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Chapter 1: Problem 107

Write each of the following in terms of the SI base unit (that is, express the prefix as the power of ten). a. \(1.07 \mathrm{ps}\) b. \(5.8 \mu \mathrm{m}\) c. \(319 \mathrm{~nm}\) d. \(15.3 \mathrm{~ms}\)

Short Answer

Expert verified
a. \(1.07 \times 10^{-12} \text{s}\); b. \(5.8 \times 10^{-6} \text{m}\); c. \(319 \times 10^{-9} \text{m}\); d. \(15.3 \times 10^{-3} \text{s}\).

Step by step solution

01

Understanding the Problem

The task requires converting the given measurements with prefixes (ps, 碌m, nm, ms) into the standard SI base units using powers of ten.
02

Conversion of Picoseconds

The prefix "pico" (p) means \(10^{-12}\). Therefore, 1.07 picoseconds (ps) is converted as follows:\[1.07 \text{ ps} = 1.07 \times 10^{-12} \text{ seconds (s)}\].
03

Conversion of Micrometers

The prefix "micro" (碌) means \(10^{-6}\). Therefore, 5.8 micrometers (碌m) is converted as follows:\[5.8 \text{ 碌m} = 5.8 \times 10^{-6} \text{ meters (m)}\].
04

Conversion of Nanometers

The prefix "nano" (n) means \(10^{-9}\). Therefore, 319 nanometers (nm) is converted as follows:\[319 \text{ nm} = 319 \times 10^{-9} \text{ meters (m)}\].
05

Conversion of Milliseconds

The prefix "milli" (m) means \(10^{-3}\). Therefore, 15.3 milliseconds (ms) is converted as follows:\[15.3 \text{ ms} = 15.3 \times 10^{-3} \text{ seconds (s)}\].

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Key Concepts

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

SI base units
The International System of Units, commonly known as the SI system, is the most widely used measurement system in the world. It is built on seven base units that describe key physical properties.
Each base unit is linked to a specific physical dimension.
  • Meter (m) for length
  • Kilogram (kg) for mass
  • Second (s) for time
  • Ampere (A) for electric current
  • Kelvin (K) for temperature
  • Mole (mol) for the amount of substance
  • Candela (cd) for luminous intensity
These base units form the foundation for derived units, which are constructed using combinations of these base units, allowing accurate and consistent measurements across disciplines.
Metric prefixes
Metric prefixes are an integral part of the metric system, designed to simplify the expression of units.
They allow us to express very large or small quantities by adding a prefix to the base unit. This prefix shows by how many powers of ten a unit should be multiplied.
Here are some common metric prefixes:
  • Kilo (k), meaning \(10^3\)
  • Centi (c), meaning \(10^{-2}\)
  • Milli (m), meaning \(10^{-3}\)
  • Micro (碌), meaning \(10^{-6}\)
  • Nano (n), meaning \(10^{-9}\)
  • Pico (p), meaning \(10^{-12}\)
Understanding these prefixes is crucial for converting units effectively, as it simplifies calculations by allowing direct multiplications with powers of ten.
Powers of ten
Powers of ten are a fundamental concept for expressing and understanding very large or very small numbers in a compact form.
They are used extensively in various scientific fields, especially when dealing with metric prefixes.
  • A positive power of ten indicates a large number. For example, \(10^3 = 1000\).
  • A negative power of ten, such as \(10^{-12}\), indicates a small fraction, equal to 0.000000000001.
The use of powers of ten allows for easier comprehension and computation, especially in scientific notation. It ensures precision and clarity in mathematical operations and measurements.
Unit conversion
Unit conversion is the process of converting a quantity expressed in one unit into another unit.
This is particularly important when dealing with units that involve metric prefixes.To convert a measurement to an SI base unit, follow these simple steps:
  • Identify the metric prefix and its corresponding power of ten.
  • Multiply the given number by the power of ten associated with the prefix.
  • Express the result in terms of the base unit.
For example, to convert 5.8 碌m to meters, recognize that 'micro' stands for \(10^{-6}\), and hence, \(5.8 \, \mu \mathrm{m} = 5.8 \times 10^{-6} \, \mathrm{m}\).
Mastering unit conversion is crucial for accurately interpreting and communicating scientific data.

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Most popular questions from this chapter

A sample of mercury(II) oxide was heated to produce mercury metal and oxygen gas. Then the liquid mercury was cooled to \(-40^{\circ} \mathrm{C}\), where it solidified. A glowing wood splint was thrust into the oxygen, and the splint burst into flame. Identify each physical change and each chemical change.

Do the indicated arithmetic and give the answer to the correct number of significant figures. a. \(\frac{0.871 \times 0.57}{5.871}\) b. \(8.937-8.930\) c. \(8.937+8.930\) d. \(0.00015 \times 54.6+1.002\)

Which of the following are pure substances and which are mixtures? For each, list all of the different phases present. a. bromine liquid and its vapor b. paint, containing a liquid solution and a dispersed solid pigment c. partially molten iron d. baking powder containing sodium hydrogen carbonate and potassium hydrogen tartrate

All of the following processes involve a separation of either a mixture into substances or a compound into elements. For each, decide whether a physical process or a chemical reaction is required. a. Sodium metal is obtained from the substance sodium chloride. b. Iron filings are separated from sand by using a magnet. c. Sugar crystals are separated from a sugar syrup by evaporation of water. d. Fine crystals of silver chloride are separated from a suspension of the crystals in water. e. Copper is produced when zinc metal is placed in a solution of copper(II) sulfate, a compound.

A weather balloon filled with helium has a diameter of \(3.00 \mathrm{ft}\). What is the mass in grams of the helium in the balloon at \(21^{\circ} \mathrm{C}\) and normal pressure? The density of helium under these conditions is \(0.166 \mathrm{~g} / \mathrm{L}\).
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