Understand 10-to-1 Place Value Relationships

Students recognize that each place in a multi-digit number is 10 times the value of the place to its right. They use whole number examples to build the foundational understanding of multiplicative place value relationships before extending to decimals.

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Grade 5 · Place Value Understanding for Whole Numbers and Decimals · question 1 of 3

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20 rungs. A star at the top.

At the science fair, Raj has 500 stickers in a big box and 50 stickers in a small bag. How many times as many stickers are in the box as in the bag?

How it is taught

0:00 of 3:41

Each place is ten times the place on its right.

A digit's value depends on which place it sits in.

Read it: Ten times, one place left

In 4.44 every digit is a 4. The 4 in the ones is 10 times the 4 in the tenths, and that 4 is 10 times the 4 in the hundredths.

Find the digit and the place it stands in, under the chart's heading.
One place to the left, the same digit is worth 10 times as much.
One place to the right, it is worth a tenth as much.

Ten tenths make one, and ten hundredths make one tenth, so every place holds ten of the place to its right.

Times 10, every digit moves one place to the left: 4.44 × 10 = 44.4.

Divided by 10, every digit moves one place to the right, so each is worth a tenth as much.

A digit is worth ten times as much one place to the left, and a tenth as much one place to the right.

Writing 4.44 × 10 as 4.440 by putting a 0 on the end.

A 0 on the end of a decimal changes nothing. Every digit moves one place left: 4.44 × 10 = 44.4.

The 8 in 0.8 is ___ times the 8 in 0.008. — 100. From the 8 in 0.008 to the 8 in 0.8 is two places to the left: 10 times 10.

3,333

Look at this number — three thousand, three hundred thirty-three. Every digit is a three!

But each three means something different. Why? Because of WHERE each three sits.

The three on the right is in the ones place. Its value is just three.

Move one place to the left. Now the three is in the tens place — its value is thirty.

Thirty is ten times three! One step left multiplied the value by ten.

Next, the hundreds place. This three is worth three hundred.

Three hundred is ten times thirty. Same pattern again.

And the leftmost three sits in the thousands place — three thousand.

Three thousand is ten times three hundred. Every step left, times ten.

See the pattern? Each place is ten times the place to its right.

That's the ten-to-one rule. Same digit, but its value grows by ten every step you move left!

Grade 5 · Each place is 10 times the place to its right

What you see

While they climb, your page writes one true line to ask about tonight, and a short note each Sunday.

MayaGrade 3 · Mathematics

Did you know?

A chessboard has 64 squares — share them out between the 8 rows and each row holds exactly 8.

Today’s goal: 1 star — one skill mastered, every rung of its ladder climbed
Climbing now: Divide within 100

An example student.

MayaGrade 3 · Mathematics

Maya earned 2 stars this week — Interpret multiplication as equal groups, which took 6 answers over 3 days before its star landed 3 days ago and Multiply by 6, 7, 8 and 9. Next up: Divide within 100.

An example week.

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