Year 6 Arithmetic (SATs): Place value to 10,000,000
Part of the Year 6 Arithmetic (SATs) place value and the four operations chapter. Chapter overview · whole chapter on one page
Place value to 10,000,000
Rule
Every column is worth ten times the column on its right: ones, tens, hundreds, thousands, ten thousands, hundred thousands, millions and ten millions.
The value of a digit is the digit multiplied by its column. In 4,702,815 the 7 is in the hundred thousands column, so it is worth 7 × 100,000 = 700,000.
Multiplying by 10 moves every digit one column to the left. For the full work on place value, read Year 6 maths, chapter 1.
Key ideas
- Each column is ten times the column on its right.
- The value of a digit is the digit times its column value.
- Compare two numbers from the left: the first column that differs decides.
- Multiplying by 10, 100 or 1000 shifts the digits to the left.
Method. Find the column of the 7, then multiply it by the column value.
- Find the column of the digit. Count from the right: this is the hundred thousands column.digit 7 in the hundred thousands column
- Multiply the digit by the column value. Each column is worth ten times the column on its right.7 × 100,000 = 700,000
- Write the answer. 700,000
Check. The 7 is in the hundred thousands column, and 700,000 + 4,002,815 = 4,702,815. ✓
Watch out. The 7 is not worth 7. Its column makes it worth seven hundred thousand.
Method. Write each part in its column, then add them.
- Write the millions. 3 millions is 3,000,000.3,000,000
- Write the thousands. 40 thousands is 40,000.3,000,000 + 40,000
- Write the hundreds. 6 hundreds is 600.3,000,000 + 40,000 + 600 = 3,040,600
- Write the answer. 3,040,600
Check. Count the zeros: the hundreds, tens and ones columns need zeros where nothing is written. ✓
Watch out. Leave the tens and ones as zeros if the question does not mention them.
Method. Compare the numbers from the left. Count the digits first.
- Count the digits. Two numbers have seven digits and two have six.509,100 and 509,010 have six digits
- Compare the six-digit numbers. Both start 509, then 1 is bigger than 0.509,010 < 509,100
- Compare the seven-digit numbers. Both start with 5 million. In the hundred thousands column 0 is less than 1, so 5,091,000 is smaller.5,091,000 < 5,190,000
- Write the answer. 509,010, 509,100, 5,091,000, 5,190,000
Check. Each number is smaller than the one after it. ✓
Watch out. 509,010 has six digits, so it is smaller than 5,091,000, which has seven.
Exercise 1A Practice: place value to ten million
Non-calculatorMethod. The 9 is in the hundred thousands column.
- Find the column of the digit. Count from the right: this is the hundred thousands column.digit 9 in the hundred thousands column
- Multiply. Hundred thousands are 100,000 each.9 × 100,000 = 900,000
- Write the answer. 900,000
Check. 3,904,216 has 9 in the hundred thousands column. ✓
Method. Find the column of the 3, then multiply.
- Find the column of the digit. Count from the right: this is the thousands column.digit 3 in the thousands column
- Multiply the digit by the column value. Each column is worth ten times the column on its right.3 × 1,000 = 3,000
- Write the answer. 3,000
Check. The 3 is in the thousands column: 3,000 + 80,000 + 457 = 83,457. ✓
Watch out. Count from the right: ones, tens, hundreds, thousands.
Method. Write each column, then add.
- Write each part. Use zeros where a column is empty.3,000,000 + 40,000 + 600
- Add the parts. The total has 3 in the millions.3,040,600
- Write the answer. 3,040,600
Check. The tens and ones columns are zero. ✓
Method. Each step adds 100,000.
- First step. 3,600,000 + 100,000 = 3,700,000.3,700,000
- Second and third steps. Add 100,000 twice more.3,800,000, then 3,900,000
- Write the answer. 3,900,000
Check. Three lots of 100,000 is 300,000. ✓
Method. Multiplying by 10 moves every digit one column to the left.
- Move each digit one column left. Add a zero at the end.46,250 × 10
- Write the answer. The digits stay the same, with a zero added.462,500
- Write the answer. 462,500
Check. Divide the answer by 10 to get back to 46,250. ✓
Method. Multiplying by 1,000 moves the digits three columns to the left.
- Move the digits three columns. Add three zeros at the end.3,072 × 1,000
- Write the answer. The total is 3,072 thousands.3,072,000
- Write the answer. 3,072,000
Check. Check: 3,072,000 ÷ 1,000 = 3,072. ✓
Method. Adding 1,000,000 changes only the millions digit.
- Find the millions digit. The millions digit is 7.7 millions
- Add 1 million. 7 millions + 1 million = 8 millions.8,250,400
- Write the answer. 8,250,400
Check. 8,250,400 - 7,250,400 = 1,000,000. ✓
Method. Put each digit in its own column.
- Write the digits in order. Ten thousands, thousands, tens, ones.9 7 0 6 3
- Read the number. There are 0 hundreds, so the number has a zero in the hundreds column.97,063
- Write the answer. 97,063
Check. Digit check: 9, 7, 0, 6, 3 from left to right. ✓
Watch out. Do not forget the zero in the hundreds column.
Method. Compare the two numbers from the left.
- Line the numbers up by place value. Both numbers must have the same columns to compare them.6,482,000 and 6,428,000
- Compare from the left. The leftmost columns that match tell you nothing; the first column that differs decides.the ten thousands columns: 8 and 2
- Say which is bigger. The number with the bigger digit in the ten thousands column is bigger.6,482,000 is bigger
- Write the answer. >
Check. 6,482,000 has 8 where 6,428,000 has 2 in the ten thousands column. ✓
Method. Test each choice against the question.
- Read what the question asks. Decide what you need to find or check.
- Test the choice. 1,452,000 has 1 million, 4 hundred thousands, 5 ten thousands and 2 thousands.1,452,000 is right
- Reject the other choices. 3,640,000 has 6 in the hundred thousands. 4,013,000 has 0 in the hundred thousands. 2,345,678 has 3 in the hundred thousands.3,640,000 and 4,013,000 and 2,345,678 are not right
- Write the answer. 1,452,000
Check. 1,452,000 is right. ✓
Method. Put the largest digit in the largest column, then go down in order.
- Order the digits from largest to smallest. Largest digit first.9, 7, 4, 4, 2, 1, 0
- Write the number. Put the digits in that order.9,744,210
- Write the answer. 9,744,210
Check. Seven digits, each used once: 9 7 4 4 2 1 0. ✓
Method. Find the value of the first 5 and of the last 5.
- Find the first 5. It is in the millions column.5,000,000
- Find the last 5. It is in the ones column.5
- Write the answer. No, the 5s are worth different amounts because they are in different columns.
Check. 5,000,000 and 5 are not equal. ✓