553\) B. \(31.550\) C. \(31.55\) D. \(31.6\) E. 32
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