Scientific Notation Basics

Global energy consumption in 2023 was approximately 580,000,000,000,000,000,000 joules. Written out like that, the number is useless; you cannot even count the zeros reliably. Written as 5.8 x 10²⁰ J, it becomes manageable, comparable, and less error-prone.

Scientific notation expresses any number as a coefficient (between 1 and 10) multiplied by a power of 10. The exponent tells you the order of magnitude. 10³ is a thousand. 10⁶ is a million. 10⁹ is a billion. Each step up by one in the exponent means the number is ten times larger.

Energy data relies on SI prefixes that map directly to these powers: kilo (10³), mega (10⁶), giga (10⁹), tera (10¹²), peta (10¹⁵). A kilowatt-hour is a thousand watt-hours. A gigawatt is a billion watts. A terawatt-hour is a trillion watt-hours. Confusing mega with giga (a factor of 1,000) is the kind of error that turns a policy memo into a correction.

Worked Example

A news article says U.S. electricity generation in 2023 was about 4,000 TWh (terawatt-hours). You need this in watt-hours for a calculation.

• Replace the prefix. Tera = 10¹². So 4,000 TWh = 4,000 x 10¹² Wh.
• Convert to standard notation. 4,000 = 4 x 10³. So 4 x 10³ x 10¹² = 4 x 10¹⁵ Wh.

How would you express this in petawatt-hours (peta = 10¹⁵)?

4 x 10¹⁵ Wh = 4 PWh. U.S. electricity generation is about 4 petawatt-hours per year. The prefix system makes enormous numbers portable.

Every figure in this course, from a household's kilowatt-hours to the world's exajoules, is the same handful of digits moved by a power of ten. Losing track of that power of ten is how a rounding error becomes a policy talking point.

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