Use appropriate metric prefixes to write the following measurements without use of exponents: (d) 3.523×10⁹ m³ (e) 9.62×10² m/s (f) 8.923×10^-12 kg

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Identify the appropriate metric prefix for the given exponent. In this case, 10^9 corresponds to the prefix 'giga' (G).

Rewrite the measurement using the identified metric prefix. Replace 10^9 with 'G'.

Express the measurement as 3.523 Gm^3, where 'G' stands for 'giga'.

Ensure that the unit of measurement (m^3) remains consistent and correctly represents cubic meters.

Verify that the conversion maintains the original value's magnitude and unit.

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주요 개념

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Metric Prefixes

Metric prefixes are standardized terms used to denote specific powers of ten in the metric system. They simplify the representation of large or small quantities by providing a shorthand notation, such as 'kilo-' for 10^3 or 'giga-' for 10^9. Understanding these prefixes is essential for converting and expressing measurements in a more manageable form.

Scientific Notation

Scientific notation is a method of expressing numbers as a product of a coefficient and a power of ten, which allows for easier handling of very large or very small numbers. For example, 3.523×10^9 can be interpreted as 3.523 billion. Converting from scientific notation to standard metric prefixes requires knowledge of the appropriate prefix that corresponds to the exponent.

Volume Measurement

Volume is a measure of the three-dimensional space occupied by a substance, commonly expressed in cubic meters (m³) in the metric system. When converting large volumes, it is important to apply the correct metric prefix to convey the measurement accurately. For instance, 3.523×10^9 m³ can be expressed as 3.523 gigameters cubed (Gm³) using the appropriate metric prefix.

Use appropriate metric prefixes to write the following measurements without use of exponents: (d) 3.523×109 m3 (e) 9.62×102 m/s (f) 8.923×10-12 kg