Step-by-step Maths Level 5: Digits and place value to a million
Part of the Step-by-step Maths Level 5 place value to a million and decimals to tenths chapter. Chapter overview · whole chapter on one page
Digits and place value to a million
Each digit in a number has a value that depends on its column. In 472,893, the 4 is in the hundred thousands column, so it is worth 400,000. The 7 is in the ten thousands column, so it is worth 70,000.
Groups of three digits are separated by commas to make big numbers easier to read. Read the thousands, then the rest.
Key ideas
- Each column is ten times the column on its right.
- The value of a digit = the digit × the value of its column.
- Partitioning splits a number into the value of each digit.
Method. Read the column, then multiply the digit by the value of that column.
- Find the ten thousands column. Count the columns from the right: ones, tens, hundreds and so on.The digit is 7
- Multiply the digit by the value of its column. Each place in the ten thousands column is worth 10,000.7 × 10,000 = 70,000
- Write the value. This is the value of the digit in this number, not just the digit.70,000
Check. Check: 70,000 is 7 groups of 10,000.
Watch out. Say the value, such as 70,000, not only the digit 7.
Method. Read the thousands, then the last three digits, and join them with the word thousand.
- Split the number into thousands and the last three digits. Read the thousands first, then the rest.472 thousand and 893
- Say the thousands. Say the number before the thousand, then the word thousand.four hundred and seventy-two thousand
- Say the last three digits. Say them as a number up to 999.eight hundred and ninety-three
- Put the words together. Use a space between the two parts; use and before a number under 100.four hundred and seventy-two thousand eight hundred and ninety-three
Check. Check: count the words so that each part matches its digits.
Watch out. Do not write the digits in words one by one. Say the parts. Use and before the tens and ones.
Method. Partition the number into the value of each digit.
- Find the value of each digit. Multiply each digit by the value of its column; leave out zeros.400,000, 70,000, 2,000, 800, 90, 3
- Write the parts as an addition. Add the parts together to make the number.400,000 + 70,000 + 2,000 + 800 + 90 + 3
- Check by adding. Adding the parts again must give the number we started with.400,000 + 70,000 + 2,000 + 800 + 90 + 3
Check. Check: the parts add to 472,893.
Watch out. Leave out any digit that is zero. Zero adds nothing.
Watch out
Watch out. The 7 in 472,893 is worth 70,000, not 7. Name the column first, then multiply.
Exam tip
Grown-up tip. Ask the child to read a big number in parts: “472 thousand, 893.” Practise saying the value of each digit aloud.
Exercise 1A Practice: digits, words and partitioning
Non-calculatorMethod. Partition the number into the value of each digit.
- Find the value of each digit. Multiply each digit by the value of its column; leave out zeros.500,000, 3,000, 900, 20, 4
- Write the parts as an addition. Add the parts together to make the number.500,000 + 3,000 + 900 + 20 + 4
- Check by adding. Adding the parts again must give the number we started with.500,000 + 3,000 + 900 + 20 + 4
Check. Check: the parts add to 503,924.
Watch out. Leave out any digit that is zero. Zero adds nothing.
Method. Read the thousands, then the last three digits, and join them with the word thousand.
- Split the number into thousands and the last three digits. Read the thousands first, then the rest.723 thousand and 202
- Say the thousands. Say the number before the thousand, then the word thousand.seven hundred and twenty-three thousand
- Say the last three digits. Say them as a number up to 999.two hundred and two
- Put the words together. Use a space between the two parts; use and before a number under 100.seven hundred and twenty-three thousand two hundred and two
Check. Check: count the words so that each part matches its digits.
Watch out. Do not write the digits in words one by one. Say the parts. Use and before the tens and ones.
Method. Read the column, then multiply the digit by the value of that column.
- Find the hundreds column. Count the columns from the right: ones, tens, hundreds and so on.The digit is 6
- Multiply the digit by the value of its column. Each place in the hundreds column is worth 100.6 × 100 = 600
- Write the value. This is the value of the digit in this number, not just the digit.600
Check. Check: 600 is 6 groups of 100.
Watch out. Say the value, such as 70,000, not only the digit 7.
Method. Read the thousands, then the last three digits, and join them with the word thousand.
- Split the number into thousands and the last three digits. Read the thousands first, then the rest.435 thousand and 751
- Say the thousands. Say the number before the thousand, then the word thousand.four hundred and thirty-five thousand
- Say the last three digits. Say them as a number up to 999.seven hundred and fifty-one
- Put the words together. Use a space between the two parts; use and before a number under 100.four hundred and thirty-five thousand seven hundred and fifty-one
Check. Check: count the words so that each part matches its digits.
Watch out. Do not write the digits in words one by one. Say the parts. Use and before the tens and ones.
Method. Read the thousands, then the last three digits, and join them with the word thousand.
- Split the number into thousands and the last three digits. Read the thousands first, then the rest.672 thousand and 537
- Say the thousands. Say the number before the thousand, then the word thousand.six hundred and seventy-two thousand
- Say the last three digits. Say them as a number up to 999.five hundred and thirty-seven
- Put the words together. Use a space between the two parts; use and before a number under 100.six hundred and seventy-two thousand five hundred and thirty-seven
Check. Check: count the words so that each part matches its digits.
Watch out. Do not write the digits in words one by one. Say the parts. Use and before the tens and ones.
Method. Partition the number into the value of each digit.
- Find the value of each digit. Multiply each digit by the value of its column; leave out zeros.100,000, 60,000, 9,000, 200, 80, 6
- Write the parts as an addition. Add the parts together to make the number.100,000 + 60,000 + 9,000 + 200 + 80 + 6
- Check by adding. Adding the parts again must give the number we started with.100,000 + 60,000 + 9,000 + 200 + 80 + 6
Check. Check: the parts add to 169,286.
Watch out. Leave out any digit that is zero. Zero adds nothing.
Method. Read the column, then multiply the digit by the value of that column.
- Find the ten thousands column. Count the columns from the right: ones, tens, hundreds and so on.The digit is 6
- Multiply the digit by the value of its column. Each place in the ten thousands column is worth 10,000.6 × 10,000 = 60,000
- Write the value. This is the value of the digit in this number, not just the digit.60,000
Check. Check: 60,000 is 6 groups of 10,000.
Watch out. Say the value, such as 70,000, not only the digit 7.
Method. Partition the number into the value of each digit.
- Find the value of each digit. Multiply each digit by the value of its column; leave out zeros.400,000, 50,000, 6,000, 900, 10
- Write the parts as an addition. Add the parts together to make the number.400,000 + 50,000 + 6,000 + 900 + 10
- Check by adding. Adding the parts again must give the number we started with.400,000 + 50,000 + 6,000 + 900 + 10
Check. Check: the parts add to 456,910.
Watch out. Leave out any digit that is zero. Zero adds nothing.
Method. Read the thousands, then the last three digits, and join them with the word thousand.
- Split the number into thousands and the last three digits. Read the thousands first, then the rest.825 thousand and 546
- Say the thousands. Say the number before the thousand, then the word thousand.eight hundred and twenty-five thousand
- Say the last three digits. Say them as a number up to 999.five hundred and forty-six
- Put the words together. Use a space between the two parts; use and before a number under 100.eight hundred and twenty-five thousand five hundred and forty-six
Check. Check: count the words so that each part matches its digits.
Watch out. Do not write the digits in words one by one. Say the parts. Use and before the tens and ones.
Method. Read the column, then multiply the digit by the value of that column.
- Find the hundred thousands column. Count the columns from the right: ones, tens, hundreds and so on.The digit is 7
- Multiply the digit by the value of its column. Each place in the hundred thousands column is worth 100,000.7 × 100,000 = 700,000
- Write the value. This is the value of the digit in this number, not just the digit.700,000
Check. Check: 700,000 is 7 groups of 100,000.
Watch out. Say the value, such as 70,000, not only the digit 7.
Method. Read the column, then multiply the digit by the value of that column.
- Find the thousands column. Count the columns from the right: ones, tens, hundreds and so on.The digit is 8
- Multiply the digit by the value of its column. Each place in the thousands column is worth 1,000.8 × 1,000 = 8,000
- Write the value. This is the value of the digit in this number, not just the digit.8,000
Check. Check: 8,000 is 8 groups of 1,000.
Watch out. Say the value, such as 70,000, not only the digit 7.
Method. Read the column, then multiply the digit by the value of that column.
- Find the thousands column. Count the columns from the right: ones, tens, hundreds and so on.The digit is 3
- Multiply the digit by the value of its column. Each place in the thousands column is worth 1,000.3 × 1,000 = 3,000
- Write the value. This is the value of the digit in this number, not just the digit.3,000
Check. Check: 3,000 is 3 groups of 1,000.
Watch out. Say the value, such as 70,000, not only the digit 7.
Method. Read the thousands, then the last three digits, and join them with the word thousand.
- Split the number into thousands and the last three digits. Read the thousands first, then the rest.798 thousand and 648
- Say the thousands. Say the number before the thousand, then the word thousand.seven hundred and ninety-eight thousand
- Say the last three digits. Say them as a number up to 999.six hundred and forty-eight
- Put the words together. Use a space between the two parts; use and before a number under 100.seven hundred and ninety-eight thousand six hundred and forty-eight
Check. Check: count the words so that each part matches its digits.
Watch out. Do not write the digits in words one by one. Say the parts. Use and before the tens and ones.
Method. Read the thousands, then the last three digits, and join them with the word thousand.
- Split the number into thousands and the last three digits. Read the thousands first, then the rest.594 thousand and 527
- Say the thousands. Say the number before the thousand, then the word thousand.five hundred and ninety-four thousand
- Say the last three digits. Say them as a number up to 999.five hundred and twenty-seven
- Put the words together. Use a space between the two parts; use and before a number under 100.five hundred and ninety-four thousand five hundred and twenty-seven
Check. Check: count the words so that each part matches its digits.
Watch out. Do not write the digits in words one by one. Say the parts. Use and before the tens and ones.
Method. Partition the number into the value of each digit.
- Find the value of each digit. Multiply each digit by the value of its column; leave out zeros.500,000, 90,000, 4,000, 600, 30, 1
- Write the parts as an addition. Add the parts together to make the number.500,000 + 90,000 + 4,000 + 600 + 30 + 1
- Check by adding. Adding the parts again must give the number we started with.500,000 + 90,000 + 4,000 + 600 + 30 + 1
Check. Check: the parts add to 594,631.
Watch out. Leave out any digit that is zero. Zero adds nothing.
Method. Read the column, then multiply the digit by the value of that column.
- Find the hundred thousands column. Count the columns from the right: ones, tens, hundreds and so on.The digit is 5
- Multiply the digit by the value of its column. Each place in the hundred thousands column is worth 100,000.5 × 100,000 = 500,000
- Write the value. This is the value of the digit in this number, not just the digit.500,000
Check. Check: 500,000 is 5 groups of 100,000.
Watch out. Say the value, such as 70,000, not only the digit 7.