Decimal Place Value to the Trillions

Instructor: Thomas Higginbotham

Tom has taught math / science at secondary & post-secondary, and a K-12 school administrator. He has a B.S. in Biology and a PhD in Curriculum & Instruction.

Really large numbers, like those in the trillions, can sometimes be confusing. In this lesson, learn about the details of decimal place value, which help us organize and recognize numbers, and find out how to name place value up to the trillions.

Trillions of Dollars

For fiscal year 2016, the United States Federal Government will spend 3.871 trillion dollars. Wow, that's a huge number! It's so big in fact, that it's hard to understand the thousands, millions, and billions of dollars included in that figure. To do that, it is helpful to know how decimal place values, or positional systems, work in the trillions.

What is Place Value?

In our number system, the same digit can have different values in different numbers. For example, the digit 'three' in the number 413 has a different value than does the digit 'three' in the number 386. In the first number, the value of three is 3. In the second number, the value of three is 300. This is all due to place value. Let's take a look at the place values of numbers up to 15 digits long.

trillions

The first thing you might notice about the place value chart above is that the numbers are grouped in threes. You might also notice that commas separate each group of three. Do you see that the right-side place of each group has no prefix, the middle places are preceded by a 'ten', and the third place preceded by a 'hundred'? These notations are all part of the lovely symmetry of place value.

Place Value Reference Groups

You can see that between each group of three is a comma. This comma, which is always at the end of a reference group, helps us keep track of the quantity of the group we are referring to; it also makes really big numbers easier to look at.

Place Value to Trillions References
Place Value to Trillions Separators

The first reference group refers to the thousands, the second group to the millions, the third group to the billions, and the fourth group to the trillions. Unless all of the digits within a reference group are zero, we always state the group's name when saying the number.

In deciphering the names of the groups, you can take advantage of a little trick. The prefix 'bi' means two, while the prefix 'tri' means three. If you know the prefixes for four and five, you can probably guess the names of the next reference groups: quadrillion and quintillion. Beginning with a million, the reference groups are listed below: see if you can predict or find the prefix in them.

  • Million
  • Billion
  • Trillion
  • Quadrillion
  • Quintillion
  • Sextillion
  • Septillion
  • Octillion
  • Nonillion
  • Decillion

Saying Big Numbers Out Loud

We say the decimal number 3,456,529,809 as three billion, four hundred fifty-six million, five hundred twenty-nine thousand, eight hundred nine. However, when referring to 3,000,000,529, we say three billion, five hundred twenty-nine. Notice that we did not mention either the millions or the thousands in the second number. Also, notice that nowhere in the verbalization of the number did we use the word 'and'. We only use the word 'and' when talking about mixed numbers, like five and three quarters. However, I'll bet if you watch TV or listen to radio news, you'll find someone misusing the word 'and' in a big number.

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