Interpret, compare and order numbers with more than 2 decimal places, including numbers greater than one, using place value understanding; represent these on a number line

Students extend place value to thousandths and beyond, align decimal places, use placeholder zeros and locate values between labelled points on a number line.

Compare decimals from the highest place value, treating missing places as zero where useful.

The zero holds the hundredths place. Read 3.407 as three and four hundred seven thousandths, or 3 + 4/10 + 7/1000.

Writing 3.42 as 3.420 makes the comparison with 3.407 transparent. Number-line position confirms the place-value reasoning.

Learning routine: Represent → Reason → Calculate → Interpret → Verify

Success looks like

• Represent the concept accurately
• Explain the place-value or number relationship
• Select an efficient strategy
• Apply it to a new context
• Verify and justify the result

Content description: interpret, compare and order numbers with more than 2 decimal places, including numbers greater than one, using place value understanding; represent these on a number line.

• E1: making models of decimals including tenths, hundredths and thousandths by subdividing materials or grids, and explaining the multiplicative relationship between consecutive places; for example, thousandths are 10 times smaller than hundredths; writing numbers into a place value chart to compare and order them
• E2: renaming decimals to assist with mental computation; for example, when asked to solve 0.6 ÷ 10 they rename 6 tenths as 60 hundredths and say, “if I divide 60 hundredths by 10, I get 6 hundredths” and write 0.6 ÷ 10 = 0.06
• E3: using a number line or number track to represent and locate decimals with varying numbers of decimal places and numbers greater than one and justifying the placement; for example, 2.335 is halfway between 2.33 and 2.34; that is, 2.33 < 2.335 < 2.34 and 5.283 is between 5.28 and 5.29, but closer to 5.28
• E4: interpreting and comparing the digits in decimal measures; for example, the length or mass of animals or plants, such as a baby echidna weighing 1.78 kilograms and a platypus weighing 1.708 kilograms
• E5: interpreting plans or diagrams showing length measures as decimals, placing the numbers into a decimal place value chart to connect the digits to their value

Core idea: Compare decimals from the highest place value, treating missing places as zero where useful.

Remember

• Represent the concept accurately
• Explain the place-value or number relationship
• Select an efficient strategy
• Apply it to a new context
• Verify and justify the result

Important questions

• Write 5.063 in expanded form. Explain using the model or evidence above.
• Compare 2.508 and 2.58. Explain using the model or evidence above.
• Order 0.905, 0.95 and 0.509. Explain using the model or evidence above.
• Locate 3.407 between 3.4 and 3.5. Explain using the model or evidence above.
• Explain why 4.7 = 4.700. Explain using the model or evidence above.

• More digits means greater value — 3.407 is less than 3.42 because 3.407 < 3.420.
• Zero ignored inside a decimal — The zero in 3.407 keeps 7 in the thousandths place.
• Decimal points not aligned — Compare like place values by aligning the decimal points.
• Number-line intervals assumed unequal — Equal numerical steps require equal spatial intervals.

Learn from the Topic Guide and fixed Teacher Slides, complete the Practice Sheet, use Practice for supported feedback, then take the Test when ready.

Students extend place value to thousandths and beyond, align decimal places, use placeholder zeros and locate values between labelled points on a number line.

Compare decimals from the highest place value, treating missing places as zero where useful.

The zero holds the hundredths place. Read 3.407 as three and four hundred seven thousandths, or 3 + 4/10 + 7/1000.

Writing 3.42 as 3.420 makes the comparison with 3.407 transparent. Number-line position confirms the place-value reasoning.

Learning routine: Represent → Reason → Calculate → Interpret → Verify

Success looks like

• Represent the concept accurately
• Explain the place-value or number relationship
• Select an efficient strategy
• Apply it to a new context
• Verify and justify the result

Australian Curriculum Version 9.0

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