Read & represent numbers to the millions
Theory
Reading and representing numbers to the millions is a Year 5 place value skill: reading a large number in groups of three digits (millions, thousands and ones), writing it in words and as a numeral, and finding the value of each digit. This Year 5 maths page explains place value houses, zero as a placeholder, how thousands, millions and billions are linked, and how to round large numbers to the nearest hundred thousand or million.
Place value is the value a digit has because of where it sits in a number. The same digit is worth more further to the left: in \(4\,619\,352\) the \(6\) means \(600\,000\), but in \(3\,965\) the \(6\) means only \(60\).
Large numbers are split into groups of three digits, counting from the right: the ones, the thousands and the millions. These groups are called place value houses. Each house has its own hundreds, tens and ones, and each group is read as a three-digit number followed by the house name.
A zero is a placeholder. It keeps a column open so the digits around it stay in the right places. In \(7\,020\,300\) the zeros show there are no hundred thousands, no thousands, no tens and no ones.
The places keep growing by ten times: \(1000\) thousands make one million (\(1\,000\,000\)), and \(1000\) millions make one billion (\(1\,000\,000\,000\)).
Each column is worth ten times the column on its right. These are the place values up to the ten millions:
| Column | Place value |
|---|---|
| Ten millions | \(10\,000\,000\) |
| Millions | \(1\,000\,000\) |
| Hundred thousands | \(100\,000\) |
| Ten thousands | \(10\,000\) |
| Thousands | \(1000\) |
| Hundreds | \(100\) |
| Tens | \(10\) |
| Ones | \(1\) |
How to read a number to the millions
- Group the digits into threes from the right: ones, thousands, millions.
- Read each group as its own number up to three digits.
- Say the house name (million or thousand) after each group. A group of three zeros is not spoken.
How to write words as a numeral
- Write each group the words give you: the millions, then the thousands, then the ones.
- Fill every house with three digits (except the first), using zeros for any empty places.
- Check the number of digits: a number in the millions has seven digits.
How to round to the nearest million
- Find the millions digit and look at the digit just to its right (the hundred thousands).
- Decide: \(5\) or more rounds up, \(4\) or less stays the same.
- Write zeros in every place after the millions.
| \(6 \text{ hundred thousands}\) | \(=\) | \(600\,000\) |
| \(5 \text{ tens}\) | \(=\) | \(50\) |
The \(6\) is worth \(600\,000\) and the \(5\) is worth \(50\).
Split into houses: \(3 \mid 070 \mid 800\).
Three million, seventy thousand, eight hundred. The zero in the hundred thousands place is not said.
| \(\text{millions}\) | \(:\) | \(8\) |
| \(\text{thousands}\) | \(:\) | \(004\) |
| \(\text{ones}\) | \(:\) | \(030\) |
Each house after the millions needs three digits, so the number is \(8\,004\,030\).
Houses: \(25 \mid 310 \mid 047\).
Twenty-five million, three hundred and ten thousand and forty-seven. The millions house can hold two digits.
(i) to the nearest million
(ii) to the nearest hundred thousand.
(i) Look at the hundred thousands digit.
(ii) Look at the ten thousands digit.
| \(\text{(i) digit } 5\) | \(:\) | \(\text{round up}\) |
| \(\text{(ii) digit } 8\) | \(:\) | \(\text{round up}\) |
(i) \(7\,000\,000\).
(ii) \(6\,600\,000\).
(ii) How many millions are in \(3\) billion?
| \(1 \text{ million}\) | \(=\) | \(1000 \text{ thousands}\) |
| \(4 \text{ million}\) | \(=\) | \(4000 \text{ thousands}\) |
| \(3 \text{ billion}\) | \(=\) | \(3000 \text{ millions}\) |
(i) \(4000\) thousands.
(ii) \(3000\) millions.
(i) What is the value of the digit \(4\)?
(ii) What is the value of the digit \(1\)?
| \(4 \text{ hundred thousands}\) | \(=\) | \(\$400\,000\) |
| \(1 \text{ hundred}\) | \(=\) | \(\$100\) |
(i) \(\$400\,000\).
(ii) \(\$100\).
Find the digit just after the millions digit in each number.
| \(8\,402\,519\) | \(:\) | \(\text{digit } 4\) |
| \(8\,042\,519\) | \(:\) | \(\text{digit } 0\) |
\(8\,042\,519\) has the \(0\) in the hundred thousands place.
Common pitfalls
Frequently asked questions
How do you read large numbers to the millions?
Split the number into groups of three digits from the right: ones, thousands and millions. Read each group as its own number and say the house name after it. For example, \(5\,738\,216\) is five million, seven hundred and thirty-eight thousand, two hundred and sixteen.
What is place value?
Place value is the value a digit has because of its position. In \(4\,619\,352\) the \(6\) is in the hundred thousands place, so its value is \(600\,000\).
Why is zero important in a number?
Zero is a placeholder. It keeps a column open so the other digits stay in the right places. In \(7\,020\,300\) the zeros show there are no hundred thousands, no thousands, no tens and no ones.
How do you write a number in words?
Group the digits into millions, thousands and ones, write each group in words, and add its house name. So \(3\,070\,800\) is three million, seventy thousand, eight hundred.
How many zeros are in one million?
One million is written \(1\,000\,000\), which has six zeros. One thousand thousands make one million.
What is a billion?
One billion is \(1000\) millions, written \(1\,000\,000\,000\) with nine zeros.
How do you round to the nearest million?
Look at the hundred thousands digit. If it is \(5\) or more, round the millions up; if it is \(4\) or less, keep them. So \(6\,583\,940\) rounds to \(7\,000\,000\).