Lesson 5: Place Value Through Hundred Trillions, Reading and Writing Whole Numbers

New Concept

The value of a digit depends on its position in a number; this is its place value. We use this to write numbers in expanded notation.

We write a number in expanded notation by writing each nonzero digit times its place value. For example, we write $4320$ in expanded notation this way:

What’s next

Next, you'll tackle worked examples on reading and writing enormous numbers and solve challenge problems using expanded notation.

Property

In our number system the value of a digit depends upon its position within a number. The value of each position is its place value.

Examples

In the number $32,567,890,000,000$, the digit in the trillions place is $2$.
In $12,457,697,380,000$, the place value of the digit $4$ is hundred billions.
In $217,534,896,000,000$, the digit in the ten-billions place is $3$.

Explanation

Think of place value as a digit's address on a very long street! The further left a digit lives, the bigger its house is—from tiny 'ones' all the way up to huge 'trillions' mansions. A digit like 7 in the thousands place is way mightier than a 7 chilling in the tens place.

Property

We write a number in expanded notation by writing each nonzero digit times its place value.

Examples

$5280$ in expanded notation is $(5 \times 1000) + (2 \times 100) + (8 \times 10)$.
$25,000$ in expanded notation is $(2 \times 10,000) + (5 \times 1000)$.
$750,000$ in expanded notation is $(7 \times 100,000) + (5 \times 10,000)$.

Explanation

Expanded notation is like taking a number apart to see its secret formula! You take each digit, multiply it by its personal place value (like thousands or hundreds), and then add all those pieces together. It's a fantastic way to show the true power and value hiding behind each digit in a number.

Property

Put commas after the words trillion, billion, million, and thousand. Hyphenate numbers between 20 and 100 that do not end in zero (e.g., fifty-two). We never include "and" when saying or writing whole numbers.

Examples

$3,406,521$ is written as Three million, four hundred six thousand, five hundred twenty-one.
$1,380,000,050,200$ is written as One trillion, three hundred eighty billion, fifty thousand, two hundred.
Twenty trillion, five hundred ten million is written with placeholders as $20,000,510,000,000$.

Explanation

Writing big numbers is like reading a map where commas are your landmarks, telling you to announce 'million' or 'billion.' Just read the three-digit chunk before each comma and say the period name. Remember to hyphenate numbers like seventy-six, and most importantly, never, ever say the word 'and'—it's forbidden in whole-number-land!