How big are millions, billions, and trillions?

The numeral system of the natural numbers is decimal, because the groupings of the units are made in groups of ten. Thus, the numbers can be counted like this:

• Units , from one to nine.
• Tens , from ten to ninety.
• Hundreds , from one hundred to nine hundred.
• Thousands , from one thousand to nine thousand.
• Tens of thousands , from one hundred thousand to nine hundred thousand.
• Millions , from one million to nine million.
• Tens of millions , from ten million to ninety million.
• Hundreds of millions , from one hundred million to nine hundred million.

What happens to numbers that exceed hundreds of millions? At the end of the 17th century, the numbers went from being separated into groups of six digits to the modern grouping of three digits. Consequently, the so-called short and long numbering scales appeared .

English-speaking countries, as well as Brazil, Puerto Rico, Russia, Turkey, and Greece, use the short scale, in which numbers after hundreds of millions are called trillions. This, while in most European and Latin American countries, which use the long scale, the following numbers are known as “thousands of millions”; although the use of the term trillion has become widespread.

Origin of the terms million and billion

The word million dates from the 13th century and is of English origin. In the dictionary of the Royal Spanish Academy, million to quintillion are accepted words, but from then on the terms that follow in the scale do not appear: “sextillion”, “septillion”… However, they are commonly used words in Spanish.

On the other hand, the names billions and trillions were first used in 1475 in France. The original meaning of the trillion was one million one million, a number followed by twelve zeros (such as 1,000,000,000,000); this is the definition used in most non-English speaking countries. By contrast, English-speaking countries and those using the short scale designate a trillion as a number followed by nine zeros (such as 1,000,000,000).

Naming large numbers

Scientific notation expresses numbers as multiples of a number between 1 and 10, and 10 raised to an exponent, which indicates how many times the first factor must be multiplied by 10. This allows expressing very small or too large numbers that are difficult to operate. Thus, instead of writing 10, write 10 ¹ , instead of writing 100, write 10 ² , and so on. The exponent also indicates the number of zeros that will follow the 1, which makes it easier to write numbers with many digits with few symbols.

According to the long numbering scale, these are the names of some numbers.

In addition to scientific notation, authorities such as the Fundación del Español Urgente FundéuRAE recommend a series of keys for writing figures that have many digits:

1. Thousands are separated with a space, every three digits. It is not correct to use a point or a comma, since these are used to separate decimals.
2. In four-digit numbers, the space can be omitted. For example, write 2022, not 2022.
3. Millions are not denoted by symbols such as apostrophes, commas, and periods. For example, you write 5,000,000, not 5,000,000 or 5,000,000.
4. It is not appropriate to add words between figures. For example, write 2,809,900, not 2,809,900.
5. The sets of digits that are codes, such as identification numbers, telephone numbers, among others, are written without taking into account the previous recommendations, but according to the conventions established according to the context.
6. To express millions in currency, the prefixes mega (M) or kilo (k) can be written, as stipulated by local convention.

Sources

Aponte, Gladys., Pagan, Estela., Pons, Francisca. Basic Mathematics Fundamentals . Editorial Pearson., Mexico, 1998.  

FundéuRAE. Thousands and millions, writing keys . Urgent Spanish Foundation, sf

Population Sáez, Alfonso. What is a trillion and why does it confuse us so much ? ABC Ciencia, May 13, 2019.