Use decimal place value up to three places

What you will learn

• Use decimal place value up to three places

Models used: number sentences, stories, diagrams.

Before you start

• Express decimals as fractions

Each place is ten times smaller

What does each digit in 0.347 tell us about the amount?

1. Read the place heading before the digit. A counter in a different column has a different value.

   Start with three tenths. The 3 belongs in the tenths column because it counts pieces of size one tenth.

   0.3 = 3 tenths

   Splitting keeps the whole amount but makes each counted part smaller. That is how place value continues after ones.

   Ones0

   Tenths3

   0.3 = 3 tenths

2. Read the place heading before the digit. A counter in a different column has a different value.

   Split a tenth into ten hundredths. Add four hundredths; the three tenths stay where they are.

   0.34 = 0.3 + 0.04

   Ones0

   Tenths3

   Hundredths4

   0.34 = 3 tenths + 4 hundredths

3. Read the place heading before the digit. A counter in a different column has a different value.

   Split a hundredth into ten thousandths. Add seven thousandths in the next column.

   0.347 = 0.3 + 0.04 + 0.007

   Ones0

   Tenths3

   Hundredths4

   Thousandths7

   0.347 = 3 tenths + 4 hundredths + 7 thousandths

4. Read the place heading before the digit. A counter in a different column has a different value.

   A digit tells us how many; its column tells us the size of each piece. Here the 7 means seven thousandths, not seven ones.

   Value of 7: 0.007

   Ones0

   Tenths3

   Hundredths4

   Thousandths7

   0.347 = 3 tenths + 4 hundredths + 7 thousandths

Worked example: A new example, together

What is the value of the tenths digit in 0.410?

1. Read the place heading before the digit. A counter in a different column has a different value.

   Follow one whole into tenths, then one tenth into hundredths.

   Each decimal column names a unit ten times smaller than the one before it. Matching those units keeps the value clear.

   Ones0

   Tenths4

   Hundredths1

   Thousandths0

2. Read the place heading before the digit. A counter in a different column has a different value.

   The column is tenths.

   Ones0

   Tenths4

   Hundredths1

   Thousandths0
   What is the value of the tenths digit in 0.410?

   0.4

3. Read the place heading before the digit. A counter in a different column has a different value.

   The column is tenths.

   Ones0

   Tenths4

   Hundredths1

   Thousandths0

   0.41 = 4 tenths + 1 hundredth

4. Read the place heading before the digit. A counter in a different column has a different value.

   Its digit is 4.

   Ones0

   Tenths4

   Hundredths1

   Thousandths0

   0.41 = 4 tenths + 1 hundredth

5. Read the place heading before the digit. A counter in a different column has a different value.

   4 ÷ 10 = 0.4.

   Ones0

   Tenths4

   Hundredths1

   Thousandths0

   0.41 = 4 tenths + 1 hundredth

6. Read the place heading before the digit. A counter in a different column has a different value.

   Check the result against the question we started with.

   Undo the operation to recover the starting quantity.

   We found 0.4. Each decimal column names a unit ten times smaller than the one before it. Matching those units keeps the value clear.

   Ones0

   Tenths4

   Hundredths1

   Thousandths0

   0.41 = 4 tenths + 1 hundredth

Common mistakes to discuss

• More digits means a larger number. Compare place by place from the left. 0.4 is greater than 0.35, because 4 tenths beats 3 tenths.

Check your understanding

• Use decimal place value up to three places
• explain decimal places as repeated equal subdivision
• check the answer against the original quantities and units

Explain your reasoning to an adult, then try a fresh question in the interactive lesson. A result from one attempt is not proof of lasting mastery.