Year 6 Maths reasoning (SATs): Place value, comparing and rounding
Part of the Year 6 Maths reasoning (SATs) number reasoning chapter. Chapter overview · whole chapter on one page
Place value, comparing and rounding
Rule
Each digit has a value that depends on its column. In 4,862,139 the 6 is in the ten thousands column, so it is worth 6 x 10,000 = 60,000.
To round, look at the digit next to the column you are rounding to. 5 or more: round up. 4 or less: round down.
For the full method of place value and rounding, read Year 5 and Year 6 maths, chapter 1.
Key ideas
- The value of a digit = the digit x the value of its column.
- Compare numbers by their number of digits first, then by the leading digit.
- To round to the nearest 10,000, look at the thousands digit.
Method. Find the column, then multiply the digit by its column value.
- Find the column of the digit. The digit 6 is in the ten thousands column.ten thousands
- Work out the value. The value is the digit times the column value 10,000.6 x 10,000 = 60,000
- Write the answer. 60,000
Check. 60,000 = 6 x 10,000. ✓
Watch out. The value of a digit depends on its column, not just on the digit.
Method. Look at the digit next to the rounding column.
- Find the rounding column and the digit next to it. Rounding to the nearest 1,000 looks at the hundreds digit.digit to check = 7
- Decide up or down. A 5 or more rounds up; 4 or less rounds down.7 is 5 or more, so round up
- Write the rounded number. Keep the digits to the left and make the rest zeros.57,000
- Write the answer. 57,000
Check. 57,000 is a multiple of 1,000 and is the closest one to 56,750. ✓
Watch out. Do not round a 5 down. A 5 always rounds up.
Method. Compare the digits, starting from the left.
- Count the digits in each number. A number with more digits is larger.45,000 has 5 digits, 4,500 has 4 digits, 405,000 has 6 digits, 54,000 has 5 digits
- Compare numbers with the same number of digits. Look at the leading digit, then the next one.compare from the left
- Write them in order. Put them smallest to largest.4,500, 45,000, 54,000, 405,000
- Write the answer. 4,500, 45,000, 54,000, 405,000
Check. Each number is smaller than the one after it. ✓
Watch out. 4,500 has four digits and 45,000 has five, so 45,000 is larger.
Watch out
Watch out. The 7 in 700,000 is worth 700,000, not 7. A digit is worth more the further left it is.
Exam tip
Practice guide. Check each rounding answer: it must be a multiple of the rounding unit and close to the original number.
Exercise 1A Practice: place value, comparing and rounding
Non-calculatorMethod. Find the column, then multiply the digit by its column value.
- Find the column of the digit. The digit 3 is in the hundreds column.hundreds
- Work out the value. The value is the digit times the column value 100.3 x 100 = 300
- Write the answer. 300
Check. 300 = 3 x 100. ✓
Watch out. The value of a digit depends on its column, not just on the digit.
Method. Find the column, then multiply the digit by its column value.
- Find the column of the digit. The digit 6 is in the hundred thousands column.hundred thousands
- Work out the value. The value is the digit times the column value 100,000.6 x 100,000 = 600,000
- Write the answer. 600,000
Check. 600,000 = 6 x 100,000. ✓
Watch out. The value of a digit depends on its column, not just on the digit.
Method. Write each part of the number in its column.
- Write the millions. 3 million is 3,000,000.3,000,000
- Write the thousands. 40 thousand is 40,000.40,000
- Write the units. Seven units is 7.7
- Add the parts together. Put the parts in their columns.3,040,007
- Write the answer. 3,040,007
Check. 3,000,000 + 40,000 + 7 = 3,040,007. ✓
Method. Look at the digit next to the rounding column.
- Find the rounding column and the digit next to it. Rounding to the nearest 10,000 looks at the thousands digit.digit to check = 2
- Decide up or down. A 5 or more rounds up; 4 or less rounds down.2 is 4 or less, so round down
- Write the rounded number. Keep the digits to the left and make the rest zeros.4,860,000
- Write the answer. 4,860,000
Check. 4,860,000 is a multiple of 10,000 and is the closest one to 4,862,139. ✓
Watch out. Do not round a 5 down. A 5 always rounds up.
Method. Look at the digit next to the rounding column.
- Find the rounding column and the digit next to it. Rounding to the nearest 1,000 looks at the hundreds digit.digit to check = 7
- Decide up or down. A 5 or more rounds up; 4 or less rounds down.7 is 5 or more, so round up
- Write the rounded number. Keep the digits to the left and make the rest zeros.57,000
- Write the answer. 57,000
Check. 57,000 is a multiple of 1,000 and is the closest one to 56,750. ✓
Watch out. Do not round a 5 down. A 5 always rounds up.
Method. Look at the digit next to the rounding column.
- Find the rounding column and the digit next to it. Rounding to the nearest 100 looks at the tens digit.digit to check = 9
- Decide up or down. A 5 or more rounds up; 4 or less rounds down.9 is 5 or more, so round up
- Write the rounded number. Keep the digits to the left and make the rest zeros.10,000
- Write the answer. 10,000
Check. 10,000 is a multiple of 100 and is the closest one to 9,996. ✓
Watch out. Do not round a 5 down. A 5 always rounds up.
Method. Compare the digits, starting from the left.
- Count the digits in each number. A number with more digits is larger.4,500 has 4 digits, 45,000 has 5 digits, 405,000 has 6 digits, 54,000 has 5 digits
- Compare numbers with the same number of digits. Look at the leading digit, then the next one.compare from the left
- Write them in order. Put them smallest to largest.4,500, 45,000, 54,000, 405,000
- Write the answer. 4,500, 45,000, 54,000, 405,000
Check. Each number is smaller than the one after it. ✓
Watch out. 4,500 has four digits and 45,000 has five, so 45,000 is larger.
Method. Compare the digits, starting from the left.
- Count the digits in each number. A number with more digits is larger.7,063 has 4 digits, 1,700 has 4 digits, 70,630 has 5 digits, 1,070 has 4 digits
- Compare numbers with the same number of digits. Look at the leading digit, then the next one.compare from the left
- Write them in order. Put them largest to smallest.70,630, 7,063, 1,700, 1,070
- Write the answer. 70,630, 7,063, 1,700, 1,070
Check. Each number is larger than the one after it. ✓
Watch out. 4,500 has four digits and 45,000 has five, so 45,000 is larger.
Method. Compare the digits from the left until they differ.
- Compare the digits from the left. The first two digits, 3 and 4, are the same in both numbers.3 and 4 match
- Find the first place where they differ. The third digit is 0 in the first number and 2 in the second, so the second number is bigger.3402871 is less than 3420871
- Write the sign. The smaller number is on the left, so use the less than sign.<
- Write the answer. <
Check. 3,402,871 is less than 3,420,871. ✓
Method. Add 1,000 to the thousands column.
- Add 1,000. Add one thousand to the number.6,495,300 + 1,000
- Write the answer. 6,496,300
Check. 6,496,300 - 1,000 = 6,495,300. ✓
Method. Subtract 10,000 from the ten thousands column.
- Subtract 10,000. Take one ten thousand away.6,495,300 - 10,000
- Write the answer. 6,485,300
Check. 6,485,300 + 10,000 = 6,495,300. ✓
Method. Test each option.
- Check each option. Test each one against the rule or the calculation.
- Tick the true ones. Each ticked number has more than seven digits and is above 2,000,000.2,004,500, 2,400,000
- Leave the others unticked. These do not match.1,990,000, 2,000,000, 1,999,999 are not ticked
- Write the answer. 2,004,500, 2,400,000
Check. Each ticked option is true. ✓
Watch out. 1,999,999 is less than 2 million, so it is not ticked.
Method. Test each choice against the question.
- Read what the question asks. Decide what the answer must do or show.
- Test the choice. The 7 is in the hundred thousands column: 7 x 100,000 = 700,000.No, the 7 is worth 700,000 fits
- Reject the other choices. Yes, Sam is right is wrong because 7 is not in the thousands column.Yes, Sam is right and No, the 7 is worth 70 do not fit
- Write the answer. No, the 7 is worth 700,000
Check. No, the 7 is worth 700,000 is the one that fits. ✓
Method. Put the largest digit first, then the next largest.
- Find the largest digit. Nine is the largest digit, so it goes first in the millions column.9 million
- Put the rest in order. Put the remaining digits in order from largest to smallest.8, 6, 4, 2, 1, 0
- Write the number. Each digit is used once.9,864,210
- Write the answer. 9,864,210.
Check. All seven digits are used once. ✓
Method. Numbers that round to 4,500 to the nearest 100 are from 4,450 up to 4,549.
- Find the range. Half of 100 is 50, so numbers from 4,450 to 4,549 round to 4,500.4,450 to 4,549
- Pick one. Any number in this range is correct.4,450
- Write the answer. 4,450.
Check. 4,450 rounds to 4,500 to the nearest 100. ✓
Method. Look at the digit next to the rounding column.
- Find the rounding column and the digit next to it. Rounding to the nearest 100 looks at the tens digit.digit to check = 5
- Decide up or down. A 5 or more rounds up; 4 or less rounds down.5 is 5 or more, so round up
- Write the rounded number. Keep the digits to the left and make the rest zeros.7,500
- Write the answer. 7,500
Check. 7,500 is a multiple of 100 and is the closest one to 7,458. ✓
Watch out. Do not round a 5 down. A 5 always rounds up.
Method. The smallest number that rounds up to 60,000 is the first one at or above 55,000.
- Find the halfway point. Halfway between 50,000 and 60,000 is 55,000.55,000
- Check the round. From 55,000 upwards the number rounds to 60,000.55,000 rounds to 60,000
- Write the answer. 55,000
Check. 55,000 rounds up to 60,000. ✓
Watch out. The number 54,999 would round down to 50,000.