Place value and rounding multi-digit numbers (grade 4) · lesson

What a digit is worth

💡 A digit's value is the digit times its place: ones, tens, hundreds, thousands, or ten thousands.

Read the places from the right: ones, tens, hundreds, thousands, ten thousands.

In 35,091 the 5 is in the thousands place. It is worth 5,000.

🧠 Let's work it out

What is the 2 in 12,906 worth?

What do you think comes next?

💡 When a place has nothing in it, write a 0 there to hold the place.

60,000 + 400 + 3 has ten thousands, hundreds, and ones. It has no thousands and no tens.

Write a 0 in each empty place. So the number is 60,403.

🧠 Let's work it out

Write 30,000 + 2,000 + 80 + 5 as one number.

What do you think comes next?

💡 Compare digits from left to right, and the first place that is different decides.

Start at the biggest place. If the digits match, move one place right.

Stop at the first place where the digits differ. The bigger digit wins, no matter what comes after.

🧠 Let's work it out

Which is greater, 54,320 or 54,302?

What do you think comes next?

💡 To round, look at the digit just to the right of the place you round to: 5 or more rounds up.

To round to the nearest hundred, look at the tens digit. To round to the nearest thousand, look at the hundreds digit.

5 or more rounds up. 4 or less rounds down. Every digit after the rounded place becomes 0.

Rounding up can carry into the next places. 99,600 rounds up to 100,000.

🧠 Let's work it out

Round 31,782 to the nearest thousand.

What do you think comes next?

💡 A digit in one place is worth ten times what it is worth one place to the right.

In 5,555 the hundreds 5 is worth 500. The tens 5 is worth 50.

500 is ten times 50. Every move one place left makes a digit worth ten times more.

🧠 Let's work it out

In 3,333, how many times is the thousands 3 worth the hundreds 3?

What do you think comes next?