Year 5: Reading and writing numbers to 1,000,000
Part of the Year 5 place value to 1,000,000 chapter. Chapter overview · whole chapter on one page · Download worksheet (PDF) · Answers (PDF)
Reading and writing numbers to 1,000,000
In Year 4 you worked with numbers up to 10,000. Now the numbers get much bigger. We will go all the way up to 1,000,000, which is one million! Big numbers are easier to read if the digits are split into groups of three, called periods. We put a comma between the periods. Reading from the right, the first period is Ones (O, T, H), the next is Thousands (Th, TTh, HTh) and the next is Millions (M).
Each column is 10 times bigger than the column on its right. 10 ones make 1 ten, 10 tens make 1 hundred, 10 hundreds make 1 thousand, 10 thousands make 1 ten thousand, and 10 ten thousands make 1 hundred thousand. This chart uses counters to show 306,075. The ten thousands column has no counters, so its digit is a 0, a place holder.
Reading a number in words. Read the digits before the comma as one number and add the word thousand. Then read the last three digits. 306,075 is three hundred and six thousand and seventy-five. We put “and” before the last two digits (the tens and ones). Zeros are not said out loud, but they must be written.
Partitioning. This means splitting a number into the value of each digit: 306,075 = 300,000 + 6,000 + 70 + 5. The value of a digit is the digit times the value of its column. In 306,075, the 3 is worth 300,000 because it is in the hundred thousands column.
| Millions | Thousands | Ones | ||||
|---|---|---|---|---|---|---|
| M | HTh | TTh | Th | H | T | O |
| 1 | 0 | 0 | 0 | 0 | 0 | 0 |
Key words. A digit is one of 0 to 9. A period is a group of three columns. A place holder is a zero that keeps the other digits in the right columns. To partition a number is to split it into the values of its digits.
Key ideas
- The columns, from the right: O, T, H | Th, TTh, HTh | M. Each is 10 times the one on its right.
- Commas split a number into periods of three digits.
- Value of a digit = the digit times the value of its column. The 4 in 340,000 is worth 40,000.
- A zero is a place holder: 405,060 is not the same as 45,060.
- In words, say the thousands period, then “thousand”, then the last three digits. Put “and” before the last two digits.
- 999,999 + 1 = 1,000,000 (one million).
Key words. A digit is one of 0 to 9. The value of a digit is what it is worth. A period is a group of three columns: Ones, Thousands, Millions.
Method. The value of a digit depends on its column. Find the column, then multiply the digit by the value of the column.
- Write the number in a place-value table. Each column has a name and a value. The coloured digit is the one we want.
Thousands Ones HTh TTh Th H T O 3 8 4 7 2 9 - Find which column the digit is in. The digit is 8 and it sits in the ten thousands column.1 ten thousand = 10,000
- Multiply the digit by the value of the column. There are 8 ten thousands.8 × 10,000 = 80,000
Check. Say it in words: 8 ten thousands is eighty thousand. ✓
Watch out. The digit is 8 but its value is 80,000. The same digit is worth different amounts in different columns.
Key words. A digit is one of 0 to 9. The value of a digit is what it is worth. A period is a group of three columns: Ones, Thousands, Millions.
Method. Say the number in parts, from left to right: the thousands period first, then the hundreds, then the last two digits.
- Write the number in a place-value table. The comma splits the digits into the Thousands period and the Ones period.
Thousands Ones HTh TTh Th H T O 4 0 8 5 0 7 - Read each part and say it in words. Say the thousands period as a number and then add the word thousand.Thousands period: 408 → four hundred and eight thousand
Hundreds: 5 → five hundred
Last two digits: 7 → seven - Join the parts together. Put “and” before the last two digits (the tens and ones) when there are hundreds or thousands before them.four hundred and eight thousand, five hundred and seven
Check. Read it out loud. It sounds like 408,507. ✓
Watch out. Zeros are never said aloud. 400,060 is “four hundred thousand and sixty”: nothing is said for the empty columns, but they still need a 0 when you write the digits.
Key words. A digit is one of 0 to 9. The value of a digit is what it is worth. A period is a group of three columns: Ones, Thousands, Millions.
Method. Say the number in parts, from left to right: the thousands period first, then the hundreds, then the last two digits.
- Write the number in a place-value table. The comma splits the digits into the Thousands period and the Ones period.
Thousands Ones HTh TTh Th H T O 3 0 0 0 4 0 - Read each part and say it in words. Say the thousands period as a number and then add the word thousand.Thousands period: 300 → three hundred thousand
Last two digits: 40 → forty - Join the parts together. Put “and” before the last two digits (the tens and ones) when there are hundreds or thousands before them.three hundred thousand and forty
Check. Read it out loud. It sounds like 300,040. ✓
Watch out. Zeros are never said aloud. 400,060 is “four hundred thousand and sixty”: nothing is said for the empty columns, but they still need a 0 when you write the digits.
Key words. A digit is one of 0 to 9. The value of a digit is what it is worth. A period is a group of three columns: Ones, Thousands, Millions.
Method. Listen for the words “thousand” and “hundred”. They tell you which period and column each part goes in.
- Split the words into parts. Each part belongs to one period or column.“six hundred and five thousand” → the Thousands period is 605
“two hundred” → 2 in the hundreds column
“nine” → 0 in the tens column and 9 in the ones column - Write the digits in a place-value table. Write a zero in every column that was not mentioned. Each period has three digits (except the first).
Thousands Ones HTh TTh Th H T O 6 0 5 2 0 9 - Write the number. Put a comma between the periods.605,209
Check. Say 605,209 in words: six hundred and five thousand, two hundred and nine. It matches. ✓
Watch out. A zero is a place holder. Without it the digits slip into the wrong columns and the number changes.
Key words. To partition a number is to split it into parts, one part for each digit.
Method. Partition means splitting a number into the value of each of its digits.
- Write the number in a place-value table. This shows how many of each column there are.
Thousands Ones HTh TTh Th H T O 5 3 0 4 0 8 - Work out the value of each digit. Digit times the value of its column.5 hundred thousands = 500,000
3 ten thousands = 30,000
0 thousands = nothing to write
4 hundreds = 400
0 tens = nothing to write
8 ones = 8 - Leave out the zeros. A zero means the column is empty, so there is nothing to add.
- Write the values as an addition. Start with the biggest value.530,408 = 500,000 + 30,000 + 400 + 8
Check. Add them up: 500,000 + 30,000 + 400 + 8 = 530,408. ✓
Watch out. Write 300,000 for 3 hundred thousands, not just 3. Each part keeps its full value.
Key words. A digit is one of 0 to 9. The value of a digit is what it is worth. A period is a group of three columns: Ones, Thousands, Millions.
Method. Count the counters in each column. Each counter is worth the value of its column, so the number of counters is the digit.
- Count the counters in each column. No counters in a column means a zero.HTh column: 2 counters → 2
TTh column: 4 counters → 4
Th column: 7 counters → 7
H column: 0 counters → 0
T column: 3 counters → 3
O column: 6 counters → 6 - Put the digits in a place-value table. Keep the columns in the same order.
Thousands Ones HTh TTh Th H T O 2 4 7 0 3 6 - Read the number. Put a comma between the Thousands period and the Ones period.247,036
Check. Say it in words: two hundred and forty-seven thousand and thirty-six. ✓
Watch out. A column with no counters is a zero. Do not leave it out.
Key words. A place holder is a zero that holds an empty column so the other digits stay in the right place.
Method. Put each part into its own column of a place-value table. Write a zero in any column with nothing in it.
- Read the parts: 3 hundred thousands, 5 ten thousands, 2 hundreds and 8 ones. Each part tells us which column it goes in and how many.
- Put each digit in its column. Start with the biggest column on the left.3 hundred thousands → write 3 in the HTh column
5 ten thousands → write 5 in the TTh column
0 thousands → write 0 in the Th column (nothing here, so write a zero)
2 hundreds → write 2 in the H column
0 tens → write 0 in the T column (nothing here, so write a zero)
8 ones → write 8 in the O column - Read the digits across the table. Put commas between the periods.
Thousands Ones HTh TTh Th H T O 3 5 0 2 0 8
The number is 350,208.
Check. Say it in words: three hundred and fifty thousand, two hundred and eight. It matches the parts. ✓
Watch out. A zero is a place holder. 405,060 and 45,060 are very different numbers.
Method. To find how many hundreds are in a number, read all the digits from the left up to the hundreds column as one number.
- Write the number in a place-value table. Find the hundreds column.
Thousands Ones TTh Th H T O 3 6 4 0 0 - Read the digits up to the H column. Every column on the left is a bigger column. They can all be swapped for hundreds. 1 thousand is 10 hundreds, and so on.The digits 364, read as one number, are 364.
- Write the answer. 364 hundreds
Check. 364 × 100 = 36,400. ✓
Watch out. Do not just read the digit in that column. There are 364 hundreds in 36,400, not 4.
Method. Add 1 to the ones column and carry the 1 all the way along. Then write the answer in digits and words.
- Write the number in a place-value table. Every column is a 9.
Thousands Ones HTh TTh Th H T O 9 9 9 9 9 9 - Add 1 to the ones. 9 + 1 = 10, so write 0 and carry 1. The next column is also 9, so the carry keeps going.9 ones + 1 = 10 ones → 1 ten
9 tens + 1 ten = 10 tens → 1 hundred
… and so on, all the way to the left - Write the new number. Every column is now 0 and there is a new column on the left, the Millions column.
Millions Thousands Ones M HTh TTh Th H T O 1 0 0 0 0 0 0
1,000,000 - Say it in words. 1,000,000 is 1 thousand thousands. We call it one million.one million
Check. 10 × 100,000 = 1,000,000, so there are 10 hundred thousands in one million. ✓
Watch out. 999,999 has six digits. One more has seven. A new column appears when every column is full.
Watch out
Do not forget the place-holder zeros. “Three hundred and five thousand and forty” is 305,040, not 35,040 and not 350,040. Also remember that the value of a digit is not the digit itself: in 460,000 the 6 is worth 60,000.Exercise 1A Reading, writing and partitioning numbers
Non-calculatorKey words. A digit is one of 0 to 9. The value of a digit is what it is worth. A period is a group of three columns: Ones, Thousands, Millions.
Method. Count the counters in each column. Each counter is worth the value of its column, so the number of counters is the digit.
- Count the counters in each column. No counters in a column means a zero.HTh column: 4 counters → 4
TTh column: 7 counters → 7
Th column: 3 counters → 3
H column: 0 counters → 0
T column: 5 counters → 5
O column: 2 counters → 2 - Put the digits in a place-value table. Keep the columns in the same order.
Thousands Ones HTh TTh Th H T O 4 7 3 0 5 2 - Read the number. Put a comma between the Thousands period and the Ones period.473,052
Check. Say it in words: four hundred and seventy-three thousand and fifty-two. ✓
Watch out. A column with no counters is a zero. Do not leave it out.
Key words. A digit is one of 0 to 9. The value of a digit is what it is worth. A period is a group of three columns: Ones, Thousands, Millions.
Method. Count the counters in each column. Each counter is worth the value of its column, so the number of counters is the digit.
- Count the counters in each column. No counters in a column means a zero.HTh column: 5 counters → 5
TTh column: 0 counters → 0
Th column: 8 counters → 8
H column: 0 counters → 0
T column: 6 counters → 6
O column: 0 counters → 0 - Put the digits in a place-value table. Keep the columns in the same order.
Thousands Ones HTh TTh Th H T O 5 0 8 0 6 0 - Read the number. Put a comma between the Thousands period and the Ones period.508,060
Check. Say it in words: five hundred and eight thousand and sixty. ✓
Watch out. A column with no counters is a zero. Do not leave it out.
Key words. A digit is one of 0 to 9. The value of a digit is what it is worth. A period is a group of three columns: Ones, Thousands, Millions.
Method. The value of a digit depends on its column. Find the column, then multiply the digit by the value of the column.
- Write the number in a place-value table. Each column has a name and a value. The coloured digit is the one we want.
Thousands Ones HTh TTh Th H T O 6 3 8 2 4 5 - Find which column the digit is in. The digit is 6 and it sits in the hundred thousands column.1 hundred thousand = 100,000
- Multiply the digit by the value of the column. There are 6 hundred thousands.6 × 100,000 = 600,000
Check. Say it in words: 6 hundred thousands is six hundred thousand. ✓
Watch out. The digit is 6 but its value is 600,000. The same digit is worth different amounts in different columns.
Key words. A digit is one of 0 to 9. The value of a digit is what it is worth. A period is a group of three columns: Ones, Thousands, Millions.
Method. The value of a digit depends on its column. Find the column, then multiply the digit by the value of the column.
- Write the number in a place-value table. Each column has a name and a value. The coloured digit is the one we want.
Thousands Ones TTh Th H T O 9 2 8 1 6 - Find which column the digit is in. The digit is 9 and it sits in the ten thousands column.1 ten thousand = 10,000
- Multiply the digit by the value of the column. There are 9 ten thousands.9 × 10,000 = 90,000
Check. Say it in words: 9 ten thousands is ninety thousand. ✓
Watch out. The digit is 9 but its value is 90,000. The same digit is worth different amounts in different columns.
Key words. A digit is one of 0 to 9. The value of a digit is what it is worth. A period is a group of three columns: Ones, Thousands, Millions.
Method. The value of a digit depends on its column. Find the column, then multiply the digit by the value of the column.
- Write the number in a place-value table. Each column has a name and a value. The coloured digit is the one we want.
Thousands Ones HTh TTh Th H T O 4 0 7 1 5 3 - Find which column the digit is in. The digit is 7 and it sits in the thousands column.1 thousand = 1,000
- Multiply the digit by the value of the column. There are 7 thousands.7 × 1,000 = 7,000
Check. Say it in words: 7 thousands is seven thousand. ✓
Watch out. The digit is 7 but its value is 7,000. The same digit is worth different amounts in different columns.
Key words. A digit is one of 0 to 9. The value of a digit is what it is worth. A period is a group of three columns: Ones, Thousands, Millions.
Method. The value of a digit depends on its column. Find the column, then multiply the digit by the value of the column.
- Write the number in a place-value table. Each column has a name and a value. The coloured digit is the one we want.
Thousands Ones HTh TTh Th H T O 5 2 0 8 9 4 - Find which column the digit is in. The digit is 9 and it sits in the tens column.1 ten = 10
- Multiply the digit by the value of the column. There are 9 tens.9 × 10 = 90
Check. Say it in words: 9 tens is ninety. ✓
Watch out. The digit is 9 but its value is 90. The same digit is worth different amounts in different columns.
Key words. A digit is one of 0 to 9. The value of a digit is what it is worth. A period is a group of three columns: Ones, Thousands, Millions.
Method. Say the number in parts, from left to right: the thousands period first, then the hundreds, then the last two digits.
- Write the number in a place-value table. The comma splits the digits into the Thousands period and the Ones period.
Thousands Ones TTh Th H T O 3 8 2 0 5 - Read each part and say it in words. Say the thousands period as a number and then add the word thousand.Thousands period: 38 → thirty-eight thousand
Hundreds: 2 → two hundred
Last two digits: 5 → five - Join the parts together. Put “and” before the last two digits (the tens and ones) when there are hundreds or thousands before them.thirty-eight thousand, two hundred and five
Check. Read it out loud. It sounds like 38,205. ✓
Watch out. Zeros are never said aloud. 400,060 is “four hundred thousand and sixty”: nothing is said for the empty columns, but they still need a 0 when you write the digits.
Key words. A digit is one of 0 to 9. The value of a digit is what it is worth. A period is a group of three columns: Ones, Thousands, Millions.
Method. Say the number in parts, from left to right: the thousands period first, then the hundreds, then the last two digits.
- Write the number in a place-value table. The comma splits the digits into the Thousands period and the Ones period.
Thousands Ones HTh TTh Th H T O 2 7 0 0 4 0 - Read each part and say it in words. Say the thousands period as a number and then add the word thousand.Thousands period: 270 → two hundred and seventy thousand
Last two digits: 40 → forty - Join the parts together. Put “and” before the last two digits (the tens and ones) when there are hundreds or thousands before them.two hundred and seventy thousand and forty
Check. Read it out loud. It sounds like 270,040. ✓
Watch out. Zeros are never said aloud. 400,060 is “four hundred thousand and sixty”: nothing is said for the empty columns, but they still need a 0 when you write the digits.
Key words. A digit is one of 0 to 9. The value of a digit is what it is worth. A period is a group of three columns: Ones, Thousands, Millions.
Method. Say the number in parts, from left to right: the thousands period first, then the hundreds, then the last two digits.
- Write the number in a place-value table. The comma splits the digits into the Thousands period and the Ones period.
Thousands Ones HTh TTh Th H T O 6 0 4 3 0 0 - Read each part and say it in words. Say the thousands period as a number and then add the word thousand.Thousands period: 604 → six hundred and four thousand
Hundreds: 3 → three hundred - Join the parts together. Put “and” before the last two digits (the tens and ones) when there are hundreds or thousands before them.six hundred and four thousand, three hundred
Check. Read it out loud. It sounds like 604,300. ✓
Watch out. Zeros are never said aloud. 400,060 is “four hundred thousand and sixty”: nothing is said for the empty columns, but they still need a 0 when you write the digits.
Key words. A digit is one of 0 to 9. The value of a digit is what it is worth. A period is a group of three columns: Ones, Thousands, Millions.
Method. Say the number in parts, from left to right: the thousands period first, then the hundreds, then the last two digits.
- Write the number in a place-value table. The comma splits the digits into the Thousands period and the Ones period.
Thousands Ones HTh TTh Th H T O 9 0 0 0 0 9 - Read each part and say it in words. Say the thousands period as a number and then add the word thousand.Thousands period: 900 → nine hundred thousand
Last two digits: 9 → nine - Join the parts together. Put “and” before the last two digits (the tens and ones) when there are hundreds or thousands before them.nine hundred thousand and nine
Check. Read it out loud. It sounds like 900,009. ✓
Watch out. Zeros are never said aloud. 400,060 is “four hundred thousand and sixty”: nothing is said for the empty columns, but they still need a 0 when you write the digits.
Key words. A digit is one of 0 to 9. The value of a digit is what it is worth. A period is a group of three columns: Ones, Thousands, Millions.
Method. Listen for the words “thousand” and “hundred”. They tell you which period and column each part goes in.
- Split the words into parts. Each part belongs to one period or column.“fifty-two thousand” → the Thousands period is 52
“six hundred” → 6 in the hundreds column
“eight” → 0 in the tens column and 8 in the ones column - Write the digits in a place-value table. Write a zero in every column that was not mentioned. Each period has three digits (except the first).
Thousands Ones TTh Th H T O 5 2 6 0 8 - Write the number. Put a comma between the periods.52,608
Check. Say 52,608 in words: fifty-two thousand, six hundred and eight. It matches. ✓
Watch out. A zero is a place holder. Without it the digits slip into the wrong columns and the number changes.
Key words. A digit is one of 0 to 9. The value of a digit is what it is worth. A period is a group of three columns: Ones, Thousands, Millions.
Method. Listen for the words “thousand” and “hundred”. They tell you which period and column each part goes in.
- Split the words into parts. Each part belongs to one period or column.“three hundred and forty thousand” → the Thousands period is 340
no hundreds are said → 0 in the hundreds column
“seven” → 0 in the tens column and 7 in the ones column - Write the digits in a place-value table. Write a zero in every column that was not mentioned. Each period has three digits (except the first).
Thousands Ones HTh TTh Th H T O 3 4 0 0 0 7 - Write the number. Put a comma between the periods.340,007
Check. Say 340,007 in words: three hundred and forty thousand and seven. It matches. ✓
Watch out. A zero is a place holder. Without it the digits slip into the wrong columns and the number changes.
Key words. A digit is one of 0 to 9. The value of a digit is what it is worth. A period is a group of three columns: Ones, Thousands, Millions.
Method. Listen for the words “thousand” and “hundred”. They tell you which period and column each part goes in.
- Split the words into parts. Each part belongs to one period or column.“six hundred and six thousand” → the Thousands period is 606
“six hundred” → 6 in the hundreds column
“six” → 0 in the tens column and 6 in the ones column - Write the digits in a place-value table. Write a zero in every column that was not mentioned. Each period has three digits (except the first).
Thousands Ones HTh TTh Th H T O 6 0 6 6 0 6 - Write the number. Put a comma between the periods.606,606
Check. Say 606,606 in words: six hundred and six thousand, six hundred and six. It matches. ✓
Watch out. A zero is a place holder. Without it the digits slip into the wrong columns and the number changes.
Key words. A digit is one of 0 to 9. The value of a digit is what it is worth. A period is a group of three columns: Ones, Thousands, Millions.
Method. Listen for the words “thousand” and “hundred”. They tell you which period and column each part goes in.
- Split the words into parts. Each part belongs to one period or column.“nine hundred thousand” → the Thousands period is 900
no hundreds are said → 0 in the hundreds column
“ninety” → 9 in the tens column and 0 in the ones column - Write the digits in a place-value table. Write a zero in every column that was not mentioned. Each period has three digits (except the first).
Thousands Ones HTh TTh Th H T O 9 0 0 0 9 0 - Write the number. Put a comma between the periods.900,090
Check. Say 900,090 in words: nine hundred thousand and ninety. It matches. ✓
Watch out. A zero is a place holder. Without it the digits slip into the wrong columns and the number changes.
Key words. To partition a number is to split it into parts, one part for each digit.
Method. Partition means splitting a number into the value of each of its digits.
- Write the number in a place-value table. This shows how many of each column there are.
Thousands Ones HTh TTh Th H T O 4 8 2 6 1 5 - Work out the value of each digit. Digit times the value of its column.4 hundred thousands = 400,000
8 ten thousands = 80,000
2 thousands = 2,000
6 hundreds = 600
1 ten = 10
5 ones = 5 - Write the values as an addition. Start with the biggest value.482,615 = 400,000 + 80,000 + 2,000 + 600 + 10 + 5
Check. Add them up: 400,000 + 80,000 + 2,000 + 600 + 10 + 5 = 482,615. ✓
Watch out. Write 300,000 for 3 hundred thousands, not just 3. Each part keeps its full value.
Key words. To partition a number is to split it into parts, one part for each digit.
Method. Partition means splitting a number into the value of each of its digits.
- Write the number in a place-value table. This shows how many of each column there are.
Thousands Ones HTh TTh Th H T O 7 0 3 0 4 0 - Work out the value of each digit. Digit times the value of its column.7 hundred thousands = 700,000
0 ten thousands = nothing to write
3 thousands = 3,000
0 hundreds = nothing to write
4 tens = 40
0 ones = nothing to write - Leave out the zeros. A zero means the column is empty, so there is nothing to add.
- Write the values as an addition. Start with the biggest value.703,040 = 700,000 + 3,000 + 40
Check. Add them up: 700,000 + 3,000 + 40 = 703,040. ✓
Watch out. Write 300,000 for 3 hundred thousands, not just 3. Each part keeps its full value.
Key words. To partition a number is to split it into parts, one part for each digit.
Method. Partition means splitting a number into the value of each of its digits.
- Write the number in a place-value table. This shows how many of each column there are.
Thousands Ones HTh TTh Th H T O 2 5 0 0 0 8 - Work out the value of each digit. Digit times the value of its column.2 hundred thousands = 200,000
5 ten thousands = 50,000
0 thousands = nothing to write
0 hundreds = nothing to write
0 tens = nothing to write
8 ones = 8 - Leave out the zeros. A zero means the column is empty, so there is nothing to add.
- Write the values as an addition. Start with the biggest value.250,008 = 200,000 + 50,000 + 8
Check. Add them up: 200,000 + 50,000 + 8 = 250,008. ✓
Watch out. Write 300,000 for 3 hundred thousands, not just 3. Each part keeps its full value.
Key words. To partition a number is to split it into parts, one part for each digit.
Method. Partition means splitting a number into the value of each of its digits.
- Write the number in a place-value table. This shows how many of each column there are.
Thousands Ones TTh Th H T O 9 6 0 7 0 - Work out the value of each digit. Digit times the value of its column.9 ten thousands = 90,000
6 thousands = 6,000
0 hundreds = nothing to write
7 tens = 70
0 ones = nothing to write - Leave out the zeros. A zero means the column is empty, so there is nothing to add.
- Write the values as an addition. Start with the biggest value.96,070 = 90,000 + 6,000 + 70
Check. Add them up: 90,000 + 6,000 + 70 = 96,070. ✓
Watch out. Write 300,000 for 3 hundred thousands, not just 3. Each part keeps its full value.
Key words. A place holder is a zero that holds an empty column so the other digits stay in the right place.
Method. Put each part into its own column of a place-value table. Write a zero in any column with nothing in it.
- Read the parts: 6 hundred thousands, 4 thousands and 9 tens. Each part tells us which column it goes in and how many.
- Put each digit in its column. Start with the biggest column on the left.6 hundred thousands → write 6 in the HTh column
0 ten thousands → write 0 in the TTh column (nothing here, so write a zero)
4 thousands → write 4 in the Th column
0 hundreds → write 0 in the H column (nothing here, so write a zero)
9 tens → write 9 in the T column
0 ones → write 0 in the O column (nothing here, so write a zero) - Read the digits across the table. Put commas between the periods.
Thousands Ones HTh TTh Th H T O 6 0 4 0 9 0
The number is 604,090.
Check. Say it in words: six hundred and four thousand and ninety. It matches the parts. ✓
Watch out. A zero is a place holder. 405,060 and 45,060 are very different numbers.
Key words. A place holder is a zero that holds an empty column so the other digits stay in the right place.
Method. Put each part into its own column of a place-value table. Write a zero in any column with nothing in it.
- Read the parts: 3 hundred thousands, 7 ten thousands and 2 hundreds. Each part tells us which column it goes in and how many.
- Put each digit in its column. Start with the biggest column on the left.3 hundred thousands → write 3 in the HTh column
7 ten thousands → write 7 in the TTh column
0 thousands → write 0 in the Th column (nothing here, so write a zero)
2 hundreds → write 2 in the H column
0 tens → write 0 in the T column (nothing here, so write a zero)
0 ones → write 0 in the O column (nothing here, so write a zero) - Read the digits across the table. Put commas between the periods.
Thousands Ones HTh TTh Th H T O 3 7 0 2 0 0
The number is 370,200.
Check. Say it in words: three hundred and seventy thousand, two hundred. It matches the parts. ✓
Watch out. A zero is a place holder. 405,060 and 45,060 are very different numbers.
Key words. A place holder is a zero that holds an empty column so the other digits stay in the right place.
Method. Put each part into its own column of a place-value table. Write a zero in any column with nothing in it.
- Read the parts: 800,000 + 5,000 + 40 + 3. Each part tells us which column it goes in and how many.
- Put each digit in its column. Start with the biggest column on the left.8 hundred thousands → write 8 in the HTh column
0 ten thousands → write 0 in the TTh column (nothing here, so write a zero)
5 thousands → write 5 in the Th column
0 hundreds → write 0 in the H column (nothing here, so write a zero)
4 tens → write 4 in the T column
3 ones → write 3 in the O column - Read the digits across the table. Put commas between the periods.
Thousands Ones HTh TTh Th H T O 8 0 5 0 4 3
The number is 805,043.
Check. Say it in words: eight hundred and five thousand and forty-three. It matches the parts. ✓
Watch out. A zero is a place holder. 405,060 and 45,060 are very different numbers.
Key words. A place holder is a zero that holds an empty column so the other digits stay in the right place.
Method. Put each part into its own column of a place-value table. Write a zero in any column with nothing in it.
- Read the parts: 200,000 + 90,000 + 6. Each part tells us which column it goes in and how many.
- Put each digit in its column. Start with the biggest column on the left.2 hundred thousands → write 2 in the HTh column
9 ten thousands → write 9 in the TTh column
0 thousands → write 0 in the Th column (nothing here, so write a zero)
0 hundreds → write 0 in the H column (nothing here, so write a zero)
0 tens → write 0 in the T column (nothing here, so write a zero)
6 ones → write 6 in the O column - Read the digits across the table. Put commas between the periods.
Thousands Ones HTh TTh Th H T O 2 9 0 0 0 6
The number is 290,006.
Check. Say it in words: two hundred and ninety thousand and six. It matches the parts. ✓
Watch out. A zero is a place holder. 405,060 and 45,060 are very different numbers.
Method. Find the ten thousands digit in each number. It is the second digit from the left in a six-digit number.
- Write each number in a place-value table. This shows which column each digit is in.
Thousands Ones HTh TTh Th H T O 7 1 0 4 5 8 Thousands Ones HTh TTh Th H T O 1 0 7 4 5 8 Thousands Ones HTh TTh Th H T O 1 7 0 4 5 8 Thousands Ones HTh TTh Th H T O 1 0 0 7 4 5 - Look at the coloured ten thousands digit in each. We want the one that is a 7.710,458: ten thousands digit is 1
107,458: ten thousands digit is 0
170,458: ten thousands digit is 7
100,745: ten thousands digit is 0 - Choose the number. C (170,458)
Check. 170,458 = 100,000 + 70,000 + 400 + 50 + 8. The 7 is worth 70,000. ✓
Watch out. 710,458 has a 7 too, but it is in the hundred thousands column.
Method. To find how many thousands are in a number, read all the digits from the left up to the thousands column as one number.
- Write the number in a place-value table. Find the thousands column.
Thousands Ones TTh Th H T O 7 2 0 0 0 - Read the digits up to the Th column. Every column on the left is a bigger column. They can all be swapped for thousands. 1 ten thousand is 10 thousands, and so on.The digits 72, read as one number, are 72.
- Write the answer. 72 thousands
Check. 72 × 1,000 = 72,000. ✓
Watch out. Do not just read the digit in that column. There are 72 thousands in 72,000, not 2.
Method. To find how many hundreds are in a number, read all the digits from the left up to the hundreds column as one number.
- Write the number in a place-value table. Find the hundreds column.
Thousands Ones TTh Th H T O 4 5 3 0 0 - Read the digits up to the H column. Every column on the left is a bigger column. They can all be swapped for hundreds. 1 thousand is 10 hundreds, and so on.The digits 453, read as one number, are 453.
- Write the answer. 453 hundreds
Check. 453 × 100 = 45,300. ✓
Watch out. Do not just read the digit in that column. There are 453 hundreds in 45,300, not 3.
Method. To find how many tens are in a number, read all the digits from the left up to the tens column as one number.
- Write the number in a place-value table. Find the tens column.
Thousands Ones Th H T O 8 7 4 0 - Read the digits up to the T column. Every column on the left is a bigger column. They can all be swapped for tens. 1 hundred is 10 tens, and so on.The digits 874, read as one number, are 874.
- Write the answer. 874 tens
Check. 874 × 10 = 8,740. ✓
Watch out. Do not just read the digit in that column. There are 874 tens in 8,740, not 4.
Method. To find how many hundreds are in a number, read all the digits from the left up to the hundreds column as one number.
- Write the number in a place-value table. Find the hundreds column.
Thousands Ones HTh TTh Th H T O 1 0 0 0 0 0 - Read the digits up to the H column. Every column on the left is a bigger column. They can all be swapped for hundreds. 1 thousand is 10 hundreds, and so on.The digits 1000, read as one number, are 1,000.
- Write the answer. 1,000 hundreds
Check. 1,000 × 100 = 100,000. ✓
Watch out. Do not just read the digit in that column. There are 1,000 hundreds in 100,000, not 0.
Key words. A place holder is a zero that holds an empty column so the other digits stay in the right place.
Method. Put each part into its own column of a place-value table. Write a zero in any column with nothing in it.
- Read the parts: 4 boxes of 100,000 + 2 boxes of 10,000 + 6 boxes of 1,000 + 5 loose coins. Each part tells us which column it goes in and how many.
- Put each digit in its column. Start with the biggest column on the left.4 hundred thousands → write 4 in the HTh column
2 ten thousands → write 2 in the TTh column
6 thousands → write 6 in the Th column
0 hundreds → write 0 in the H column (nothing here, so write a zero)
0 tens → write 0 in the T column (nothing here, so write a zero)
5 ones → write 5 in the O column - Read the digits across the table. Put commas between the periods.
Thousands Ones HTh TTh Th H T O 4 2 6 0 0 5
The number is 426,005.
Check. Say it in words: four hundred and twenty-six thousand and five. It matches the parts. ✓
Watch out. A zero is a place holder. 405,060 and 45,060 are very different numbers.
Method. A six-digit number cannot start with 0. The smallest digit for the hundred thousands column is 1, and every other column is 0.
- Choose the first digit. It cannot be 0, so the smallest choice is 1.HTh = 1
- Make every other column as small as possible. 0 is the smallest digit.TTh = 0, Th = 0, H = 0, T = 0, O = 0
- Write the number. 100,000
Check. 99,999 has only five digits, and 100,000 is one more than 99,999. ✓
Method. Use the biggest digit, 9, in every column.
- Choose the biggest digit for each column. 9 is the biggest digit.HTh = 9, TTh = 9, Th = 9, H = 9, T = 9, O = 9
- Write the number. 999,999
Check. One more makes a seven-digit number: 1,000,000. ✓
Method. Add 1 to the ones column and carry the 1 all the way along. Then write the answer in digits and words.
- Write the number in a place-value table. Every column is a 9.
Thousands Ones HTh TTh Th H T O 9 9 9 9 9 9 - Add 1 to the ones. 9 + 1 = 10, so write 0 and carry 1. The next column is also 9, so the carry keeps going.9 ones + 1 = 10 ones → 1 ten
9 tens + 1 ten = 10 tens → 1 hundred
… and so on, all the way to the left - Write the new number. Every column is now 0 and there is a new column on the left, the Millions column.
Millions Thousands Ones M HTh TTh Th H T O 1 0 0 0 0 0 0
1,000,000 - Say it in words. 1,000,000 is 1 thousand thousands. We call it one million.one million
Check. 10 × 100,000 = 1,000,000, so there are 10 hundred thousands in one million. ✓
Watch out. 999,999 has six digits. One more has seven. A new column appears when every column is full.
Method. Say the words in parts and write each part in the right column. Then compare with Noah’s number.
- Say the words in parts. “Three hundred and five thousand” is the thousands period: 305. “And forty” is the last two digits: 4 tens and 0 ones. No hundreds are said.305 | 0 hundreds, 4 tens, 0 ones
- Write it in a place-value table. The empty hundreds column and the ones column need zeros.
Thousands Ones HTh TTh Th H T O 3 0 5 0 4 0 - Compare with Noah’s number. Noah wrote 350,040. That has 5 ten thousands and 0 thousands, but the words say 0 ten thousands and 5 thousands.350,040 is three hundred and fifty thousand and forty.
He swapped the 0 and the 5.
Check. Say 305,040 in words: three hundred and five thousand and forty. ✓
Watch out. Each word group tells you exactly which columns to fill. Write the thousands period first.
Method. Write each one as a six-digit number, then find the one that is different.
- Write each as a number. Use place value.400,050
400,000 + 50 = 400,050
4 hundred thousands and 5 tens = 400,000 + 50 = 400,050
450,000 - Compare them. Three are 400,050 but one is 450,000.400,050, 400,050, 400,050, 450,000
- Write the odd one out. 450,000
Check. 450,000 has 5 ten thousands. The others have 5 tens. ✓
Watch out. Look at which column the 5 is in.
“The value of a digit is bigger than the digit itself.”
Method. Try some digits in different columns. If it works for some and not others, the answer is “sometimes”.
- Try the 3 in 300,000. The 3 is in the hundred thousands column.Value = 300,000. That is bigger than 3. It works here.
- Try the 7 in 5,347. The 7 is in the ones column.Value = 7. That is the same as the digit, not bigger. It does not work here.
- Try a zero. A 0 in any column is worth nothing.Value = 0. Not bigger than 0.
- Write the answer. It works for some digits and not for others.Sometimes
Check. It is bigger for digits 1 to 9 that are not in the ones column. ✓
Watch out. One example that works does not prove “always”. Look for one that breaks the rule.
Method. Work out 10 lots of 100,000 and compare with one million.
- Count in hundred thousands. Add 100,000 each time.1 × 100,000 = 100,000
2 × 100,000 = 200,000
3 × 100,000 = 300,000
4 × 100,000 = 400,000
5 × 100,000 = 500,000
6 × 100,000 = 600,000
7 × 100,000 = 700,000
8 × 100,000 = 800,000
9 × 100,000 = 900,000
10 × 100,000 = 1,000,000 - Find the tenth number. 10 hundred thousands is the last line.10 × 100,000 = 1,000,000
- Answer Amira. Yes. There are 10 hundred thousands in one million.
Check. Using the chart: the Millions column is 10 times the HTh column. ✓
Watch out. Each column is 10 times the column on its right. That is why a new column starts after ten of the last one.
My hundred thousands digit is twice my ten thousands digit.
My thousands digit is 0.
My hundreds digit is the same as my ten thousands digit.
My tens digit is 5 more than my ones digit.
My digits add up to 21.
My ones digit is not 0 and I am more than 500,000.
What number am I?
Method. Use the easy clues first to write the shape of the number. Then use the digit total to find the possible numbers.
- Write what we know. Let the ten thousands digit be k. Then the hundred thousands digit is 2k, the thousands digit is 0 and the hundreds digit is k. The tens digit is 5 more than the ones digit.2k | k | 0 | k | (ones + 5) | ones
- Use the digit total. The digits add up to 21, so 2k + k + 0 + k + (ones + 5) + ones = 21.4k + 2 × ones + 5 = 21
4k + 2 × ones = 16 - Try each possible k. k can be 1, 2, 3 or 4 (2k must be one digit). Work out the ones digit each time. (k = 1 fails: the ones digit would be 6 and the tens digit 11, which is too big.)k = 2: ones = 4, tens = 9, number = 420,294
k = 3: ones = 2, tens = 7, number = 630,372
k = 4: ones = 0, tens = 5, number = 840,450 - Use the last clue. The ones digit is not 0, and the number is more than 500,000.420,294 is less than 500,000, so no. 840,450 has ones digit 0, so no.
Only 630,372 is left.
Check. 630,372: 6 = 2 × 3 ✓, thousands 0 ✓, hundreds 3 ✓, tens 7 = 2 + 5 ✓, 6+3+0+3+7+2 = 21 ✓, ones not 0 ✓, more than 500,000 ✓.
Watch out. Check your answer against every clue.