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Chapter 1: Problem 5

The mass of the parasitic wasp Caraphractus cintus can be as small as \(5 \times 10^{-6} \mathrm{~kg}\). What is this mass in (a) grams (g), (b) milligrams (mg), and (c) micrograms\((\mu g) ?\)

Short Answer

Expert verified
5 \times 10^{-3} g, 5 mg, 5000 \mu g

Step by step solution

01

Convert Kilograms to Grams

To convert the mass from kilograms (kg) to grams (g), use the conversion factor that 1 kg = 1000 g. Multiply the mass in kilograms by this factor: \[5 \times 10^{-6} \text{ kg} \times 1000 \frac{\text{g}}{\text{kg}} = 5 \times 10^{-3} \text{ g}\]
02

Convert Grams to Milligrams

Now, convert the grams to milligrams. Knowing that 1 gram is equal to 1000 milligrams, multiply the mass in grams by this factor:\[5 \times 10^{-3} \text{ g} \times 1000 \frac{\text{mg}}{\text{g}} = 5 \text{ mg}\]
03

Convert Grams to Micrograms

Finally, convert the mass from grams to micrograms. There are 1,000,000 micrograms in a gram, so multiply the mass in grams by this factor:\[5 \times 10^{-3} \text{ g} \times 1,000,000 \frac{\text{\mu g}}{\text{g}} = 5000 \text{ \mu g}\]

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Key Concepts

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

Mass Conversion
Mass conversion is the process of changing the measurement of mass from one unit to another. It is an essential skill in science and engineering because different scenarios require mass to be expressed in various units.
To convert mass, you need to know the relationships between units. For instance:
  • 1 kilogram (kg) is 1000 grams (g).
  • 1 gram (g) is 1000 milligrams (mg).
  • 1 gram (g) is also 1,000,000 micrograms (碌g).
With these conversion factors, you can switch between units by multiplying the original mass by the appropriate conversion factor. This step-by-step conversion helps solve various real-world problems, such as determining the tiny mass of microscopic objects like the Caraphractus cintus wasp.
Kilograms to Grams
Kilograms to grams conversion is a straightforward process. Since 1 kilogram contains 1000 grams, you convert kilograms into grams by multiplying by 1000. This type of conversion is common in science because kilograms and grams are part of the metric system, which is based on powers of ten.
To illustrate, let's consider the parasitic wasp Caraphractus cintus. If it weighs as little as \(5 \times 10^{-6}\) kg, multiplying by 1000 converts this weight to grams: \[5 \times 10^{-6} \text{ kg} \times 1000 = 5 \times 10^{-3} \text{ g} \]Thus, despite the intricate appearance of scientific notation, the conversion is simply a matter of applying the basic multiplication rule.
Metric Units Conversion
Metric units conversion allows for quick and easy calculations when you are converting different units within the metric system, which is highly systematic and decimal-based.

The metric system is useful because each unit is a factor of ten from the next, making conversions simple. Some typical conversions include:
  • To convert grams to milligrams, multiply by 1000.
  • To convert grams to micrograms, multiply by 1,000,000.
  • To revert from smaller to larger units, divide by the same factors.
For example, after determining the mass of Caraphractus cintus in grams, it was converted to milligrams by multiplying by 1000. This methodology ensures precision and enhances understanding of small-scale quantities.
Microscopic Mass Conversion
Microscopic mass conversion deals with measuring and converting the mass of extremely small objects. In such cases, it is often necessary to use units smaller than grams for accuracy and convenience.
Specifically, milligrams (mg) and micrograms (碌g) come into play. The conversion process is essential when handling these measurements, as is common in fields like microbiology or pharmacology.
  • From grams to milligrams, multiply by 1000.
  • From grams to micrograms, go further and multiply by 1,000,000.
Consider that for the wasp Caraphractus cintus, these conversions yielded 5 mg and 5000 碌g respectively, demonstrating how conversion factors facilitate understanding and comparison of microscopic masses. This allows researchers to accurately account for minute differences in mass.

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Most popular questions from this chapter

A chimpanzee sitting against his favorite tree gets up and walks \(51 \mathrm{~m}\) due east and \(39 \mathrm{~m}\) due south to reach a termite mound, where he eats lunch. (a) What is the shortest distance between the tree and the termite mound? (b) What angle does the shortest distance make with respect to due east?

Vector \(\overrightarrow{\text { A }}\) points along the \(+y\) axis and has a magnitude of 100.0 units. Vector \(\overrightarrow{\mathbf{B}}\) points at an angle of \(60.0^{\circ}\) above the \(+x\) axis and has a magnitude of 200.0 units. Vector \(\overrightarrow{\mathrm{C}}\) points along the \(+x\) axis and has a magnitude of 150.0 units. Which vector has (a) the largest \(x\) component and (b) the largest \(y\) component?

A baby elephant is stuck in a mud hole. To help pull it out, game keepers use a rope to apply force \(\overrightarrow{\mathbf{F}}_{\mathbf{A}}\), as part \(a\) of the drawing shows. By itself, however, force \(\overrightarrow{\mathbf{F}}_{\mathbf{A}}\) is insufficient. Therefore, two additional forces \(\overrightarrow{\mathbf{F}}_{\mathbf{B}}\) and \(\overrightarrow{\mathbf{F}}_{\mathbf{C}}\) are applied, as in part \(b\) of the drawing. Each of these additional forces has the same magnitude \(F\). The magnitude of the resultant force acting on the elephant in part \(b\) of the drawing is twice that in part \(a\). Find the ratio \(F / F_{\mathrm{A}}\).

An observer, whose eyes are \(1.83 \mathrm{~m}\) above the ground, is standing \(32.0 \mathrm{~m}\) away from a tree. The ground is level, and the tree is growing perpendicular to it. The observer's line of sight with the treetop makes an angle of \(20.0^{\circ}\) above the horizontal. How tall is the tree?

A car is being pulled out of the mud by two forces that are applied by the two ropes shown in the drawing. The dashed line in the drawing bisects the \(30.0^{\circ}\) angle. The magnitude of the force applied by each rope is 2900 newtons. Arrange the force vectors tail to head and use the graphical technique to answer the following questions, (a) How much force would a single rope need to apply to accomplish the same effect as the two forces added together? (b) How would the single rope be directed relative to the dashed line?
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