Reading, Writing, and Comparing Big Numbers

Grade 4 Number and Operations in Base Ten: 4.NBT.A.2

In this lesson:

• Write numbers in standard, word, and expanded form
• Compare multi-digit numbers using place value

Learning Objectives for Today's Lesson

You will learn to:

1. Write numbers in standard, word, and expanded form
2. Convert fluently among all three forms
3. Read and write large numbers using periods
4. Compare numbers place by place from the left
5. Explain comparisons using place value

Can You Read This Number?

7042518

Try reading it out loud, right now, before you know any special tricks.

Quick Check: Why Is the 3 Worth 300?

• In a number like 365, the 3 is worth 300, not 30.
• Reason: each place is ten times the place to its right.

Warming Up With a Familiar Number

• Say it: "two thousand, three hundred sixty-five."
• Value each digit: 2,000, 300, 60, 5.
• Combine: 2,000 + 300 + 60 + 5.

Naming the Three Forms of a Number

• Standard form: 2,365 — compact digits and commas.
• Word form: two thousand, three hundred sixty-five.
• Expanded form: 2,000 + 300 + 60 + 5.

The Period Chart Cracks 7,042,518 Open

Read each period as its own small number, then say the period name.

Zeros Hold the Place, But Not a Term

• 7,042,518 has a 0 in the hundred-thousands place.
• That zero must appear in standard form to hold the place.
• But it produces no term in expanded form — there are zero hundred-thousands.

No "And" Except at the Decimal Point

• Correct: three hundred twenty-seven
• Not for whole numbers: three hundred and twenty-seven

"And" is saved for the decimal point — you'll see why next year.

Predict First: Which Expanded Form Is Right?

For 915,403 — is expanded form 9 + 1 + 5 + 4 + 0 + 3, or 900,000 + 10,000 + 5,000 + 400 + 3?

Place Value, Not Face Value: 915,403

• Word form: nine hundred fifteen thousand, four hundred three.
• Standard form: 915,403.
• Correct expanded form: 900,000 + 10,000 + 5,000 + 400 + 3.

Starting From Expanded Form: 260,801

• Expanded form: 200,000 + 60,000 + 800 + 1.
• Standard form: 260,801.
• Word form: two hundred sixty thousand, eight hundred one.

Convert Every Direction, Every Time

Convert each number to the other two forms. Read your word-form answers aloud — no "and."

1. Standard form: 4,120,036
2. Word form: eighty-three thousand, five
3. Expanded form: 500,000 + 7,000 + 90 + 2

Zeros Don't Always Sit Quietly

Every number so far kept its zeros in one tidy spot.

Real numbers scatter zeros across periods — and that's exactly where errors happen.

Predict First: How Do We Read 4,008,200?

Some students will stumble on this one because of the zeros. Try it before advancing.

Reading Period by Period, Even With Zeros

• Millions period: 4 → "four million"
• Thousands period: 008 → "eight thousand"
• Ones period: 200 → "two hundred"

Word form: four million, eight thousand, two hundred.

Find the Error in This Answer

A student writes "four million, eight thousand, two hundred" as 4,800,200.

What went wrong?

Word to Standard: "Six Hundred Two Thousand, Fifty"

• Thousands period: six hundred two → 602.
• Ones period: fifty → 050.
• Standard form: 602,050.

Dictation: Four Numbers, Increasing Difficulty

1. Thirty-five thousand, nine hundred twelve
2. Two hundred seven thousand, sixty
3. Five million, forty thousand, three hundred eight
4. Given in standard form this time — write 100,010 in words.

From Writing Numbers to Judging Them

You can already read and write any number we throw at you.

Now: given two numbers, which one is bigger?

More Digits Always Wins: 52,481 vs. 9,999

• 52,481 has 5 digits. 9,999 has 4 digits.
• A five-digit number is at least 10,000. A four-digit number is at most 9,999.
• So 52,481 > 9,999 — no need to compare individual digits.

Same Digit Count: Scan Left to Right

• 74,856 vs. 74,912 — both have 5 digits.
• Ten-thousands: 7 = 7 (tied). Thousands: 4 = 4 (tied).
• Hundreds: 8 vs. 9 — since 9 > 8, 74,912 > 74,856.

Predict First: Does the Tail Matter?

You already found 74,912 > 74,856 from the hundreds place — but the last two digits are 56 and 12, and 56 is bigger. Does that change anything? Predict before advancing.

One Place Beats Everything After It

• Compare 900 and 899: hundreds digit 9 vs. 8 — 900 wins.
• The tens and ones in 899 total 99 — still less than one more hundred.
• No combination of smaller places can ever overturn a higher place.

The Backward-Looking Trap: 403,200 vs. 403,099

• Hundred-thousands 4 = 4. Ten-thousands 0 = 0. Thousands 3 = 3.
• Hundreds: 2 vs. 0 — since 2 > 0, 403,200 > 403,099.
• 403,099 only looks bigger because of its long tail of 9s.

Equal, and Justify Your Reasoning

• 815,400 = 815,400 — every place matches, so the numbers are equal.
• Explain: why is 549,000 > 548,999?

Same Value, Wearing Different Disguises

Reading, writing, and comparing have been three separate skills so far.

Real problems rarely hand you numbers already in the same form.

Convert Both, Then Compare: A vs. B

• Number A: "three hundred forty-two thousand, five hundred eight" → 342,508.
• Number B: 300,000 + 40,000 + 2,000 + 600 + 8 → 342,608.
• Hundreds: 5 vs. 6 — since 6 > 5, 342,508 < 342,608.

City Populations and a Word Trap

• City A: population 1,025,300.
• City B: "one million, twenty-five thousand, thirty" → 1,025,030.
• Hundreds: 3 vs. 0 — City A has the larger population.

Solo Commit: One Pair, No Help

Which is greater, 67,204 or 67,240? Decide alone before comparing with a partner.

Order Three Numbers, No Scaffolding

Arrange from least to greatest: 89,450; 89,540; 89,405.

No chart is drawn for you this time — build your own strategy.

All Three Forms, Then Compare

Write 296,004 in standard, word, and expanded form. Then compare it to 296,040 using >, =, or <.

Four Common Mistakes to Double-Check

Save "and" for the decimal point, not whole numbers.

Assign words to periods before writing any digit.

Expanded form uses each digit's value, not the bare digit.

Compare from the leftmost place — a longer tail can lie to you.

Key Takeaways From This Lesson

✓ Standard, word, and expanded form are three ways to write one number.
✓ Periods let you read any number as small ones in a row.
✓ Compare from the left — the first differing place decides.
✓ No smaller place can ever overturn a higher one.

Coming Up Next: Rounding Multi-Digit Numbers

Rounding asks which of two neighboring "round" numbers your number is actually closer to — and that's a comparison in disguise.