Read & represent numbers to 1000
In Year 3 (NSW Stage 2, outcome MA2-RN-01), students learn to read and represent whole numbers to 1000. They write numbers as digits and in words, show them with base ten blocks and place value charts, and describe the value of each digit in the hundreds, tens and ones places.
This topic also covers standard and expanded form, the role of zero as a placeholder, reading number lines, counting on and back by tens and hundreds, renaming hundreds as tens, and how to compare and order three-digit numbers. These place value skills build the foundation for addition, subtraction and larger numbers later in Stage 2.
Theory
Reading and representing numbers to 1000 is a Year 3 place value skill: writing numbers as digits and in words, showing them with base ten blocks and place value charts, and using standard and expanded form. This page explains hundreds, tens and ones, the role of zero, number lines, counting on and back, renaming, and how to compare and order three-digit numbers.
A three-digit number is built from three places: hundreds, tens and ones. The place a digit sits in tells you its value. In 234 the 2 means 2 hundreds, the 3 means 3 tens and the 4 means 4 ones.
The same number can be shown in different ways. Standard form is just the digits, like \(234\). Word form says it out loud: two hundred and thirty-four. Expanded form shows each part added together: \(234 = 200 + 30 + 4\).
Place value means a digit is worth different amounts in different columns. The 5 in \(152\) is worth 50, but the 5 in \(521\) is worth 500. A zero is a placeholder: in \(608\) it shows there are no tens and keeps the 6 in the hundreds place.
Renaming means writing the same number with different groups. Ten tens make one hundred, so \(500\) is 5 hundreds or 50 tens. A number can even be shown with more than 9 tens: 2 hundreds, 16 tens and 3 ones is still a number to 1000 (it is \(363\)).
Numbers to 1000 do not need formulas, but these place value facts help you build and rename them.
How to read and write a number to 1000
- Split into places. Look at each digit and name its column: hundreds, tens and ones.
- Find each value. The hundreds digit tells how many hundreds, the tens digit how many tens, and the ones digit how many ones.
- Put it together. Read the hundreds first, then the tens and ones for word form, or add the parts for expanded form.
How to read a number line
- Find the jump. Look at two labelled numbers and count the gaps between them. \(100\) split into 10 gaps means each gap is \(10\).
- Count on from a label. Start at the labelled number before the arrow and count on in jumps.
How to compare and order
- Compare the hundreds first. If they are the same, compare the tens, then the ones.
- Explain with place value. Say which place decides, for example “both have 4 hundreds, but one has more tens”.
How to rename and trade
- Trade 10 for 1. Swap 10 tens for 1 hundred (or 1 hundred for 10 tens). The number does not change.
- Count the tens in a hundred number. Each hundred is 10 tens, so \(500\) is \(50\) tens.
| \(6\text{ hundreds}\) | \(=\) | \(600\) |
| \(0\text{ tens},\ 8\text{ ones}\) | \(=\) | \(8\) |
| \(600 + 8\) | \(=\) | \(608\) |
There are no tens, so a 0 holds the tens place: \(608\).
| \(3\text{ tens}\) | \(=\) | \(30\) |
| \(739\) | \(=\) | \(700 + 30 + 9\) |
The 3 is in the tens place, so it is worth \(30\).
| \(\text{each gap}\) | \(=\) | \(100 \div 10 = 10\) |
| \(500 + 8\text{ tens}\) | \(=\) | \(580\) |
The arrow points to \(580\).
| \(148,\ 184\) | \(\to\) | \(1\text{ hundred}\) |
| \(418,\ 481\) | \(\to\) | \(4\text{ hundreds}\) |
| \(148\text{ vs }184\) | \(:\) | \(4\text{ tens} < 8\text{ tens}\) |
| \(418\text{ vs }481\) | \(:\) | \(1\text{ ten} < 8\text{ tens}\) |
In order: \(148,\ 184,\ 418,\ 481\).
(ii) What is one less than \(700\)?
(iii) Count back by hundreds from \(860\): write the next three numbers.
| \(490 + 10\) | \(=\) | \(500\) |
| \(700 - 1\) | \(=\) | \(699\) |
| \(860 - 100\) | \(=\) | \(760\) |
(i) \(500\): 10 tens make a new hundred.
(ii) \(699\).
(iii) \(760,\ 660,\ 560\): only the hundreds digit changes.
(i) What number do the blocks show?
(ii) She trades 10 tens for 1 hundred. What does she have now?
| \(200 + 160 + 3\) | \(=\) | \(363\) |
| \(16\text{ tens}\) | \(=\) | \(1\text{ hundred} + 6\text{ tens}\) |
(i) \(363\).
(ii) 3 hundreds, 6 tens and 3 ones. Trading does not change the number.
| \(1\text{ hundred}\) | \(=\) | \(10\text{ tens}\) |
| \(5\text{ hundreds}\) | \(=\) | \(5 \times 10 = 50\text{ tens}\) |
\(500\) is the same as \(50\) tens.
(i) What is the largest number?
(ii) What is the smallest three-digit number?
| \(\text{largest}\) | \(:\) | \(9,\ 2,\ 0 \to 920\) |
| \(\text{smallest}\) | \(:\) | \(2,\ 0,\ 9 \to 209\) |
(i) \(920\).
(ii) \(209\). The 0 cannot go first, or the number would only have two digits.
Common pitfalls
Frequently asked questions
How do you write a three-digit number in words?
Read the hundreds first, then the tens and ones together. For \(462\) you say four hundred and sixty-two.
What is expanded form?
Expanded form breaks a number into the value of each digit added together. For example, \(572 = 500 + 70 + 2\).
What does place value mean?
Place value means the value of a digit depends on its column. In \(152\) the 5 sits in the tens column, so it is worth 50, not 5.
What is the value of zero in a number like 608?
The zero is a placeholder. In \(608\) it shows there are no tens and keeps the 6 in the hundreds place. Without it the number would be \(68\).
How do you compare two three-digit numbers?
Compare the hundreds digits first. If they are equal, compare the tens, then the ones. The number with the larger digit in the first place that is different is bigger.
How many tens are in a hundred?
There are 10 tens in one hundred, so 2 hundreds is 20 tens and 8 hundreds is 80 tens.
What is the largest three-digit number?
The largest three-digit number is \(999\). One more than \(999\) is \(1000\), which is the first four-digit number.