ACARA v9 CONTENT DESCRIPTION “recognise and extend the application of place value to tenths and hundredths and use the conventions of decimal notation to name and represent decimals”
Builds on Year 3, where place value reached left past 10 000, each new place worth ten times the one before. This unit turns that same machine to the right of the ones, where each new place is worth ten times less. The decimal point is the hinge it all turns on.
Past the ones, the pattern keeps going
By Year 3 the places could grow without limit: tens, hundreds, thousands, ten thousands. Decimals ask the opposite question — what sits to the right of a single one? Nothing new has to be invented, because each step to the right is worth ten times less, mirroring the steps that went left. First comes the tenth, then the hundredth, and the same logic would run on forever. The work here is to make those two new places, the tenth and the hundredth, feel as ordinary as the ones and tens already do.
Split one into ten
One whole bar, ten equal parts. Each part is a tenth.
The whole bar is 1. Split one into ten and each part is one tenth, written 0.1.
What one tenth really is
A tenth is not a strange new object; it is what you get from one whole, split into ten equal parts, keeping a single piece. Hands convince faster than symbols, so the bar is shaded before any digit is written. Ten of these pieces rebuild the whole, which is why 0.1 counted ten times returns to 1.0. A child who has shaded the bar stops reading 0.1 as a tiny whole number and starts reading it as one part out of ten.
A tenth into a hundred
Split every tenth into ten again. Each little cell is a hundredth.
Now cut each tenth into ten. The big square is one whole; one little cell is one hundredth, 0.01.
Splitting the tenth again
To reach hundredths, repeat the move once more: take a tenth and cut it into ten. Now the whole is a hundred little squares, and ten hundredths make one tenth. The hundred-square shows both places at once — a full column is a tenth, a single cell is a hundredth — so a number like 0.27 is two full columns and seven loose cells. This is the picture that ends the classic mix-up between 0.27 and 0.027.
The place-value chart
Ones, then the point, then tenths and hundredths.
Read each digit by its place, then build the number from its parts.
Reading across the point
Line the digits up in a chart and the decimal does its quiet job: the point marks the ones place, not the middle of the number. Whatever stands immediately to its left is ones; the first place to the right is tenths, the next hundredths. Reading 3.27 becomes three ones, two tenths and seven hundredths, and the value is assembled from those parts. The chart makes the shrinking visible, the same ten-times ratio that separates ones, tens and hundreds.
Find it on the line
Locate the tenth, then zoom in to the hundredth.
Which tenth does 0.47 fall in? Find it, then zoom in.
Every decimal has an address
The number line gives decimals a home: a decimal is simply a position on the number line, found by the same jumps as whole numbers, only smaller. To place 0.47, first find the tenth it falls in, between 0.4 and 0.5, then zoom in and count seven hundredths along. Zooming is no trick; it is the hundred-square stretched into a line. Once children can find the rough tenth and then refine to the hundredth, they compare and order decimals without lining up columns, because further along the line always means larger.
Name the decimal
Read it aloud, then check the words against the places.
Read the decimal, say its name aloud, then check the words against the places.
Saying it and writing it
Naming pins the value down. Australians read 0.6 as six tenths and 0.06 as six hundredths, and the gap between them is a full factor of ten, so place matters every time it is spoken. The conventions also explain the friendly trailing zero: 0.4 and 0.40 name the same amount, because a zero in the hundredths place adds no value. Money is the everyday proof, since cents are hundredths of a dollar, which is why a price always shows two decimal places. With tenths and hundredths read, built, placed and named, the rest of Year 4 Number can lean on decimals with confidence.