Decimals explained for parents

"$3.45" makes sense at the shops. Then homework asks what the 4 means in 3.45, why 0.8 is larger than 0.75, or how to multiply 2.4 × 3 - and kitchen-table confidence wobbles. This guide unpacks decimals across Years 4 to 6 in Australian Curriculum language, with home activities that stay concrete.

It goes deeper than the short decimal mentions inside our Year 4 maths, Year 5 maths and Year 6 maths guides. Strong place value is the floor; fractions and money maths are the everyday bridges.

The big idea: place value to the right of the point

A decimal is still place value - just continuing to the right of the ones place. The first digit after the decimal point is tenths; the second is hundredths. So in 3.45:

• 3 means three ones
• 4 means four tenths (4/10)
• 5 means five hundredths (5/100)

Ten tenths make one one; ten hundredths make one tenth - the same "ten of these make one of the next place" rule children already know for ones, tens and hundreds.

Australian Curriculum Mathematics (version 9) builds this carefully from Year 4 tenths and hundredths, through Year 5 ordering (including decimals greater than one), into Year 6 calculation with all four operations and links to percentages (Year 4, Year 5, Year 6).

If hundreds-tens-ones still wobble, pause decimal lessons and rebuild via the place value guide first. Decimals on a shaky floor tip over.

Year 4: tenths, hundredths and money clothes

By the end of Year 4, students use place value for tenths and hundredths in decimal form, and make connections between fractions and decimal notation (Year 4 mathematics; Year 4 place value planning).

Money is the friendliest model: $0.70 is seventy cents, or seven tenths of a dollar; $0.05 is five cents, or five hundredths. Metres and centimetres help too (1.25 m is one metre and twenty-five centimetres).

At home:

• Write a price two ways: "$0.70" and "70 cents"; ask what digit sits in the tenths place.
• Count in tenths along a tape number line from 0 to 2 (0.1, 0.2, … 1.0, 1.1…).
• Show 0.5 as five tenths and as one-half of the same whole - the fraction–decimal link from fractions explained.

More Year 4 context: what a Year 4 child should know in maths.

Year 5: ordering decimals (including past one)

Year 5 asks children to write and order decimals, including values greater than one - 2.35, 10.07, 0.8 versus 0.75 (Year 5 mathematics; Year 5 place value planning). Money still helps, but so do metres, kilograms and sports times.

The classic trap: thinking 0.75 is larger than 0.8 because "75 is bigger than 8". Line them up by place: 0.80 has eight tenths; 0.75 has seven tenths - so 0.8 is larger. Zeros after the point are doing a job, just as in whole-number place value.

At home:

• Order 0.8, 0.75 and 1.05 on a number line; ask which digit decided each comparison.
• Rewrite 2.4 as "2 ones and 4 tenths".
• Compare two catalogue prices and say the deciding place out loud.

Common percentages (10%, 25%, 50%, 75%) start connecting to fraction and decimal equivalents in Year 5 - shopping "half off" language is enough without a secondary syllabus. Full Year 5 map: what a Year 5 child should know in maths.

Year 6: operating with decimals

Year 6 expects children to use all four operations with decimals, connect decimal measurements to the metric system, and solve problems involving a fraction, decimal or percentage of a quantity (Year 6 mathematics).

Kitchen-table versions beat worksheet fog: multiply a friendly decimal (2.5 × 4 for a recipe), divide money amounts, estimate whether 3.8 × 2.1 is nearer 8 or 6 before calculating. Equivalence remains the bridge between fractions, decimals and percentages - see fractions explained for the progression.

At home:

• Estimate first: "Is 4.9 × 3 about 15?"
• Convert a measurement story (1.5 kg + 0.25 kg) before jumping to a written method.
• Find 10% or 25% of a pocket-money amount, then name the decimal and fraction cousins.

Full Year 6 map: what a Year 6 child should know in maths.

Common mix-ups (and kinder fixes)

"Longer decimal = bigger number." Children sometimes think 0.75 > 0.8 because more digits. Fix: line digits in columns (ones | tenths | hundredths) or place both on a number line.

Reading 3.45 as "three point forty-five." Prefer "three point four five" or "three and forty-five hundredths" so place value stays visible. Money talk ("three dollars forty-five") is fine in context - just switch models when the page is about places, not prices.

Writing $1.5 instead of $1.50. Money conventionally uses two decimal places for cents. Fix: say "one dollar and fifty cents" while writing; show that 50 cents needs the zero in the hundredths place. More in money maths at home.

Treating the decimal point as "and" glue. 2.3 is not "two and three" as unrelated digits - it is two ones and three tenths. Always name the places.

Skipping straight to algorithms. Years 4–5 are still building meaning. Number lines, money and place-value charts first; written methods when the floor is steady.

If decimal wobbles sit inside a broader "are they behind?" worry, see Is my child behind in maths?.

A simple weekly home routine

1. Two minutes of naming - point to a price, a sports time or a metre mark and say its places (ones, tenths, hundredths).
2. Five minutes of placing - put two or three decimals on a tape number line and explain the order.
3. Five minutes of using it - a short money, measurement or estimate story (Year 6: a friendly multiply or divide).

Stop while it is still friendly. Confidence is part of the foundation. If evenings turn into tears, shrink the session and tell the teacher which bit collapsed - "ordering 0.8 and 0.75" is more useful than "maths is hard". For rising worry, see maths anxiety in primary kids.

Decimal games that do not feel like homework

Price hunt. Find three prices at home or in a catalogue. Order them; name the tenths digit in each.

Make me a decimal. Say "two ones and seven tenths"; your child writes 2.7, then shows it on a number line or with play money.

Zero job. Compare 1.5 and 1.50 in a money context (same amount) versus lining up 1.5 and 1.05 on a number line (different amounts). Talk about what the zero is doing.

Estimate then check. "About how much is 3 × $1.95?" Guess near $6, then refine. Estimation is decimal sense in everyday clothes.

Keep each game under ten minutes. The win is flexible thinking, not speed.

How this links to other guides

• Place value explained - the floor under tenths and hundredths
• Fractions explained - equivalence and fraction–decimal links
• Money maths at home - dollars and cents as decimal models
• Year 4 maths / Year 5 maths / Year 6 maths - full year maps where decimals sit among other topics

A useful parent-teacher question: "Which decimal models and which places (tenths only, or hundredths too) are you using this term?" Matching home language reduces crossed wires.

FAQ

When do children first meet decimals at school?

Formal tenths and hundredths in decimal notation are a Year 4 headline in the Australian Curriculum, often introduced with money and measurement. Informal "point" talk can appear earlier in everyday life - that is fine; keep it playful until school builds the places.

My child can read money but freezes on 0.8 vs 0.75. Why?

Money often stays in two decimal places ($0.80 vs $0.75), which hides the "longer looks bigger" trap. Practise the same comparison on a number line without dollar signs, naming tenths out loud.

Should we teach long multiplication of decimals in Year 4?

Not as the main goal. Year 4 is meaning: tenths, hundredths, fraction links. Written calculation with decimals grows through Year 5–6 once place value is solid.

How do decimals connect to percentages?

Year 5–6 connect common percentages to fraction and decimal equivalents (50% = 1/2 = 0.5). Keep shopping and "ten percent of" stories concrete before leaping to complicated percentage-increase worksheets.

Do we need special decimal toys?

No. Play money, a tape number line, catalogues and kitchen scales are enough. A simple place-value chart (ones | tenths | hundredths) helps when digits start sliding.

A calm next step

When tenths talk feels settled and you want a wider number-skill snapshot at home, Ziado's free check is a one-off, roughly 10-minute adaptive diagnostic with partial results only - no account and no card. The full placement unlocks after signup. It is not NAPLAN practice and it is not the full product; Ziado's ongoing path is adaptive maths (Foundation–Year 6) plus phonics reading (Foundation–Year 4). Explore Ziado maths if you want practice that can meet decimal and place-value skills at the right step. Individual and Family plans, if you continue later, start with a 14-day free trial of the full app — see pricing for current plans.