ACARA v9 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”
Builds on Year 4, where place value first reached to the right of the ones, giving the tenth and the hundredth their own places, each step right worth ten times less than the place before. Year 5 keeps that same machine turning: past the hundredth comes the thousandth, and the pattern need never stop. The work now is to read, compare and order numbers that carry three or more decimal places, including numbers larger than one, and to find their exact home on a number line.
The places keep going to the right
In Year 4 the places to the right stopped, for most purposes, at the hundredth. Nothing forces them to stop there. Take a hundredth and split it into ten equal parts, and each part is a thousandth, written 0.001. The same ten-times rule that built tens, hundreds and thousands to the left of the ones now runs to the right: ones, then tenths, then hundredths, then thousandths, each place exactly ten times smaller than the one before it. Seeing the ladder of places laid out side by side makes the shrinking feel ordinary rather than mysterious, and it shows why a fourth or fifth decimal place is simply more of the same.
The ladder of places
Each place to the right is ten times smaller than the one before.
Start with one whole. Reveal the places to its right, each one ten times smaller.
Past the hundredth: the thousandth
A thousandth is not a strange new object; it is one whole shared into a thousand equal parts, or equally one hundredth shared into ten. Because ten thousandths rebuild a single hundredth, and ten hundredths rebuild a tenth, the three small places nest neatly inside one another. A number such as 2.375 is then two ones, three tenths, seven hundredths and five thousandths, every digit reporting how many of its own place are present. Building such a number from its parts, rather than reading it as a long string of figures, is what keeps the thousandths place honest and stops the familiar slip between 2.375 and 2.0375.
Build a number to thousandths
Ones, then the point, then tenths, hundredths and thousandths.
Read each digit by its place, then build the number greater than one from its parts.
Numbers larger than one, read to the thousandth
Whole-number value and decimal value live together in one number, divided only by the point. To the left of the point the digits count ones, tens and hundreds in the usual way; to the right they count tenths, hundredths and thousandths. Reading 12.406 is therefore one ten, two ones, four tenths, no hundredths and six thousandths, and the value is assembled from those parts just as a whole number is. The point is not the middle of the number and not a comma; it simply marks where the ones place ends and the shrinking places begin, so a number greater than one is read across the point in a single, steady sweep.
Zoom in on the line
Find the tenth, then the hundredth, then the thousandth.
Which tenth does 1.425 fall in? Find it, then zoom in.
Every decimal has a place on the line
The number line gives every decimal an exact address, found by the same jumps as whole numbers, only smaller. To place 1.425, first decide which tenth it falls in, between 1.4 and 1.5; then zoom into that tenth and find the hundredth, between 1.42 and 1.43; then zoom once more to count the thousandths and land precisely on 1.425. Each zoom is the previous interval shared into ten, the very same move that created the next place. Once a child can locate the rough tenth and then refine, step by step, to the thousandth, ordering several decimals becomes a matter of reading positions along the line, because further to the right always means larger.
Which is larger?
Line the decimals up by place, then compare from the left.
A longer decimal is not always larger. Line them up by place, then compare.
Comparing by place, not by length
A longer string of digits does not make a decimal larger; only the value in each place does. Comparing 2.305 with 2.35 catches this trap directly: line the numbers up by place, padding the shorter with a zero so 2.35 reads as 2.350, then compare from the left. The ones match, the tenths match, and at the hundredths place a five beats a zero, so 2.35 is the larger number despite having fewer digits written. The rule is always the same, working left to right and stopping at the first place where the digits differ, which is exactly how the number line orders them too.
Equal, or not?
A trailing zero adds no value; a zero that holds a place does.
Decide whether the number equals a shorter decimal, then check the places.
Trailing zeros tell the truth
A zero on the far right of a decimal adds no value, so 2.5, 2.50 and 2.500 are three names for one number, and writing the extra zeros is sometimes useful for lining numbers up to compare. A zero that sits between the point and a digit is a different matter entirely, because it holds a place open: 2.05 is two ones and five hundredths, far smaller than 2.5. Place is everything, every time a decimal is read, compared or ordered. With thousandths built, numbers greater than one read across the point, positions found on the line and values compared by place, the rest of Year 5 Number can lean on decimals with confidence.
Quick self-check
1. In the number 3.408, what is the 8 worth?
2. Which number is larger, 2.305 or 2.35?
3. On a number line, 1.425 sits...
4. Which decimal is equal to 3.7?
5. Ordered from smallest, which of 4.06, 4.6 and 4.006 comes first?