Number Digit Blog

Short Scale vs Long Scale: Why Billion and Trillion Can Mean Different Numbers

Understand why large number names like billion and trillion change value. Learn how short scale and long scale systems differ, what a milliard is, and how to read large numbers accurately.

A side-by-side comparison diagram showing how short scale and long scale systems name large numbers like 10^9 and 10^12 differently.

Short scale and long scale are two systems for naming large numbers. In the short scale, one billion is 1,000,000,000, or 109. In the long scale, one billion is 1,000,000,000,000, or 1012, while 109 is called one milliard. This is why the same word, especially “billion” or “trillion,” can mean different numbers depending on the scale.

Quick Answer

The main difference between the short scale and the long scale is how they name large numbers after one million. The short scale names 1,000,000,000 as one billion, while the long scale names 1,000,000,000 as one milliard and uses one billion for 1,000,000,000,000. In the short scale, each new “-illion” name is 1,000 times larger than the last, whereas the long scale increases by a factor of 1,000,000 and uses “-illiard” names in between.

What Are Short Scale and Long Scale?

Short scale and long scale are systems used to assign names to large numeric values. Both systems agree on the value of one million, which is written as 1,000,000 or 106. However, once numbers grow larger than a million, the two naming systems diverge.

The short scale names 1,000,000,000 as one billion, while the long scale names 1,000,000,000 as one milliard and uses one billion for 1,000,000,000,000. Because of this split, reading a large number word without knowing which system is in use can lead to significant misunderstandings.

Key Rule

In the short scale, each new -illion name after million is 1,000 times larger. In the long scale, each new -illion name is 1,000,000 times larger, with -illiard names between them.

Why Billion Can Mean Different Numbers

The word “billion” is the most common source of confusion when dealing with large numbers. In many modern English contexts, a billion represents 1,000,000,000 (one thousand million, or nine zeros). This is the short scale value.

In other regions, historically, or in different languages, a billion represents 1,000,000,000,000 (one million million, or twelve zeros). This is the long scale value. If you are reading a document where the scale is unclear, the safest approach is to check the actual digits or the power of ten rather than relying on the word alone.

Step-by-Step: 109 and 1012

  1. Start with 1,000,000, which is one million in both systems.
  2. Multiply by 1,000 to get 1,000,000,000, or 109.
  3. In the short scale, 109 is one billion.
  4. In the long scale, 109 is one milliard.
  5. Multiply by another 1,000 to get 1,000,000,000,000, or 1012.
  6. In the short scale, 1012 is one trillion.
  7. In the long scale, 1012 is one billion.

Short Scale Large Number Names

The short scale is commonly used in modern English-speaking countries. In this system, each step up the scale is 1,000 times larger than the previous step. Here is how the names progress:

  • Million: 106 (1,000,000)
  • Billion: 109 (1,000,000,000)
  • Trillion: 1012 (1,000,000,000,000)
  • Quadrillion: 1015 (1,000,000,000,000,000)
  • Quintillion: 1018 (1,000,000,000,000,000,000)

Because each new name is multiplied by one thousand, the short scale moves through names quickly as numbers grow.

Long Scale Large Number Names

The long scale is used in many European countries and in various non-English languages. In this system, each new “-illion” name is 1,000,000 times larger than the previous one. To fill the gaps between these massive steps, the system uses names ending in “-illiard.” Here is how the long scale names progress:

  • Million: 106 (1,000,000)
  • Milliard: 109 (1,000,000,000)
  • Billion: 1012 (1,000,000,000,000)
  • Billiard: 1015 (1,000,000,000,000,000)
  • Trillion: 1018 (1,000,000,000,000,000,000)
  • Trilliard: 1021 (1,000,000,000,000,000,000,000)
  • Quadrillion: 1024 (1,000,000,000,000,000,000,000,000)

Billion vs. Milliard

The comparison between billion and milliard is a clear example of how the two scales interact. In the long scale, the word milliard represents 1,000,000,000 (109). In the short scale, this exact same value is called one billion.

If you translate a document from a language that uses the long scale, a number listed as a milliard must be written as a billion in short-scale English to keep the value correct.

Trillion in Short Scale and Long Scale

The word “trillion” behaves differently in each system. In the short scale, a trillion is 1012 (1,000,000,000,000). In the long scale, a trillion is 1018 (1,000,000,000,000,000,000).

This means a long-scale trillion is one million times larger than a short-scale trillion. In the long scale, the value of 1012 is called one billion, not one trillion.

When Scale Differences Matter

Understanding which scale is being used is helpful in several specific situations:

  • Reading historical documents or older texts where regional terms may differ.
  • Translating books, articles, or data from languages that use the long scale.
  • Comparing international statistics, population data, or scientific reports.
  • Studying number systems or completing math worksheets.

When looking at international data, it is best to verify the actual digits or the power of ten to ensure you interpret the values correctly.

Common Mistake

Wrong: Assuming that the word "billion" always means 1,000,000,000 in every country, document, or historical text.

Correct: Recognizing that billion means 109 in the short scale and 1012 in the long scale.

Why: Short scale and long scale use different naming patterns after million, which can lead to a difference of a thousand-fold for the same word.

Comparison Table

Power of Ten Ordinary Number Short Scale Name Long Scale Name What to Notice
106 1,000,000 One million One million Both systems agree here.
109 1,000,000,000 One billion One milliard Short scale uses billion; long scale uses milliard.
1012 1,000,000,000,000 One trillion One billion Long-scale billion is 1,000 times larger than short-scale billion.
1015 1,000,000,000,000,000 One quadrillion One billiard Short scale uses quadrillion; long scale uses billiard.
1018 1,000,000,000,000,000,000 One quintillion One trillion Long-scale trillion is 1,000,000 times larger than short-scale trillion.
1021 1,000,000,000,000,000,000,000 One sextillion One trilliard Short scale uses sextillion; long scale uses trilliard.
1024 1,000,000,000,000,000,000,000,000 One septillion One quadrillion The names continue to diverge further as the exponents grow.

Common Naming Mistakes

  • Assuming million is different: Both systems use “million” for 1,000,000. The differences only begin after this point.
  • Confusing milliard with million: A milliard is 1,000,000,000 (one billion in the short scale), which is one thousand times larger than a million.
  • Reading long-scale billion as short-scale billion: If a European document written in the long scale mentions a billion, it means 1012, not 109.
  • Relying only on the word: It is safer to look for the raw digits or scientific notation to confirm the value.

Quick Practice

  1. What is 1,000,000 called in both scales?
  2. What is 109 called in the short scale?
  3. What is 109 called in the long scale?
  4. What is 1012 called in the short scale?
  5. What is 1012 called in the long scale?
  6. Why can the word “billion” be confusing?

Answers

  1. It is called one million in both scales.
  2. It is called one billion.
  3. It is called one milliard.
  4. It is called one trillion.
  5. It is called one billion.
  6. It can mean either 109 (nine zeros) or 1012 (twelve zeros) depending on the scale system being used.

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FAQs

What is the difference between short scale and long scale?

The short scale increases by factors of 1,000 for each new large number name after million. The long scale increases by factors of 1,000,000 and uses intermediate “-illiard” names for the values in between.

Is a billion 109 or 1012?

It depends on the scale. In the short scale, a billion is 109 (1,000,000,000). In the long scale, a billion is 1012 (1,000,000,000,000).

What is a milliard?

A milliard is the long scale name for 1,000,000,000 (109). In the short scale, this same value is called one billion.

What is a trillion in the short scale?

In the short scale, a trillion is 1,000,000,000,000, which is written as 1012.

What is a trillion in the long scale?

In the long scale, a trillion is 1,000,000,000,000,000,000, which is written as 1018.

How can I avoid confusion with large number names?

The safest way to avoid confusion is to check the actual digits, count the zeros, or look for scientific notation (powers of ten) to verify the intended value.

Short Practical Summary

The short scale and long scale are two distinct systems for naming large numbers. While they both agree that one million is 1,000,000, they differ on everything after. The short scale uses “billion” for 109, whereas the long scale uses “milliard” for 109 and reserves “billion” for 1012. To avoid errors, always verify the numeric digits or power of ten when working with international or historical documents.