Lesson 1.1.4

Place Value (Hundreds, Thousands)

New columns, same rule

You already know that the right-hand digit counts ones and the next digit counts tens. We keep adding columns to the left: the hundreds digit counts how many whole hundreds ( $100$ , $200$ , $300$ …), and the thousands digit counts how many whole thousands ( $1000$ , $2000$ , $3000$ …).

So in $4$ , $052$ the $4$ is not “four ones” — it is four thousands. The $0$ in the hundreds place means “no extra hundreds” after those thousands; the $5$ is five tens; the $2$ is two ones.

Why $10 \times 100 = 1000$

Ten tens make one hundred. Ten hundreds make one thousand. That is why each step left multiplies by ten again: ones → tens → hundreds → thousands.

A number like $3$ , $456$ reads as three thousands, four hundreds, five tens, and six ones — or $3000 + 400 + 50 + 6$ in expanded form. The commas in large numbers are just helpers for the eyes; the place-value chart is the real structure.

Build numbers up to $9$ , $999$

Use the sliders to set each digit. The picture is simplified: each thousand block stands for a full thousand (ten hundreds); each small grid is one hundred; you still see tens rods and ones like before. Match the chart to the total and to the expanded sum.

It is the same idea as tens and ones: each column to the left is worth ten times more. A digit in the hundreds place counts how many whole hundreds; in the thousands place, how many whole thousands.

Thousands: 3

Hundreds: 4

Tens: 5

Ones: 6

Base-ten idea (simplified)

Thousands

Hundreds

Tens and ones

Thousands	Hundreds	Tens	Ones
3	4	5	6

The number: 3,456
Expanded form: 3000 + 400 + 50 + 6 = 3456

Try setting one column to zero and notice what disappears from the picture — the digit $0$ holds the place so the other digits stay in the right columns.

Try it

Answer in your head or on paper, then open “Show answer” to check.

In $7$ , $218$ , what does the $7$ stand for? What does the $1$ stand for?
Show answer
$7$ is in the thousands place, so it means $7000$ . $1$ is in the tens place, so it means $10$ . (The $2$ is two hundreds; the $8$ is eight ones.)
Write $5$ , $030$ in expanded form (thousands + hundreds + tens + ones).
Show answer
$5000 + 0 + 30 + 0$ , or simply $5000 + 30$ — five thousands, no extra hundreds, three tens, no extra ones.
What number is six thousands, two hundreds, and four ones? (No extra tens.)
Show answer
$6204$ . You need a $0$ in the tens place: $6$ thousands, $2$ hundreds, $0$ tens, $4$ ones.
Which is larger, $2$ , $899$ or $2$ , $988$ ? Use place value to explain without calculating the full difference.
Show answer
$2$ , $988$ is larger. Both have $2$ thousands, but $988$ is greater than $899$ in the last three digits — in particular, the hundreds digit $9$ beats $8$ .
How many hundreds are in $4000$ ?
Show answer
$40$ . Each thousand is ten hundreds, so four thousands is $4 \times 10 = 40$ hundreds.

Repeatable practice

Pool order and variants change each time you open the lesson. After a correct answer, use “New question (same type)” for another draw.

1. $Which expanded form matches 6,070?$
Choose one answer6000 + 706000 + 700600 + 70
2. $Which number is greater?$
Choose one answer4,2774,207They are equal
3. $How much is 8 thousands + 1 hundreds + 3 tens + 3 ones? (Write the number with no commas.)$
Your answer
4. $In 5,657, what digit is in the tens place?$
Your answer

What is next?

You can read and build four-digit numbers and write them in expanded form. Next, in lesson 1.1.5, we use place value and the number line to compare and order numbers with confidence.