Math // Fractions

Decimals to three places

Solve problems involving numbers with up to three decimal places

Ages
9 to 10
Type
Method
Builds on
2 topics
Leads to
0 topics
Standards
1 code

Quick check

If the learner is filling a tank that holds 5.000 litres and has poured in 2.375 litres, can they work out how much more is needed to fill it?

Ask this to see whether the topic is secure.

Topic // Mastery

What mastery looks like

What a learner can do once this topic is secure.
  • Calculate the total of three measurements: 1.234 m + 0.567 m + 2.199 m
  • A bottle holds 1.5 litres; 0.375 l is poured out — how much remains?
  • Find two numbers with 3 d.p. that add to make 1

Topic // Map

Where this fits

What to learn first and what this topic opens up, with the reason for each link. Required links come first.
  • RequiredMust come first
  • HelpfulHelps, but not essential

Before this

2 topics
  • Comparing DecimalsRequired

    Fractions // Ages 9 to 10

    Comparing decimals to 3dp feeds into solving problems with them

  • Decimal place value (age 9+)Helpful

    Fractions // Ages 9 to 10

    Rounding decimals supports problem-solving with decimals

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Decimals to three places

Ages 9 to 10 // Method

Leads to

0 topics

Nothing in the catalogue builds on this topic yet. Browse Fractions

Topic // Research-informed

Teaching notes

From the Marble Skill Taxonomy. These notes have not been validated in classrooms, so treat them as a starting point for your own judgement.

The approach

Solving problems with numbers to three decimal places extends place value to thousandths and depends on careful alignment. Adding and subtracting means lining up the decimal points, equalising lengths by padding with zeros (1.5 = 1.500), reading each column as ones, tenths, hundredths and thousandths, and carrying or borrowing across columns exactly as with whole numbers. 'Find two numbers to 3 d.p. that make 1' exercises complements to a whole (0.375 + 0.625 = 1.000). Estimating first guards against place-value slips.

Common misconceptions

  • Right-justifies ragged decimals instead of aligning the point (1.234 + 0.567 + 2.199)
  • Treats the decimal tail as a separate whole number ('longer is larger')
  • Forgets to pad and borrow across the point (1.5 − 0.375)
  • Complement-to-1 errors: completes each column to 10 independently (0.375 + 0.725) or ignores the required 3 d.p. (0.4 + 0.6)

Useful representations

  • Place-value columns to thousandths, aligned on the point
  • Number line zoomed to thousandths
  • Bar / complement model for 'make 1'
  • Measuring contexts (litres, metres) for the quantities

Teaching practices

  • Align the decimal points and pad ragged lengths with zeros (1.500 − 0.375) so every place value lines up
  • Read numbers by place value all the way to thousandths
  • Carry and borrow across decimal columns just as with whole numbers
  • Use complement-to-1 reasoning (subtract from 1.000) for 'add to make 1' tasks and check by adding
  • Estimate first (1.5 − 0.375 ≈ 1.5 − 0.4 ≈ 1.1) to catch magnitude errors

Activities to try

  1. 1

    Column workbench: aligning and padding to thousandths

    Why it works: 1.5 and 1.500 are the same number, but writing the padding zeros makes the hundredths and thousandths columns available so the digits line up and the borrow can ripple from the tenths through the hundredths to the thousandths.

    1. Set out the subtraction 1.5 − 0.375 in place-value columns (ones, tenths, hundredths, thousandths) aligned on the decimal point — the measuring context is a 1.5-litre bottle from which 0.375 l is poured out, finding how much is left.
    2. Rewrite 1.5 as 1.500 by writing zeros in the empty hundredths and thousandths columns before subtracting.
    3. Carry out the subtraction, borrowing just as with whole numbers (from the tenths through the hundredths to the thousandths), to reach 1.125 l remaining.
    4. Add the three ragged measurements 1.2 m + 0.567 m + 2.233 m by first aligning on the point and padding every number to the same length (1.2 = 1.200), then summing each column to get 4.000 m.
    5. Estimate first (1.5 − 0.375 ≈ 1.5 − 0.4 ≈ 1.1) and check the answer's size against the estimate.
  2. 2

    Make 1: complements to a whole at three decimal places

    Why it works: A complement to 1 is found by subtracting from the whole written as 1.000, not by completing each column to 10 independently; the two parts together must make exactly one whole.

    1. Given 0.375, find the second number to 3 d.p. that makes exactly 1.000, by subtracting from 1.000 (1.000 − 0.375 = 0.625).
    2. Check the pair by adding the two numbers back together and confirming they total exactly 1.000.
    3. Explain why 0.4 + 0.6, though it equals 1, does not meet the 'three decimal places' requirement, and give a valid 3-d.p. pair (such as 0.001 + 0.999).
    4. Optionally model the complement as two lengths placed end to end along a bar representing one whole, where only the correct pair closes the gap with no gap or overlap and a running total shows 1.000.

Topic // Standards

Curriculum standards

Codes for the curriculum statements this topic maps to. Each publisher owns its standard text.
The national curriculum in England: Key stages 1 and 2 framework document
Ma5/2.4j

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