Question

Write the complete name (prefix \(+\) unit) for each of the following numerical values: a. \(0.10 \mathrm{~g}\) b. \(0.000001 \mathrm{~g}\) c. \(1000 \mathrm{~g}\) d. \(0.01 \mathrm{~g}\) e. \(0.001 \mathrm{~g}\) f. \(1 \times 10^{9} \mathrm{~g}\)

Short answer

a. 1 dg, b. 1 µg, c. 1 kg, d. 1 cg, e. 1 mg, f. 1 Gg.

Step-by-step solution

Understand Prefixes for Units

A prefix is a specifier or mnemonic that is prepended to units of measurement to indicate multiples or fractions of the units. Common prefixes include kilo (k, 10³), milli (m, 10⁻³), micro (µ, 10⁻⁶), and nano (n, 10⁻⁹).

Convert 0.10 g

The number 0.10 is equal to 10⁻¹. This can be simplified to 1 decigram (1 dg). Therefore, 0.10 g = 1 dg.

Convert 0.000001 g

The number 0.000001 is equal to 10⁻⁶. This corresponds to 1 microgram (1 µg). Therefore, 0.000001 g = 1 µg.

Convert 1000 g

The number 1000 is equal to 10³. This corresponds to 1 kilogram (1 kg). Therefore, 1000 g = 1 kg.

Convert 0.01 g

The number 0.01 is equal to 10⁻². This corresponds to 1 centigram (1 cg). Therefore, 0.01 g = 1 cg.

Convert 0.001 g

The number 0.001 is equal to 10⁻³. This corresponds to 1 milligram (1 mg). Therefore, 0.001 g = 1 mg.

Convert 1×10⁹ g

The number 1×10⁹ corresponds to 10⁹. This is equal to 1 gigagram (1 Gg). Therefore, 1×10⁹ g = 1 Gg.

Key concepts

Metric Prefixes

In the metric system, prefixes are used to denote the multiples or fractions of a unit. These prefixes help simplify the representation of very large or very small numbers. For instance, the prefix 'kilo-' means 1000 times the unit, while 'milli-' means one-thousandth of the unit. These prefixes are crucial in scientific notation and daily measurements.

Here are some common metric prefixes you will encounter:

• Kilo- (k): 10³ or 1000 times the base unit
• Milli- (m): 10⁻³ or one-thousandth of the base unit
• Micro- (µ): 10⁻⁶ or one-millionth of the base unit
• Giga- (G): 10⁹ or one billion times the base unit
• Deci- (d): 10⁻¹ or one-tenth of the base unit
• Centi- (c): 10⁻² or one-hundredth of the base unit

Understanding these prefixes allows you to convert between different scales of measurement easily. They make it much more straightforward to manage calculations and interpretations in chemistry and other sciences.

Mass Units

Mass is commonly measured in grams (g) in the metric system. However, depending on the magnitude of the mass, various prefixes are used to adjust the unit accordingly. For example, 1000 grams is more conveniently expressed as 1 kilogram (kg).

Some standard mass units with prefixes include:

• Kilogram (kg): 1000 grams
• Decigram (dg): 0.1 grams
• Centigram (cg): 0.01 grams
• Milligram (mg): 0.001 grams
• Microgram (µg): 0.000001 grams
• Gigagram (Gg): 1,000,000,000 grams

This method of using different mass units prevents the need to write out long strings of numbers. For instance, instead of saying 0.000001 grams, we can just say 1 microgram (1 µg). This also makes calculations and comparisons much easier.

Scientific Notation

Scientific notation is a way to express large or small numbers compactly. It uses powers of ten to reduce the number of zeros in the number, making it easier to read and work with.

For example:

• 1000 can be written as 1 × 10³
• 0.01 can be written as 1 × 10⁻²
• 0.000001 can be written as 1 × 10⁻⁶
• 1,000,000,000 can be written as 1 × 10⁹

This notation is particularly useful in chemistry when dealing with mass units. Combined with metric prefixes, scientific notation simplifies the conversion between units. For example, converting 0.01 grams to centigrams is straightforward because 0.01 grams = 1 × 10⁻² grams, which is equal to 1 centigram (1 cg). In this way, scientific notation provides a clear and precise method of representing quantities, making calculations more manageable and understandable.