Read & represent numbers to 10 000
Theory
Reading and representing numbers to 10 000 is a Year 3 place value skill: writing four-digit numbers as digits and in words, showing them with base ten blocks and place value charts, and using standard and expanded form. This Year 3 maths page explains thousands, hundreds, tens and ones, the role of zero, number lines, counting on and back, renaming, and how to compare and order numbers to 10 000. Curriculum: VC2M3N02 / AC9M3N01.
A four-digit number is built from four places: thousands, hundreds, tens and ones. The place a digit sits in tells you its value. In 1234 the 1 means 1 thousand, 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 \(1234\). Word form says it out loud: one thousand, two hundred and thirty-four. Expanded form shows each part added together: \(1234 = 1000 + 200 + 30 + 4\).
Place value means a digit is worth different amounts in different columns. The 6 in \(6185\) is worth 6000, but the 6 in \(1263\) is worth 60. A zero is a placeholder: in \(4067\) it shows there are no hundreds and keeps the 4 in the thousands place.
Renaming means writing the same number with different groups. Ten hundreds make one thousand, so \(5000\) is 5 thousands or 50 hundreds, and \(4700\) is 47 hundreds.
Numbers to 10 000 do not need formulas, but these place value facts help you build and rename them.
How to read and write a number to 10 000
- Split into places. Look at each digit and name its column: thousands, hundreds, tens and ones.
- Find each value. The thousands digit tells how many thousands, the hundreds digit how many hundreds, and so on down to the ones.
- Put it together. Read the thousands first, then the hundreds, then the tens and ones for word form, or add the parts for expanded form.
How to read a number line
- Find the jump. Count the gaps between two labelled numbers. \(1000\) split into 10 gaps means each gap is \(100\).
- 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 thousands first. If they are the same, compare the hundreds, then the tens, then the ones.
- Explain with place value. Say which place decides, for example “both have 3 thousands, but one has more hundreds”.
How to rename and trade
- Trade 10 for 1. Swap 10 hundreds for 1 thousand (or 1 thousand for 10 hundreds). The number does not change.
- Count the hundreds. Cover the last two digits: \(4700\) shows \(47\) hundreds altogether.
| \(4\text{ thousands}\) | \(=\) | \(4000\) |
| \(0\text{ hundreds},\ 5\text{ tens},\ 2\text{ ones}\) | \(=\) | \(52\) |
| \(4000 + 52\) | \(=\) | \(4052\) |
There are no hundreds, so a 0 holds the hundreds place: \(4052\).
| \(8\text{ hundreds}\) | \(=\) | \(800\) |
| \(7815\) | \(=\) | \(7000 + 800 + 10 + 5\) |
The 8 is in the hundreds place, so it is worth \(800\).
| \(\text{each gap}\) | \(=\) | \(1000 \div 10 = 100\) |
| \(4000 + 3\text{ hundreds}\) | \(=\) | \(4300\) |
The arrow points to \(4300\).
| \(\text{thousands}\) | \(:\) | \(2 = 2 = 2\) |
| \(\text{hundreds}\) | \(:\) | \(6 < 7\) |
| \(2617\text{ vs }2671\) | \(:\) | \(1\text{ ten} < 7\text{ tens}\) |
In order: \(2617,\ 2671,\ 2716\).
(ii) What is one more than \(2999\)?
(iii) What is one less than \(6100\)?
| \(4000 + 100\) | \(=\) | \(4100\) |
| \(2999 + 1\) | \(=\) | \(3000\) |
| \(6100 - 1\) | \(=\) | \(6099\) |
(i) \(4100\).
(ii) \(3000\): the 9 ones, 9 tens and 9 hundreds all roll over.
(iii) \(6099\).
(ii) Write \(4700\) as a number of hundreds.
| \(1\text{ thousand}\) | \(=\) | \(10\text{ hundreds}\) |
| \(5\text{ thousands}\) | \(=\) | \(50\text{ hundreds}\) |
| \(4700\) | \(=\) | \(47\text{ hundreds}\) |
(i) \(50\) hundreds.
(ii) \(47\) hundreds (4 thousands is 40 hundreds, plus 7 more).
(i) What number do his blocks show?
(ii) He trades 10 hundreds for 1 thousand. What does he have now?
| \(3000 + 1200\) | \(=\) | \(4200\) |
| \(4200 + 40 + 6\) | \(=\) | \(4246\) |
| \(12\text{ hundreds}\) | \(=\) | \(1000 + 200\) |
(i) \(4246\).
(ii) 4 thousands, 2 hundreds, 4 tens and 6 ones. The number is still \(4246\).
(i) What is the largest number?
(ii) What is the smallest four-digit number?
| \(\text{largest}\) | \(:\) | \(9,\ 5,\ 2,\ 0 \to 9520\) |
| \(\text{smallest}\) | \(:\) | \(2,\ 0,\ 5,\ 9 \to 2059\) |
(i) \(9520\).
(ii) \(2059\). The 0 cannot go first, so the smallest non-zero digit leads and the 0 goes next.
Common pitfalls
Frequently asked questions
How do you write a four-digit number in words?
Read the thousands first, then the hundreds, then the tens and ones together. For \(4265\) you say four thousand, two hundred and sixty-five.
What is expanded form of a four-digit number?
Expanded form breaks a number into the value of each digit added together. For example, \(4372 = 4000 + 300 + 70 + 2\).
What is the value of a digit in the thousands place?
A digit in the thousands place is worth that many thousands. In \(6185\) the 6 sits in the thousands column, so it is worth 6000, not 6.
What does the zero do in a number like 4067?
The zero is a placeholder. In \(4067\) it shows there are no hundreds and keeps the 4 in the thousands place. Without it the number would be \(467\).
How do you compare two four-digit numbers?
Compare the thousands digits first. If they are equal, compare the hundreds, then the tens, then the ones. The number with the larger digit in the first place that is different is bigger.
How many hundreds are in a thousand?
There are 10 hundreds in one thousand, so 3 thousands is 30 hundreds and 8 thousands is 80 hundreds.
What is the largest four-digit number?
The largest four-digit number is \(9999\). One more than \(9999\) is \(10\,000\), which is the first five-digit number.