Number & place value
Place Value to 10,000,000
Year 3 · Year 4 · Year 5 · Year 6
- ✓Read and write numbers up to 10,000,000 in figures and words.
- ✓Identify the value of each digit in numbers up to 10,000,000.
- ✓Order and compare numbers up to 10,000,000.
- ✓Round any number up to 10,000,000 to the nearest 10, 100, 1,000, 10,000, 100,000 or 1,000,000.
Key concepts
Place value tells us the value of each digit in a number based on its position. For example, in the number 345, the digit '3' is in the hundreds place, so its value is 300. The digit '4' is in the tens place, so its value is 40. The digit '5' is in the ones place, so its value is 5. Understanding place value is crucial for working with large numbers, as the same digit can have a very different value depending on where it sits.
To read large numbers easily, we group digits in threes, starting from the right. These groups are often separated by commas (or sometimes spaces in the UK, though commas are common for clarity). Each group has a name: ones, thousands, millions. For example, 5,432,109 is read as 'five million, four hundred and thirty-two thousand, one hundred and nine'.
When writing large numbers from words, it's helpful to think about the place value chart. If a place value is not mentioned, you must use a zero as a placeholder to maintain the correct value of the other digits. For example, 'two million, five thousand and one' would be written as 2,005,001. Notice the zeros in the hundred thousands, ten thousands, hundreds, and tens places.
To order numbers from smallest to largest or largest to smallest, first count the number of digits in each number. The number with more digits is usually larger. If numbers have the same number of digits, compare them digit by digit, starting from the leftmost (largest place value) digit. The first digit that is different determines which number is larger.
Rounding means making a number simpler but keeping its value close to what it was. To round a number to a specific place value (e.g., the nearest 10, 100, 1,000, etc.), first identify the digit in the target place value. Then, look at the digit immediately to the right of the target place value. If this digit is 5 or more (5, 6, 7, 8, 9), you round up: increase the target digit by one and change all digits to its right to zero. If this digit is less than 5 (0, 1, 2, 3, 4), you round down: keep the target digit the same and change all digits to its right to zero.
Key facts to remember
- 1Each digit in a number has a specific value determined by its position (place value).
- 2Numbers are grouped in threes (ones, thousands, millions) to make them easier to read and write, often separated by commas.
- 3When comparing numbers, always start by looking at the digit in the largest place value (the leftmost digit).
- 4To round a number, look at the digit to the right of the target place value. If it's 5 or more, round up; if it's less than 5, round down.
- 5A zero is a crucial placeholder when a particular place value is empty in a number (e.g., 2,005,000 has zeros in the hundred thousands and ten thousands places).
- 61 million is equal to 1,000 thousands (1,000,000).
Worked examples
Example 1
Write the number 'four million, two hundred and six thousand, fifty-three' in figures and state the value of the digit '2'.
Answer
4,206,053. The value of the digit '2' is 200,000 (two hundred thousand).
Remember to use zeros as placeholders for any place values that are not explicitly mentioned in the words, such as the hundreds and tens in the 'ones' group, or the hundred thousands and ten thousands in the 'thousands' group if they were missing.
Example 2
Order the following numbers from smallest to largest: 3,456,123; 3,546,123; 3,456,099; 3,456,132.
Answer
3,456,099; 3,456,123; 3,456,132; 3,546,123.
Always start comparing from the largest place value (leftmost digit) and move to the right until you find a difference.
Example 3
Round 7,834,567 to the nearest: a) 100,000 b) 10,000 c) 1,000,000.
Answer
a) 7,800,000 b) 7,830,000 c) 8,000,000.
Identify the target place value first, then look *only* at the digit immediately to its right to decide whether to round up or down. All digits to the right of the rounded place value become zeros.
Common mistakes
- ✗Confusing the value of a digit with its position (e.g., thinking the '2' in 2,000,000 is 200,000 instead of 2 million).
- ✗Incorrectly using zeros as placeholders when writing numbers from words, leading to numbers that are too large or too small (e.g., writing 'two million, fifty' as 2,50 instead of 2,000,050).
- ✗Rounding incorrectly by looking at a digit other than the one immediately to the right of the target place value.
- ✗Comparing numbers from right to left instead of from left to right, especially when numbers have different numbers of digits.
- ✗Forgetting to change all digits to the right of the rounded digit to zero, or changing digits to the left of the rounded digit.
Exam tips
- ★Always use a place value chart to help you visualise the value of each digit, especially with large numbers. You can draw one out if needed.
- ★Read the question carefully to understand exactly what place value you need to round to or what order numbers should be in.
- ★When writing numbers from words, say the number aloud to yourself to check if it sounds correct and matches the figures you've written.
- ★After rounding, check if your answer is sensible and close to the original number. For example, rounding 7,834,567 to the nearest million should be 8,000,000, not 7,000,000.
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