Metric Prefixes: Videos & Practice Problems

Understanding metric prefixes is essential for scientific measurements and calculations. These prefixes represent different powers of ten, ranging from:

${10}^{12}\text{(tera, symbolized by T) to}{10}^{-12}\text{(pico, symbolized by p).}$

Familiarity with these terms and their corresponding symbols allows for the conversion and expression of various units, such as volume in liters, time in seconds, substance amount in moles, and electrical current in amperes. A helpful mnemonic to remember the order of metric prefixes is: "King Henry Died By Drinking Chocolate Milk Until Nine PM," where each initial corresponds to a metric prefix from tera to pico. Applying these prefixes to base units is crucial for accurate scientific communication and conversions between different scales. For instance, milliliters (mL) uses the milli prefix to denote:

${10}^{-3}\text{liters, while kiloamperes (kA) indicates}{10}^3\text{amperes.}$

Understanding and correctly using metric prefixes ensures precision and clarity in scientific measurements.

Metric Prefixes Chart

Understanding metric prefixes is essential for performing calculations in chemistry, as they serve as modifiers that represent multiples of ten. The metric prefix multipliers range from \(10^{12}\) to \(10^{-12}\), which is typically sufficient for introductory chemistry courses. For more advanced studies, prefixes like \(10^{-15}\) and \(10^{15}\) may be encountered.

Here’s a breakdown of the common metric prefixes:

• Terra (T)
• Giga (G): \(10^{9}\)
• Mega (M): \(10^{6}\)
• Kilo (k): \(10^{3}\) (as in kilometer)
• Hecto (h): \(10^{2}\)
• Deka (da): \(10^{1}\)
• Base Unit: \(10^{0}\) (e.g., liters, seconds)
• Deci (d): \(10^{-1}\)
• Centi (c): \(10^{-2}\) (as in centimeter)
• Milli (m): \(10^{-3}\) (as in milliliter)
• Micro (µ): \(10^{-6}\)
• Nano (n): \(10^{-9}\)
• Pico (p): \(10^{-12}\)

To aid in memorization, a mnemonic device can be helpful. The phrase "The Great Monarch King Henry's Daughter Barbara Drinks Chocolate Milk Until 9 PM" corresponds to the order of the metric prefixes, with each highlighted letter representing a specific prefix. This memory tool effectively encapsulates the range from \(10^{12}\) down to \(10^{-12}\).

As you study metric prefixes, remember to consult with your professor to confirm the specific range you need to know for your coursework. Mastering these prefixes will enhance your ability to work with base units and perform calculations accurately in chemistry.

Metric Prefixes Usage

Metric prefixes serve as essential labels that modify base units, allowing for a clearer understanding of measurements across various scientific disciplines. For instance, the base unit for volume is the liter, while time is measured in seconds, the amount of substance in moles, and electrical current in amperes. These base units are integral to the International System of Units (SI).

By applying metric prefixes to these base units, we can create a range of measurements that reflect different scales. For example, when we add the prefix "milli-" to liters, we obtain milliliters (mL), which represents one-thousandth of a liter. Similarly, "nano-" can be prefixed to seconds to yield nanoseconds (ns), indicating one-billionth of a second. In the case of moles, the prefix "giga-" results in gigamoles (Gmol), denoting one billion moles, while "kilo-" in front of amperes gives us kiloamperes (kA), equivalent to one thousand amperes.

This process of prefixing is crucial for metric conversions, as it allows scientists and engineers to express quantities in a more manageable form. Understanding how to transition between different metric prefixes is a fundamental skill in scientific calculations and measurements.

Metric Prefixes Conversion Example

To convert units effectively, it's essential to understand metric prefixes and their relationships to base units. In this example, we will convert 694 kilograms to micrograms, following a systematic approach.

First, identify the base unit by removing the metric prefix. Here, the metric prefix is "kilo," which indicates that the base unit is grams. Therefore, we start with:

694 kilograms = 694 kilo-grams

Next, to facilitate the conversion, we need to cancel out the units. Place kilograms in the denominator to cancel them out:

694 kg × (1 kg / 10³ g)

According to the metric prefix multipliers, "kilo" corresponds to \(10^3\). This allows us to convert kilograms to grams:

694 kg × (1 / 1000) = 694 g

Now, since the goal is to convert grams to micrograms, we again set up the conversion to cancel out grams. Place grams in the denominator:

694 g × (1 microgram / 10^-6 g)

Here, "micro" corresponds to \(10^{-6}\). Now, we can perform the calculation:

694 g × (10^-6 / 1) = 694 × 10³ / 10^-6

To simplify, remember to use parentheses in your calculator for powers of ten to avoid errors:

694 × (10³ / 10^-6) = 694 × 10^{(3 - (-6))} = 694 × 10⁹

Thus, the final result is:

6.94 × 10¹¹ micrograms

This example illustrates the importance of understanding metric prefixes and the systematic approach to unit conversion. By following these steps, you can confidently tackle similar problems in the future.

Which quantity in the following pair is smaller?

• A. 155 pm
• B. 7.8 x 10^–9 cm

Answer: (B)

Use the prefix multipliers to express each measurement without any exponents.
a) 32 x 10-13 L
b) 7.3 x 106 g 
c) 18.5 x 1011 s

In this exercise, we focus on converting measurements expressed in scientific notation into standard notation using metric prefixes. This process involves understanding both scientific notation and the metric system's prefix multipliers.

To begin, consider the measurement of 32 times \(10^{-13}\) liters. The closest metric prefix to \(10^{-13}\) is pico, which represents \(10^{-12}\). To convert liters to picoliters, we set up the conversion as follows:

\[32 \times 10^{-13} \, \text{liters} \times \frac{1 \, \text{picoliter}}{10^{-12} \, \text{liters}} = 3.2 \, \text{picoliters}\]

Here, the liters cancel out, and we simplify the expression to arrive at 3.2 picoliters.

Next, we examine 7.3 times \(10^{6}\) grams. The metric prefix for \(10^{6}\) is mega. To convert grams to megagrams, we perform the following calculation:

\[7.3 \times 10^{6} \, \text{grams} \times \frac{1 \, \text{megagram}}{10^{6} \, \text{grams}} = 7.3 \, \text{megagrams}\]

Again, the grams cancel, resulting in 7.3 megagrams.

Finally, we consider 18.5 times \(10^{11}\) seconds. The closest metric prefix here is tera, which corresponds to \(10^{12}\). The conversion from seconds to teraseconds is set up as follows:

\[18.5 \times 10^{11} \, \text{seconds} \times \frac{1 \, \text{terasecond}}{10^{12} \, \text{seconds}} = 1.85 \, \text{teraseconds}\]

Once again, the seconds cancel out, yielding 1.85 teraseconds.

In summary, this exercise illustrates how to convert scientific notation to standard notation by utilizing metric prefixes, effectively eliminating exponents in the process. Understanding these conversions is essential for working with various measurements in scientific contexts.

Use scientific notation to express each quantity with only the base unit. 
a) 83 µm
b) 193 kg
c) 2.7 mmol

In scientific notation, expressing quantities with only the base unit involves understanding metric prefixes and their corresponding values. Each metric prefix represents a power of ten that modifies the base unit. For example, the prefix "micro" corresponds to \(10^{-6}\), "kilo" corresponds to \(10^{3}\), and "milli" corresponds to \(10^{-3}\).

To convert from micrometers to meters, we start with the quantity in micrometers. Since "micro" is the prefix, we place it in the denominator to cancel it out. For instance, converting \(8.3\) micrometers involves the equation:

\(8.3 \, \text{micrometers} \times \frac{1 \, \text{meter}}{1 \, \text{micro} \, \text{meter}} = 8.3 \times 10^{-5} \, \text{meters}\)

Next, when converting kilograms to grams, we recognize that "kilo" is the prefix. Thus, we set up the conversion as follows:

\(193 \, \text{kilograms} \times \frac{1 \, \text{gram}}{1 \, \text{kilo} \, \text{gram}} = 1.93 \times 10^{5} \, \text{grams}\)

Finally, for millimoles to moles, we again place the prefix in the denominator:

\(2.7 \, \text{millimoles} \times \frac{1 \, \text{mole}}{1 \, \text{milli} \, \text{mole}} = 2.7 \times 10^{-3} \, \text{moles}\)

These conversions illustrate the process of moving from standard notation to scientific notation by removing the metric prefix and applying the appropriate power of ten. Understanding these conversions is essential for working with different units in scientific contexts.

If a room has a volume of 1.15 x 10⁸ cm³, what is the volume in km³?

• A. 1150 km³
• B. 115 km³
• C. 1.15 x 10^-7 km³
• D. 1.15 x 10⁵ km³

Answer: (C)

Here’s what students ask on this topic:

How do the prefixes in the metric system relate to the basic units?

The prefixes in the metric system, also known as the International System of Units (SI), serve to denote multiples or fractions of the basic units. Each prefix represents a specific factor by which the base unit is multiplied or divided, making it easier to express very large or very small quantities. For example:

• Kilo- (k) multiplies the unit by 1,000. So, a kilometer (km) is 1,000 meters.
• Mega- (M) multiplies the unit by 1,000,000. A megagram (Mg) is 1,000,000 grams.
• Giga- (G) multiplies the unit by 1,000,000,000. A gigawatt (GW) is 1,000,000,000 watts.

Conversely, for smaller quantities:

• Milli- (m) divides the unit by 1,000. A millimeter (mm) is 0.001 meters.
• Micro- (µ) divides the unit by 1,000,000. A microliter (µL) is 0.000001 liters.
• Nano- (n) divides the unit by 1,000,000,000. A nanometer (nm) is 0.000000001 meters.

How can I remember metric prefixes?

Remembering metric prefixes can be easier if you use mnemonic devices. One common mnemonic for the metric prefixes from largest to smallest is "King Henry Died By Drinking Chocolate Milk." This stands for kilo-, hecto-, deka-, base unit (meter, liter, gram), deci-, centi-, and milli-. Each prefix corresponds to a factor of ten, with kilo- being a thousand times the base unit and milli- being one-thousandth of the base unit.

Here's a breakdown:

• Kilo- (k) = 1,000
• Hecto- (h) = 100
• Deka- (da) = 10
• (Base unit: meters, liters, grams)
• Deci- (d) = 0.1
• Centi- (c) = 0.01
• Milli- (m) = 0.001

For smaller or larger units, you can extend the mnemonic or create a new one. For example, "Mighty King Henry Died By Drinking Chocolate Milk Monday Night" adds micro- (µ) for one-millionth and nano- (n) for one-billionth. Creating a visual chart or flashcards can also reinforce your memory. Practice converting between units using these prefixes to become more familiar with them.

How to do metric conversion?

Metric conversion involves changing a measurement from one unit to another within the metric system. To do this, you need to understand the base units for different types of measurements, such as meters for length, liters for volume, and grams for mass. The metric system is based on multiples of ten, which makes conversion simpler. Here's a basic guide:

1. Identify the current unit and the unit you want to convert to.
2. Determine the conversion factor. For example, 1 kilometer (km) is 1000 meters (m), so the conversion factor from km to m is 1000.
3. Multiply or divide the number you are converting by the conversion factor. If you are converting to a larger unit (e.g. m to km), you divide. If you are converting to a smaller unit (e.g. km to m), you multiply.
4. Ensure your answer is in the correct unit.

Remember the prefixes: kilo- (1000), hecto- (100), deka- (10), deci- (0.1), centi- (0.01), and milli- (0.001). These prefixes help you move the decimal point to the right or left to make the conversion.