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Extend Place Value Relationships to Decimals

Students extend the 10-to-1 place value relationship across the decimal point, understanding that tenths, hundredths, and thousandths each represent 1/10 of the place to their left. They use place value charts to compare the values of the same digit in different positions.

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Extend Place Value Relationships to Decimals

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

0 of 20

20 rungs. A star at the top.

In 8.26, the 2 is worth

How it is taught

0:00 of 3:28

A tenth is ten times a hundredth.

Trailing zeros after the last digit do not change the value.

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.

  1. Find the digit and the place it stands in, under the chart's heading.
  2. One place to the left, the same digit is worth 10 times as much.
  3. 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.

3.47 ÷ 10 = ___ — 0.347. Every digit moves one place to the right: the 3 ones become 3 tenths.

The digit 5 across ones, tenths, and hundredths

Let's see what happens to the digit five as we move it across the decimal point.

Here's a place value chart with three columns: ones, tenths, and hundredths.

Put a five in the ones place. Its value is just five.

Now what if we write a five one column to the right, in the tenths?

A five in the tenths place is worth five-tenths, or zero point five.

Notice — zero point five is one-tenth of five. Moving one place right shrinks the value by ten.

Now write a five one more column to the right, in the hundredths.

A five in the hundredths place is worth five-hundredths, or zero point zero five.

And zero point zero five is one-tenth of zero point five. The same shrinking pattern!

How does the digit 5 change?5 → 0.5 → 0.05ten times smaller each stepOnesTenthsHundredths.5= 55= 0.5× 1105= 0.05× 110Each place right = 110 of the place to its leftPATTERN× 110each place right
Grade 5 · Each place is one-tenth of the place to its left

Each place to the right is one-tenth of the place to its left.

The same digit gets ten times smaller every time it moves one place to the right — and place value keeps going past the decimal point.

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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