Read & represent numbers to 100 000
Theory
Reading and representing numbers to 100 000 is a Year 4 place value skill: writing five-digit numbers as digits and in words, showing them on place value charts and number lines, and using standard and expanded form. This Year 4 maths page explains ten thousands, thousands, hundreds, tens and ones, the role of zero, renaming, rounding to the nearest thousand, and how to compare and order numbers to 100 000. In the Australian Curriculum this is Year 3 content and in the Victorian Curriculum it is Level 3; it is taught in Year 4 in Western Australia. Curriculum: VC2M3N02 (Level 3) / AC9M3N01 (Year 3).
A five-digit number is built from five places: ten thousands, thousands, hundreds, tens and ones. The place a digit sits in tells you its value. In \(71\,643\) the 7 means 7 ten thousands, the 1 means 1 thousand, the 6 means 6 hundreds, the 4 means 4 tens and the 3 means 3 ones.
The same number can be shown in different ways. Standard form is just the digits, like \(71\,643\). Word form says it out loud: seventy-one thousand, six hundred and forty-three. Expanded form shows each part added together: \(71\,643 = 70\,000 + 1000 + 600 + 40 + 3\).
When you read a five-digit number, read the first two digits together as a number of thousands: \(71\,643\) is “seventy-one thousand”, then the last three digits as usual. A small space groups the thousands, so we write \(71\,643\), not \(71643\).
Place value means a digit is worth different amounts in different columns. The 9 in \(93\,418\) is worth \(90\,000\), but the 9 in \(13\,948\) is worth 900. A zero is a placeholder: in \(60\,307\) the zeros show there are no thousands and no tens.
Numbers to 100 000 do not need formulas, but these place value facts help you build, rename and round them.
How to read and write a number to 100 000
- Split at the space. The digits before the space tell how many thousands; read them as one number (for example “seventy-one thousand”).
- Read the rest. Read the last three digits as hundreds, tens and ones.
- Check the zeros. A 0 means that place is empty, but it must still be written so the other digits stay in their columns.
How to read a number line
- Find the jump. Count the gaps between two labelled numbers. \(10\,000\) split into 10 gaps means each gap is \(1000\).
- Count on from a label. Start at the labelled number before the arrow and count on in jumps.
How to compare, rename and round
- Compare from the left. Compare ten thousands, then thousands, then hundreds, and so on. The first place that differs decides.
- Rename. To find how many thousands are in a number, cover the last three digits; for hundreds, cover the last two; for tens, cover the last one.
- Round to the nearest thousand. Check the hundreds digit and round up for 5 or more.
| \(61\text{ thousands}\) | \(=\) | \(61\,000\) |
| \(3\text{ hundreds},\ 7\text{ ones}\) | \(=\) | \(307\) |
| \(61\,000 + 307\) | \(=\) | \(61\,307\) |
The number is \(61\,307\). The 0 holds the tens place.
| \(9\text{ thousands}\) | \(=\) | \(9000\) |
| \(29\,563\) | \(=\) | \(20\,000 + 9000\) |
| \(\) | \(\) | \(+\ 500 + 60 + 3\) |
The 9 is in the thousands place, so it is worth \(9000\).
| \(\text{each gap}\) | \(=\) | \(10\,000 \div 10 = 1000\) |
| \(50\,000 + 3000\) | \(=\) | \(53\,000\) |
The arrow points to \(53\,000\).
| \(\text{ten thousands}\) | \(:\) | \(\text{all }4\) |
| \(\text{thousands}\) | \(:\) | \(0,\ 5,\ 0\) |
| \(40\,050\text{ vs }40\,500\) | \(:\) | \(0 < 5\text{ hundreds}\) |
In order: \(40\,050,\ 40\,500,\ 45\,000\).
(ii) How many hundreds are in \(85\,000\)?
(iii) Fill the gap: \(85\,000 = 70\,000 + \underline{\phantom{0000}}\)
| \(85\,000\) | \(=\) | \(85\text{ thousands}\) |
| \(85\,000\) | \(=\) | \(850\text{ hundreds}\) |
| \(85\,000 - 70\,000\) | \(=\) | \(15\,000\) |
(i) \(85\) thousands.
(ii) \(850\) hundreds.
(iii) \(15\,000\), because 8 ten thousands is the same as 7 ten thousands and 10 thousands.
(i) What number do the blocks show?
(ii) She trades 10 thousands for 1 ten thousand. What does she have now?
| \(20\,000 + 13\,000\) | \(=\) | \(33\,000\) |
| \(33\,000 + 50\) | \(=\) | \(33\,050\) |
| \(13\text{ thousands}\) | \(=\) | \(10\,000 + 3000\) |
(i) \(33\,050\).
(ii) 3 ten thousands, 3 thousands and 5 tens. The number is still \(33\,050\).
| \(9\text{ ones} + 1\) | \(=\) | \(1\text{ ten}\) |
| \(59\,999 + 1\) | \(=\) | \(60\,000\) |
Every 9 rolls over to 0 and the 5 ten thousands become 6: \(60\,000\).
| \(\text{hundreds digit}\) | \(=\) | \(7\) |
| \(7\) | \(\ge\) | \(5 \Rightarrow \text{round up}\) |
| \(26\,718\) | \(\to\) | \(27\,000\) |
\(26\,718\) is closer to \(27\,000\) than to \(26\,000\).
(i) What is the largest five-digit number?
(ii) What is the smallest five-digit number?
| \(\text{largest}\) | \(:\) | \(97\,420\) |
| \(\text{smallest}\) | \(:\) | \(20\,479\) |
(i) \(97\,420\).
(ii) \(20\,479\). The 0 cannot go first, so 2 leads and 0 comes next.
Common pitfalls
Frequently asked questions
How do you write a five-digit number in words?
Read the thousands part first, then the hundreds, tens and ones. For \(71\,643\) you say seventy-one thousand, six hundred and forty-three.
What is the value of the digit in the ten thousands place?
A digit in the ten thousands place is worth that many lots of \(10\,000\). In \(93\,418\) the 9 is worth \(90\,000\).
How do you write a number to 100 000 in expanded form?
Add the value of each digit. For example, \(60\,307 = 60\,000 + 300 + 7\). Places with a zero are left out of the sum.
How many thousands are in 38 000?
There are 38 thousands in \(38\,000\). Cover the last three digits to see the number of thousands.
How do you compare two five-digit numbers?
Compare the ten thousands digit first. If they are equal, compare the thousands, then the hundreds, then the tens, then the ones. The first place that is different decides which number is larger.
What is the largest five-digit number?
The largest five-digit number is \(99\,999\). One more than \(99\,999\) is \(100\,000\), which is the first six-digit number.