MathBored

Essential Math Primer
← Back to Primer Overview
U01 • Lesson 19 of 105

Place Value to Millions & Billions

Extends place value understanding from hundreds to millions and billions. Students explore how each place is ten times the value of the place to its right, read and write large numbers in standard, expanded, and word form, and compare and order numbers up to the billions place.

Upper Elementary • 3-5

Prerequisites: K02

Key Concepts

  • place value patterns (x10 relationship)
  • reading and writing numbers to billions
  • expanded form with large numbers
  • comparing and ordering large numbers

Place Value to Millions and Billions

You already know about ones, tens, and hundreds. Now we are going to explore numbers that reach into the millions and billions. These enormous numbers describe things like populations, distances in space, and government budgets.

The Place Value Pattern

Our number system follows one simple rule: each place is 10 times the value of the place to its right.

BillionsHundred MillionsTen MillionsMillions Hundred ThousandsTen ThousandsThousands HundredsTensOnes
1,000,000,000100,000,00010,000,0001,000,000 100,00010,0001,000 100101

Reading Large Numbers

Commas break numbers into groups of three digits called periods. Read each group, then say the period name: "45,238" is read "forty-five thousand, two hundred thirty-eight."

Three Forms of a Number

FormExample for 3,405,200
Standard form3,405,200
Word formthree million, four hundred five thousand, two hundred
Expanded form3,000,000 + 400,000 + 5,000 + 200

Worked Example 1: Reading a Large Number

Read the number 72,514,308.

  1. Break it into periods: 72 | 514 | 308
  2. Leftmost group: 72 -- say "seventy-two million"
  3. Middle group: 514 -- say "five hundred fourteen thousand"
  4. Last group: 308 -- say "three hundred eight"
seventy-two million, five hundred fourteen thousand, three hundred eight

Worked Example 2: Writing in Expanded Form

Write 6,032,007 in expanded form.

  1. 6 is in the millions place: 6,000,000
  2. 0 is in the hundred thousands place: skip it
  3. 3 is in the ten thousands place: 30,000
  4. 2 is in the thousands place: 2,000
  5. 0 in hundreds, 0 in tens: skip both
  6. 7 is in the ones place: 7
6,032,007 = 6,000,000 + 30,000 + 2,000 + 7

Comparing and Ordering Large Numbers

The strategy is the same as with small numbers: compare digits from left to right.

Worked Example 3: Comparing Millions

Which is greater: 4,583,210 or 4,589,100?

  1. Millions digit: 4 = 4 (same)
  2. Hundred thousands: 5 = 5 (same)
  3. Ten thousands: 8 = 8 (same)
  4. Thousands: 3 vs 9. Since 3 < 9, we have our answer.
4,583,210 < 4,589,100

Common Mistake

Do not confuse the digit with its value. In 5,000,000 the digit 5 has a value of five million, not five. Always check which place a digit sits in.

Real-World Connection

The population of New York City is about 8,300,000. The distance from Earth to the Moon is about 384,400 kilometers. The U.S. national debt is measured in trillions -- that is even beyond billions!

Practice Problems

1. Write 2,508,040 in word form.

Show Answer

Two million, five hundred eight thousand, forty.

2. Write the number "nine hundred fifteen million, three hundred thousand, six" in standard form.

Show Answer

915,300,006

3. What is the value of the digit 7 in 47,321,000?

Show Answer

7 is in the millions place, so its value is 7,000,000 (seven million).

4. Order from least to greatest: 3,200,000 ; 3,020,000 ; 3,200,001

Show Answer

3,020,000 < 3,200,000 < 3,200,001. The first two differ in the hundred thousands place (0 vs 2), and the last two differ only in the ones place.

5. Write 8,060,300 in expanded form.

Show Answer

8,000,000 + 60,000 + 300

Lesson Summary

Overview