Training Whole Numbers Place Value and Reading Numbers
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Place Value and Reading Numbers

15 min Whole Numbers

Place Value and Reading Numbers

Understanding place value is the very first step on the path to mathematical fluency. Every number you will ever encounter — from a bank balance to a spacecraft velocity — is built from just ten digits arranged in specific positions, each position carrying ten times the weight of the one to its right.

In this lesson you will learn how to read, write, and compare whole numbers of any size. You will also practice writing numbers in expanded form, which reveals the hidden structure inside every numeral and prepares you for the addition and subtraction algorithms ahead.

Mastering place value now pays dividends throughout every math course that follows, because the same base-ten logic reappears in decimals, scientific notation, and even computer arithmetic.

Every digit in a whole number occupies a place, and the value it represents depends entirely on that position. This is the foundation of our base-ten (decimal) number system.

Definition

Place value is the value of a digit based on its position in a number. Each place is ten times the value of the place to its right.

The Place-Value Chart

BillionsHundred MillionsTen MillionsMillionsHundred ThousandsTen ThousandsThousandsHundredsTensOnes
4507281

The number above is read as four million, five hundred seven thousand, two hundred eighty-one.

Each group of three digits is called a period. From right to left, the periods are: ones, thousands, millions, billions, and so on.

Rules for Reading Whole Numbers

  • Read each period from left to right
  • Say the name of the period after each group (except the ones period): billion, million, thousand
  • Do not say "and" when reading whole numbers — "and" is reserved for the decimal point
  • Use commas to separate periods when writing: $4{,}507{,}281$

Expanded Form

Expanded form shows the value of each digit:

$$4{,}507{,}281 = 4{,}000{,}000 + 500{,}000 + 7{,}000 + 200 + 80 + 1$$

Comparing Whole Numbers

Procedure

To compare two whole numbers:

  1. Count the digits — the number with more digits is larger.
  2. If they have the same number of digits, compare digit by digit from left to right.
  3. The first position where the digits differ determines which number is greater.
Example 1

Write $7{,}035{,}412$ in words.

Seven million, thirty-five thousand, four hundred twelve.

Example 2

Write the number "twelve billion, four hundred six million, fifty thousand, nine" in standard form.

$12{,}406{,}050{,}009$

Example 3

Which is larger: $458{,}921$ or $459{,}012$?

Both have 6 digits. Comparing from the left: $4 = 4$, $5 = 5$, but $8 < 9$ in the thousands place. Therefore $458{,}921 < 459{,}012$.

Example 4

Write $630{,}042$ in expanded form.

$630{,}042 = 600{,}000 + 30{,}000 + 40 + 2$

Example 5

What is the place value of the digit 7 in $3{,}274{,}160$?

The 7 is in the ten-thousands place, so its value is $70{,}000$.

Practice Problems

1. Write $5{,}280{,}003$ in words.
2. Write "nine hundred forty-six thousand, seventy" in standard form.
3. What is the place value of 3 in $2{,}345{,}678$?
4. Write $4{,}090{,}200$ in expanded form.
5. Order from least to greatest: $34{,}589$ ; $34{,}598$ ; $34{,}509$
6. What number is $300{,}000 + 5{,}000 + 60 + 8$?
7. Compare using < , > , or = : $7{,}045{,}200$ ____ $7{,}054{,}200$
8. Write the largest 6-digit number using the digits 3, 0, 8, 5, 2, 9 (each used once).
9. How many periods does the number $2{,}500{,}000{,}000$ have?
10. Write "two billion, seven hundred million" in standard form.
Show Answer Key

1. Five million, two hundred eighty thousand, three

2. $946{,}070$

3. Hundred-thousands place; value = $300{,}000$

4. $4{,}000{,}000 + 90{,}000 + 200$

5. $34{,}509 < 34{,}589 < 34{,}598$

6. $305{,}068$

7. $7{,}045{,}200 < 7{,}054{,}200$

8. $985{,}320$

9. 4 periods (ones, thousands, millions, billions)

10. $2{,}700{,}000{,}000$

Rounding Whole Numbers