Year 6: Reading, writing and the value of each digit
Part of the Year 6 place value and negative numbers chapter. Chapter overview · whole chapter on one page
Reading, writing and the value of each digit
Numbers up to 10,000,000 can have up to eight digits. We split them into groups of three, counting from the right. The first group is the ones, the second group is the thousands, and the third group is the millions. A comma goes between the groups, so 4,672,819 is easy to read.
Every digit has a value that depends on its column. Moving one column to the left makes the value ten times bigger. In a place-value table the columns are: ten millions (TM), millions (M), hundred thousands (HTh), ten thousands (TTh), thousands (Th), hundreds (H), tens (T) and ones (O).
| Millions | Thousands | Ones | |||||
|---|---|---|---|---|---|---|---|
| TM | M | HTh | TTh | Th | H | T | O |
| 4 | 6 | 7 | 2 | 8 | 1 | 9 | |
To read a big number, read each group and say its name. For 3,050,400 you say “three million, fifty thousand, four hundred”. Zeros are not said, but they hold the columns in place. A number with a zero in the middle can be surprising: 4,000,080 is four million and eighty.
Ten million is written 10,000,000. It has eight digits and seven zeros. One million, 1,000,000, has seven digits and six zeros. Each time you add a column, the number is ten times bigger.
Key ideas
- Put a comma after every group of three digits, counting from the right.
- The value of a digit is the digit times the value of its column: 6 in the hundred thousands column is 6 × 100,000 = 600,000.
- Each column is ten times the column on its right, so 10 thousands make 1 ten thousand.
- 1,000,000 is one million. It is also 1,000 thousands and 10 hundred thousands.
- Zeros in the middle still count: 4,000,080 is four million and eighty, because the zeros hold the columns in place.
- Read the number in groups: millions, thousands, and then the ones group.
Key words. The value of a digit depends on its column (its place). Each column is ten times the column on its right. In 4,672,819 the 6 is in the hundred thousands column, so it is worth 6 × 100,000 = 600,000.
Method. Find the column that holds the digit, then multiply the digit by the value of that column.
- Find the column of the 6. Count the columns from the right. The 6 is in the hundred thousands column.4,672,819: the 6 is in the hundred thousands column
- Multiply the digit by the column value. The value of a digit is the digit times the value of its column.6 × 100,000 = 600,000
- Check the column. Count the columns from the right to be sure.Column 6 from the right is the hundred thousands column
Check. Only the digit 6 is worth 600,000. The other digits are worth their own values, so the whole number stays 4,672,819. ✓
Watch out. The 6 is worth 600,000, not 6. Its column decides its value.
Method. Split the number into groups of three digits, then read each group and say its name.
- Split the number into groups. Each group of three has its own name: million, thousand, or the ones group.3,050,400
- Read each group in words. Say the number in each group, then its name.three million | fifty thousand | four hundred
- Join the groups with commas. Use "and" before a last group that is less than 100.three million, fifty thousand, four hundred
Check. Write the words back as figures: 3,050,400. ✓
Watch out. Zeros still count. 4,000,080 is four million and eighty, not four thousand and eighty.
Method. Find the value of each group, then add the groups together.
- Find the value of each group. Each name tells you how many zeros the group needs.6,000,000 + 209,000 + 70
- Add the groups. Put them together to make one number.6,000,000 + 209,000 + 70 = 6,209,070
- Check the groups. Read the number back in words to check.six million | two hundred and nine thousand | seventy
Check. Reading 6,209,070 back gives "six million, two hundred and nine thousand and seventy". ✓
Watch out. Put commas after every three digits from the right: 6,209,070.
Method. Write each digit with its column value, and leave out the zeros.
- Find the digit in each column. Use the place-value columns, from the left.7 4 0 6 5 1 2
- Multiply each digit by its column value. A digit is worth its digit times its column value.7,000,000 + 400,000 + 6,000 + 500 + 10 + 2
- Add the parts. Adding the parts gives the number back.7,000,000 + 400,000 + 6,000 + 500 + 10 + 2 = 7,406,512
Check. 7,000,000 + 400,000 + 6,000 + 500 + 10 + 2 gives 7,406,512 again. ✓
Watch out. Do not write 7 + 4 + 6 + 5 + 1 + 2. Each digit has its own value.
Watch out
Do not read a number by the first digit only. In 4,000,080 the 8 is worth 80, not 8, and the zeros between the 4 and the 8 are needed. Also, the 7 in 1,702,000 is worth 700,000, not 7,000: the 7 is in the hundred thousands column.Exercise 1A Reading, writing and place value
Non-calculator| Millions | Thousands | Ones | |||||
|---|---|---|---|---|---|---|---|
| TM | M | HTh | TTh | Th | H | T | O |
| 5 | 2 | 8 | 4 | 1 | 9 | 0 | |
Key words. The value of a digit depends on its column (its place). Each column is ten times the column on its right. In 4,672,819 the 6 is in the hundred thousands column, so it is worth 6 × 100,000 = 600,000.
Method. Find the column that holds the digit, then multiply the digit by the value of that column.
- Find the column of the 5. Count the columns from the right. The 5 is in the millions column.5,284,190: the 5 is in the millions column
- Multiply the digit by the column value. The value of a digit is the digit times the value of its column.5 × 1,000,000 = 5,000,000
- Check the column. Count the columns from the right to be sure.Column 7 from the right is the millions column
Check. Only the digit 5 is worth 5,000,000. The other digits are worth their own values, so the whole number stays 5,284,190. ✓
Watch out. The 5 is worth 5,000,000, not 5. Its column decides its value.
Key words. The value of a digit depends on its column (its place). Each column is ten times the column on its right. In 4,672,819 the 6 is in the hundred thousands column, so it is worth 6 × 100,000 = 600,000.
Method. Find the column that holds the digit, then multiply the digit by the value of that column.
- Find the column of the 4. Count the columns from the right. The 4 is in the hundred thousands column.1,423,600: the 4 is in the hundred thousands column
- Multiply the digit by the column value. The value of a digit is the digit times the value of its column.4 × 100,000 = 400,000
- Check the column. Count the columns from the right to be sure.Column 6 from the right is the hundred thousands column
Check. Only the digit 4 is worth 400,000. The other digits are worth their own values, so the whole number stays 1,423,600. ✓
Watch out. The 4 is worth 400,000, not 4. Its column decides its value.
Key words. The value of a digit depends on its column (its place). Each column is ten times the column on its right. In 4,672,819 the 6 is in the hundred thousands column, so it is worth 6 × 100,000 = 600,000.
Method. Find the column that holds the digit, then multiply the digit by the value of that column.
- Find the column of the 9. Count the columns from the right. The 9 is in the ten thousands column.2,093,541: the 9 is in the ten thousands column
- Multiply the digit by the column value. The value of a digit is the digit times the value of its column.9 × 10,000 = 90,000
- Check the column. Count the columns from the right to be sure.Column 5 from the right is the ten thousands column
Check. Only the digit 9 is worth 90,000. The other digits are worth their own values, so the whole number stays 2,093,541. ✓
Watch out. The 9 is worth 90,000, not 9. Its column decides its value.
Key words. The value of a digit depends on its column (its place). Each column is ten times the column on its right. In 4,672,819 the 6 is in the hundred thousands column, so it is worth 6 × 100,000 = 600,000.
Method. Find the column that holds the digit, then multiply the digit by the value of that column.
- Find the column of the 7. Count the columns from the right. The 7 is in the thousands column.807,650: the 7 is in the thousands column
- Multiply the digit by the column value. The value of a digit is the digit times the value of its column.7 × 1,000 = 7,000
- Check the column. Count the columns from the right to be sure.Column 4 from the right is the thousands column
Check. Only the digit 7 is worth 7,000. The other digits are worth their own values, so the whole number stays 807,650. ✓
Watch out. The 7 is worth 7,000, not 7. Its column decides its value.
Key words. The value of a digit depends on its column (its place). Each column is ten times the column on its right. In 4,672,819 the 6 is in the hundred thousands column, so it is worth 6 × 100,000 = 600,000.
Method. Find the column that holds the digit, then multiply the digit by the value of that column.
- Find the column of the 8. Count the columns from the right. The 8 is in the tens column.4,061,580: the 8 is in the tens column
- Multiply the digit by the column value. The value of a digit is the digit times the value of its column.8 × 10 = 80
- Check the column. Count the columns from the right to be sure.Column 2 from the right is the tens column
Check. Only the digit 8 is worth 80. The other digits are worth their own values, so the whole number stays 4,061,580. ✓
Watch out. The 8 is worth 80, not 8. Its column decides its value.
Method. Split the number into groups of three digits, then read each group and say its name.
- Split the number into groups. Each group of three has its own name: million, thousand, or the ones group.3,050,400
- Read each group in words. Say the number in each group, then its name.three million | fifty thousand | four hundred
- Join the groups with commas. Use "and" before a last group that is less than 100.three million, fifty thousand, four hundred
Check. Write the words back as figures: 3,050,400. ✓
Watch out. Zeros still count. 4,000,080 is four million and eighty, not four thousand and eighty.
Method. Split the number into groups of three digits, then read each group and say its name.
- Split the number into groups. Each group of three has its own name: million, thousand, or the ones group.1,206,070
- Read each group in words. Say the number in each group, then its name.one million | two hundred and six thousand | seventy
- Join the groups with commas. Use "and" before a last group that is less than 100.one million, two hundred and six thousand and seventy
Check. Write the words back as figures: 1,206,070. ✓
Watch out. Zeros still count. 4,000,080 is four million and eighty, not four thousand and eighty.
Method. Split the number into groups of three digits, then read each group and say its name.
- Split the number into groups. Each group of three has its own name: million, thousand, or the ones group.9,000,009
- Read each group in words. Say the number in each group, then its name.nine million | nine
- Join the groups with commas. Use "and" before a last group that is less than 100.nine million and nine
Check. Write the words back as figures: 9,000,009. ✓
Watch out. Zeros still count. 4,000,080 is four million and eighty, not four thousand and eighty.
Method. Find the value of each group, then add the groups together.
- Find the value of each group. Each name tells you how many zeros the group needs.4,000,000 + 60,000 + 12
- Add the groups. Put them together to make one number.4,000,000 + 60,000 + 12 = 4,060,012
- Check the groups. Read the number back in words to check.four million | sixty thousand | twelve
Check. Reading 4,060,012 back gives "four million, sixty thousand and twelve". ✓
Watch out. Put commas after every three digits from the right: 6,209,070.
Method. Find the value of each group, then add the groups together.
- Find the value of each group. Each name tells you how many zeros the group needs.2,000,000 + 950
- Add the groups. Put them together to make one number.2,000,000 + 950 = 2,000,950
- Check the groups. Read the number back in words to check.two million | nine hundred and fifty
Check. Reading 2,000,950 back gives "two million, nine hundred and fifty". ✓
Watch out. Put commas after every three digits from the right: 6,209,070.
Method. Find the value of each group, then add the groups together.
- Find the value of each group. Each name tells you how many zeros the group needs.7,000,000 + 100,000
- Add the groups. Put them together to make one number.7,000,000 + 100,000 = 7,100,000
- Check the groups. Read the number back in words to check.seven million | one hundred thousand
Check. Reading 7,100,000 back gives "seven million, one hundred thousand". ✓
Watch out. Put commas after every three digits from the right: 6,209,070.
Method. Write each digit with its column value, and leave out the zeros.
- Find the digit in each column. Use the place-value columns, from the left.7 4 0 6 5 1 2
- Multiply each digit by its column value. A digit is worth its digit times its column value.7,000,000 + 400,000 + 6,000 + 500 + 10 + 2
- Add the parts. Adding the parts gives the number back.7,000,000 + 400,000 + 6,000 + 500 + 10 + 2 = 7,406,512
Check. 7,000,000 + 400,000 + 6,000 + 500 + 10 + 2 gives 7,406,512 again. ✓
Watch out. Do not write 7 + 4 + 6 + 5 + 1 + 2. Each digit has its own value.
Key words. The value of a digit depends on its column (its place). Each column is ten times the column on its right. In 4,672,819 the 6 is in the hundred thousands column, so it is worth 6 × 100,000 = 600,000.
Method. Find the column that holds the digit, then multiply the digit by the value of that column.
- Find the column of the 7. Count the columns from the right. The 7 is in the hundred thousands column.1,702,000: the 7 is in the hundred thousands column
- Multiply the digit by the column value. The value of a digit is the digit times the value of its column.7 × 100,000 = 700,000
- Check the column. Count the columns from the right to be sure.Column 6 from the right is the hundred thousands column
Check. Only the digit 7 is worth 700,000. The other digits are worth their own values, so the whole number stays 1,702,000. ✓
Watch out. The 7 is worth 700,000, not 7. Its column decides its value.
Method. Count the thousands. There are 1,000 thousands in 1 million.
- Think about one million. One million is a thousand thousands.1,000,000 = 1,000 × 1,000
- Work out 2 million. Two million has twice as many thousands.2,000,000 = 2,000 thousands
- Write the answer. 2,000 thousands are in 2 million
Check. 2,000 × 1,000 = 2,000,000. ✓
Watch out. Each column is ten times the one on its right: 1 million is 1,000 times 1,000.
Method. Count the ten thousands in 1 million.
- Divide the million by ten thousand. A ten thousand is 10,000, so divide 1,000,000 by 10,000.1,000,000 ÷ 10,000
- Work out the answer. Take off four zeros from each number.1,000,000 ÷ 10,000 = 100
- Check. Count back: 100 ten thousands make 1,000,000.100 × 10,000 = 1,000,000
Check. 100 × 10,000 = 1,000,000. ✓
Watch out. Each ten thousand is 10,000, so there are fewer of them than thousands.
Method. Write each digit in its column. Put a zero in any column that has no digit.
- Write the value of each part. Each digit is worth its digit times its column value.6 × 1,000,000 = 6,000,000 and 4 × 10,000 = 40,000
- Write the other parts. Hundreds and ones have digits too.7 × 100 = 700 and 9 × 1 = 9
- Add the parts. Put the parts together. Zeros in the other columns add nothing.6,000,000 + 40,000 + 700 + 9 = 6,040,709
Check. 6,040,709 has 6 millions, 4 ten thousands, 7 hundreds and 9 ones. ✓
Watch out. Do not write the digits next to each other as 6479. Every digit needs its own column.
Method. Count the columns from the right to find the ten thousands column.
- Name the columns from the right. Ones, tens, hundreds, thousands, ten thousands.4 (ones), 1 (tens), 9 (hundreds), 8 (thousands), 5 (ten thousands), 3 (hundred thousands), 2 (millions)
- Read the digit in the ten thousands column. That is the digit we want. Its value is 5 × 10,000 = 50,000.5
Check. Read 2,358,914 from the left as well: 2 (millions), 3 (hundred thousands), 5 (ten thousands). ✓
Watch out. Count the columns from the right, not the left.
| Millions | Thousands | Ones | |||||
|---|---|---|---|---|---|---|---|
| TM | M | HTh | TTh | Th | H | T | O |
| 8 | 9 | 1 | 0 | 0 | 0 | 0 | |
Key words. The value of a digit depends on its column (its place). Each column is ten times the column on its right. In 4,672,819 the 6 is in the hundred thousands column, so it is worth 6 × 100,000 = 600,000.
Method. Find the column that holds the digit, then multiply the digit by the value of that column.
- Find the column of the 1. Count the columns from the right. The 1 is in the ten thousands column.8,910,000: the 1 is in the ten thousands column
- Multiply the digit by the column value. The value of a digit is the digit times the value of its column.1 × 10,000 = 10,000
- Check the column. Count the columns from the right to be sure.Column 5 from the right is the ten thousands column
Check. Only the digit 1 is worth 10,000. The other digits are worth their own values, so the whole number stays 8,910,000. ✓
Watch out. The 1 is worth 10,000, not 1. Its column decides its value.
Method. Write ten million out in full, then count the zeros.
- Write the number. Ten million has a 1 and then zeros.10,000,000
- Count the zeros. Count only the zeros, not the 1.1, then 0, 0, 0, 0, 0, 0, 0: seven zeros
- Compare with one million. One million has six zeros. Ten million is ten times bigger, so it has one more zero.1,000,000 has six zeros, so 10,000,000 has seven
Check. 1,000,000 × 10 = 10,000,000. ✓
Watch out. Count the zeros, not the digits. Ten million has eight digits.