Year 6: Place value to three decimal places
Part of the Year 6 decimals chapter. Chapter overview · whole chapter on one page
Place value to three decimal places
Decimals are another way of writing parts of a whole. The decimal point shows where the ones end. The places after the point get smaller as you move right: the first is tenths, then hundredths, then thousandths.
Each column is ten times bigger than the column on its right. So 1 tenth is 0.1, 1 hundredth is 0.01 and 1 thousandth is 0.001. To find the value of a digit, find its column first, then multiply the digit by the value of that column. The digit 7 in 4.273 is in the hundredths column, so it is worth 7 × 0.01 = 0.07.
Key ideas
- A decimal has a decimal point. The ones are in front of it, and the tenths, hundredths and thousandths come after it.
- Each place is ten times bigger than the place to its right: 0.001 × 10 = 0.01.
- The value of a digit = the digit × the value of its place. The digit 0 is still a place holder.
- Zeros at the end of a decimal do not change its value: 0.5 = 0.50 = 0.500.
Key words. The decimal point separates the ones from the part smaller than 1. The places after it are tenths (0.1), hundredths (0.01) and thousandths (0.001).
Method. Find the column of the digit, then multiply the digit by the value of that column.
- Find the column of the digit. Count the places from the decimal point.The 5 is in the hundredths column
- Find what one of that column is worth. Each hundredth is worth 0.01.1 hundredth = 0.01
- Multiply the digit by that value. The digit tells us how many of them there are.5 × 0.01 = 0.05
- Write the answer. Keep the zeros that show the place.0.05
Check. 3.257 = 3 + 0.2 + 0.05 + 0.007. ✓
Watch out. The 0 digits still count as places. The digit 5 is worth 0.05, not 5.
Method. Each column has its own digit. Write the number in parts, one part for each column.
- Find the digits and their columns. Ones, tenths, hundredths, thousandths.6 ones, 0 tenths, 5 hundredths, 2 thousandths
- Write each part as an addition. A zero column adds nothing, so we leave it out.6 + 0.05 + 0.002
- Check the parts add to the number. Adding the parts should give back the original number.6 + 0.05 + 0.002 = 6.052
- Write the answer. 6 + 0.05 + 0.002
Check. 6.052 = 6 + 0.05 + 0.002. ✓
Watch out. Do not write 0.5 for the 5 in 0.05. The 5 is in the hundredths column.
Key words. The decimal point separates the ones from the part smaller than 1. The places after it are tenths (0.1), hundredths (0.01) and thousandths (0.001).
Method. Count the thousandths: there are 1000 of them in each whole, so multiply by 1000.
- Write 0.25 with 3 decimal places. Zeros at the end do not change the value, but they show the place.0.250
- Find how many thousandths make one whole. Each whole one has 1000 thousandths.1 × 1000 = 1000
- Count the thousandths in 0.25. Multiply by 1000, because each whole has 1000 of them.0.25 × 1000 = 250
- Write the answer. The answer is a count, so it is a whole number.250
Check. 250 thousandths are 250 × 0.001 = 0.250. ✓
Watch out. Each thousandth is 0.001, so a count of 250 is worth 0.250.
Watch out
0.27 is smaller than 0.3, even though 27 is bigger than 3. The 2 is in the tenths column in 0.27, and 0.27 has 2 tenths. 0.3 has 3 tenths, so it is bigger.
Exam tip
Exam tip. Write the place names with a pencil under the digits if you find it hard: tenths, hundredths, thousandths.
Exercise 5A Place value to three decimal places
Non-calculatorKey words. The decimal point separates the ones from the part smaller than 1. The places after it are tenths (0.1), hundredths (0.01) and thousandths (0.001).
Method. Find the column of the digit, then multiply the digit by the value of that column.
- Find the column of the digit. Count the places from the decimal point.The 7 is in the hundredths column
- Find what one of that column is worth. Each hundredth is worth 0.01.1 hundredth = 0.01
- Multiply the digit by that value. The digit tells us how many of them there are.7 × 0.01 = 0.07
- Write the answer. Keep the zeros that show the place.0.07
Check. 4.273 = 4 + 0.2 + 0.07 + 0.003. ✓
Watch out. The 0 digits still count as places. The digit 7 is worth 0.07, not 7.
Key words. The decimal point separates the ones from the part smaller than 1. The places after it are tenths (0.1), hundredths (0.01) and thousandths (0.001).
Method. Find the column of the digit, then multiply the digit by the value of that column.
- Find the column of the digit. Count the places from the decimal point.The 3 is in the thousandths column
- Find what one of that column is worth. Each thousandth is worth 0.001.1 thousandth = 0.001
- Multiply the digit by that value. The digit tells us how many of them there are.3 × 0.001 = 0.003
- Write the answer. Keep the zeros that show the place.0.003
Check. 4.273 = 4 + 0.2 + 0.07 + 0.003. ✓
Watch out. The 0 digits still count as places. The digit 3 is worth 0.003, not 3.
Key words. The decimal point separates the ones from the part smaller than 1. The places after it are tenths (0.1), hundredths (0.01) and thousandths (0.001).
Method. Find the column of the digit, then multiply the digit by the value of that column.
- Find the column of the digit. Count the places from the decimal point.The 4 is in the tens column
- Find what one of that column is worth. Each ten is worth 10.1 ten = 10
- Multiply the digit by that value. The digit tells us how many of them there are.4 × 10 = 40
- Write the answer. Keep the zeros that show the place.40
Check. 46.8 = 40 + 6 + 0.8. ✓
Watch out. The 0 digits still count as places. The digit 4 is worth 40, not 4.
Key words. The decimal point separates the ones from the part smaller than 1. The places after it are tenths (0.1), hundredths (0.01) and thousandths (0.001).
Method. Find the column of the digit, then multiply the digit by the value of that column.
- Find the column of the digit. Count the places from the decimal point.The 8 is in the tenths column
- Find what one of that column is worth. Each tenth is worth 0.1.1 tenth = 0.1
- Multiply the digit by that value. The digit tells us how many of them there are.8 × 0.1 = 0.8
- Write the answer. Keep the zeros that show the place.0.8
Check. 46.8 = 40 + 6 + 0.8. ✓
Watch out. The 0 digits still count as places. The digit 8 is worth 0.8, not 8.
Key words. The decimal point separates the ones from the part smaller than 1. The places after it are tenths (0.1), hundredths (0.01) and thousandths (0.001).
Method. Find the column of the digit, then multiply the digit by the value of that column.
- Find the column of the digit. Count the places from the decimal point.The 9 is in the tenths column
- Find what one of that column is worth. Each tenth is worth 0.1.1 tenth = 0.1
- Multiply the digit by that value. The digit tells us how many of them there are.9 × 0.1 = 0.9
- Write the answer. Keep the zeros that show the place.0.9
Check. 15.906 = 10 + 5 + 0.9 + 0.006. ✓
Watch out. The 0 digits still count as places. The digit 9 is worth 0.9, not 9.
Key words. The decimal point separates the ones from the part smaller than 1. The places after it are tenths (0.1), hundredths (0.01) and thousandths (0.001).
Method. Find the column of the digit, then multiply the digit by the value of that column.
- Find the column of the digit. Count the places from the decimal point.The 5 is in the thousandths column
- Find what one of that column is worth. Each thousandth is worth 0.001.1 thousandth = 0.001
- Multiply the digit by that value. The digit tells us how many of them there are.5 × 0.001 = 0.005
- Write the answer. Keep the zeros that show the place.0.005
Check. 2.605 = 2 + 0.6 + 0.005. ✓
Watch out. The 0 digits still count as places. The digit 5 is worth 0.005, not 5.
Key words. The decimal point separates the ones from the part smaller than 1. The places after it are tenths (0.1), hundredths (0.01) and thousandths (0.001).
Method. Find the column of the digit, then multiply the digit by the value of that column.
- Find the column of the digit. Count the places from the decimal point.The 3 is in the hundreds column
- Find what one of that column is worth. Each hundred is worth 100.1 hundred = 100
- Multiply the digit by that value. The digit tells us how many of them there are.3 × 100 = 300
- Write the answer. Keep the zeros that show the place.300
Check. 380.4 = 300 + 80 + 0 + 0.4. ✓
Watch out. The 0 digits still count as places. The digit 3 is worth 300, not 3.
Key words. The decimal point separates the ones from the part smaller than 1. The places after it are tenths (0.1), hundredths (0.01) and thousandths (0.001).
Method. Find the column of the digit, then multiply the digit by the value of that column.
- Find the column of the digit. Count the places from the decimal point.The 2 is in the hundredths column
- Find what one of that column is worth. Each hundredth is worth 0.01.1 hundredth = 0.01
- Multiply the digit by that value. The digit tells us how many of them there are.2 × 0.01 = 0.02
- Write the answer. Keep the zeros that show the place.0.02
Check. 7.029 = 7 + 0.02 + 0.009. ✓
Watch out. The 0 digits still count as places. The digit 2 is worth 0.02, not 2.
Key words. The decimal point separates the ones from the part smaller than 1. The places after it are tenths (0.1), hundredths (0.01) and thousandths (0.001).
Method. Count the thousandths: there are 1000 of them in each whole, so multiply by 1000.
- Write 0.37 with 3 decimal places. Zeros at the end do not change the value, but they show the place.0.370
- Find how many thousandths make one whole. Each whole one has 1000 thousandths.1 × 1000 = 1000
- Count the thousandths in 0.37. Multiply by 1000, because each whole has 1000 of them.0.37 × 1000 = 370
- Write the answer. The answer is a count, so it is a whole number.370
Check. 370 thousandths are 370 × 0.001 = 0.370. ✓
Watch out. Each thousandth is 0.001, so a count of 370 is worth 0.370.
Key words. The decimal point separates the ones from the part smaller than 1. The places after it are tenths (0.1), hundredths (0.01) and thousandths (0.001).
Method. Line up the decimal points, then add each column from the right.
- Write the numbers under each other. Line up the decimal points in one column. Fill the gaps with zeros.
0.400 + 0.030 + 0.005 ------- 0.435
- Add column by column, from the right. Carry any ten into the next column to the left.0.400 + 0.030 + 0.005 = 0.435
- Write the answer with its decimal point in the same column. The decimal points line up in the question and in the answer.0.435
Check. Add the numbers in a different order and you get 0.435 again. ✓
Watch out. Line up the decimal points, not the last digits. Fill the gaps with zeros.
Key words. The decimal point separates the ones from the part smaller than 1. The places after it are tenths (0.1), hundredths (0.01) and thousandths (0.001).
Method. Line up the decimal points, then add each column from the right.
- Write the numbers under each other. Line up the decimal points in one column. Fill the gaps with zeros.
2.00 + 0.60 + 0.09 ------ 2.69
- Add column by column, from the right. Carry any ten into the next column to the left.2.00 + 0.60 + 0.09 = 2.69
- Write the answer with its decimal point in the same column. The decimal points line up in the question and in the answer.2.69
Check. Add the numbers in a different order and you get 2.69 again. ✓
Watch out. Line up the decimal points, not the last digits. Fill the gaps with zeros.
Key words. The decimal point separates the ones from the part smaller than 1. The places after it are tenths (0.1), hundredths (0.01) and thousandths (0.001).
Method. Line up the decimal points, then add each column from the right.
- Write the numbers under each other. Line up the decimal points in one column. Fill the gaps with zeros.
5.000 + 0.080 + 0.002 ------- 5.082
- Add column by column, from the right. Carry any ten into the next column to the left.5.000 + 0.080 + 0.002 = 5.082
- Write the answer with its decimal point in the same column. The decimal points line up in the question and in the answer.5.082
Check. Add the numbers in a different order and you get 5.082 again. ✓
Watch out. Line up the decimal points, not the last digits. Fill the gaps with zeros.
Key words. The decimal point separates the ones from the part smaller than 1. The places after it are tenths (0.1), hundredths (0.01) and thousandths (0.001).
Method. Divide the top number by the bottom number. A bottom of 100 gives 2 decimal places.
- Look at the bottom number. 100 tells us the place of the last digit: the last column is worth 1 out of 100.37/100
- Put the top number in that column. 37 is written with its last digit in the hundredths column.37 → 0.37
- Write the answer. Use zeros to fill the places in front of the digits.0.37
Check. 0.37 × 100 = 37. ✓
Watch out. Count the places carefully: 7/1000 is 0.007, not 0.07.
Key words. The decimal point separates the ones from the part smaller than 1. The places after it are tenths (0.1), hundredths (0.01) and thousandths (0.001).
Method. Divide the top number by the bottom number. A bottom of 1000 gives 3 decimal places.
- Look at the bottom number. 1000 tells us the place of the last digit: the last column is worth 1 out of 1000.7/1000
- Put the top number in that column. 7 is written with its last digit in the thousandths column.7 → 0.007
- Write the answer. Use zeros to fill the places in front of the digits.0.007
Check. 0.007 × 1000 = 7. ✓
Watch out. Count the places carefully: 7/1000 is 0.007, not 0.07.
Key words. The decimal point separates the ones from the part smaller than 1. The places after it are tenths (0.1), hundredths (0.01) and thousandths (0.001).
Method. Divide the top number by the bottom number. A bottom of 10 gives 1 decimal place.
- Look at the bottom number. 10 tells us the place of the last digit: the last column is worth 1 out of 10.4/10
- Put the top number in that column. 4 is written with its last digit in the tenths column.4 → 0.4
- Write the answer. Use zeros to fill the places in front of the digits.0.4
Check. 0.4 × 10 = 4. ✓
Watch out. Count the places carefully: 7/1000 is 0.007, not 0.07.
Key words. The decimal point separates the ones from the part smaller than 1. The places after it are tenths (0.1), hundredths (0.01) and thousandths (0.001).
Method. Divide the top number by the bottom number. A bottom of 1000 gives 3 decimal places.
- Look at the bottom number. 1000 tells us the place of the last digit: the last column is worth 1 out of 1000.905/1000
- Put the top number in that column. 905 is written with its last digit in the thousandths column.905 → 0.905
- Write the answer. Use zeros to fill the places in front of the digits.0.905
Check. 0.905 × 1000 = 905. ✓
Watch out. Count the places carefully: 7/1000 is 0.007, not 0.07.
Key words. The decimal point does not move when you multiply or divide by 10, 100 or 1000. The digits move instead. A digit that moves one place to the left is ten times bigger.
Method. Each digit moves 3 places to the left. The decimal point does not move.
- Count how many places the digits move. 1000 is 3 zeros, so each digit moves 3 places to the left.1.275 × 1000
- Move the digits. The decimal point stays where it is. Use zeros as place holders where a column is empty.1.275 moves 3 places to the left
- Write the answer. Leave out any extra zeros at the end of a decimal, but keep the zeros needed for the place value.1275
Check. Undo it: 1275 ÷ 1000 gives 1.275 again. ✓
Watch out. Do not move the decimal point. Move the digits, and use zeros to fill the gaps.
Key words. The decimal point separates the ones from the part smaller than 1. The places after it are tenths (0.1), hundredths (0.01) and thousandths (0.001).
Method. Build the number one column at a time, starting from the ones.
- Write the ones. The ones come before the decimal point.4
- Add the tenths. The first place after the point is tenths.4.3
- Add the hundredths, using a zero to hold the place. The 0 keeps the 6 in the thousandths column.4.30
- Add the thousandths. The third place after the point.4.306
Check. 4.306 = 4 + 0.3 + 0.006. ✓
Watch out. Do not write 4.36. The zero in the hundredths column must be there.
Key words. The decimal point separates the ones from the part smaller than 1. The places after it are tenths (0.1), hundredths (0.01) and thousandths (0.001).
Method. Write the numbers with the same number of places, then compare them from the left.
- Write both numbers with the same number of decimal places. Add zeros at the end so the places line up.0.608 and 0.680
- Compare the whole numbers, then the tenths, then the hundredths. Start at the left. The first place where the digits differ decides.0608 and 0680 (without the point)
- Choose the symbol. The bigger number is on the open side of the symbol.0.608 < 0.680
Check. Compare the two numbers on a number line: the one further right is bigger. ✓
Watch out. 0.5 is bigger than 0.45, even though 45 is less than 5 when you read the digits alone.
Key words. The decimal point separates the ones from the part smaller than 1. The places after it are tenths (0.1), hundredths (0.01) and thousandths (0.001).
Method. Write the numbers with the same number of places, then compare them from the left.
- Write both numbers with the same number of decimal places. Add zeros at the end so the places line up.4.500 and 4.050
- Compare the whole numbers, then the tenths, then the hundredths. Start at the left. The first place where the digits differ decides.4500 and 4050 (without the point)
- Choose the symbol. The bigger number is on the open side of the symbol.4.500 > 4.050
Check. Compare the two numbers on a number line: the one further right is bigger. ✓
Watch out. 0.5 is bigger than 0.45, even though 45 is less than 5 when you read the digits alone.
Key words. The decimal point separates the ones from the part smaller than 1. The places after it are tenths (0.1), hundredths (0.01) and thousandths (0.001).
Method. Write the numbers with the same number of places, then compare them from the left.
- Write both numbers with the same number of decimal places. Add zeros at the end so the places line up.0.300 and 0.299
- Compare the whole numbers, then the tenths, then the hundredths. Start at the left. The first place where the digits differ decides.0300 and 0299 (without the point)
- Choose the symbol. The bigger number is on the open side of the symbol.0.300 > 0.299
Check. Compare the two numbers on a number line: the one further right is bigger. ✓
Watch out. 0.5 is bigger than 0.45, even though 45 is less than 5 when you read the digits alone.
Key words. The decimal point separates the ones from the part smaller than 1. The places after it are tenths (0.1), hundredths (0.01) and thousandths (0.001).
Method. Use the digits from the top of the number. The biggest and smallest possible numbers come from putting the biggest digit first.
- List the arrangements. With 3 digits, there are 6 ways to put them in order.258, 285, 528, 582, 825, 852
- Keep only the numbers less than 1 with 3 decimal places. The digits make 0.258, 0.285, 0.528, 0.582, 0.825 and 0.852.All six are less than 1
- Find the biggest. The biggest starts with the biggest digit, then the next biggest.0.852 is bigger than 0.825
- Write the answer. 0.852
Check. 0.852 is the largest of the six. ✓
Watch out. The biggest digit goes in the tenths column, because that column is worth the most.
Key words. The decimal point separates the ones from the part smaller than 1. The places after it are tenths (0.1), hundredths (0.01) and thousandths (0.001).
Method. Write each part as a decimal, then add them together.
- Write 7 hundredths as a decimal. Each hundredth is worth 0.01.7 × 0.01 = 0.07
- Write 2 thousandths as a decimal. Each thousandth is worth 0.001.2 × 0.001 = 0.002
- Add the parts together. Each part goes in its own column, so the decimal points line up.0.07 + 0.002 = 0.072
Check. Read the answer back: 0.072 has the digits in the right places. ✓
Watch out. Use zeros to hold the places. 0.02 and 0.2 are different numbers.
Key words. The decimal point separates the ones from the part smaller than 1. The places after it are tenths (0.1), hundredths (0.01) and thousandths (0.001).
Method. Write each part as a decimal, then add them together.
- Write 4 tenths as a decimal. Each tenth is worth 0.1.4 × 0.1 = 0.4
- Write 9 thousandths as a decimal. Each thousandth is worth 0.001.9 × 0.001 = 0.009
- Add the parts together. Each part goes in its own column, so the decimal points line up.0.4 + 0.009 = 0.409
Check. Read the answer back: 0.409 has the digits in the right places. ✓
Watch out. Use zeros to hold the places. 0.02 and 0.2 are different numbers.
Key words. The decimal point separates the ones from the part smaller than 1. The places after it are tenths (0.1), hundredths (0.01) and thousandths (0.001).
Method. Write each part as a decimal, then add them together.
- Write 12 thousandths as a decimal. Each thousandth is worth 0.001.12 × 0.001 = 0.012
- Add the parts together. Each part goes in its own column, so the decimal points line up.0.012 = 0.012
Check. Read the answer back: 0.012 has the digits in the right places. ✓
Watch out. Use zeros to hold the places. 0.02 and 0.2 are different numbers.
Key words. The decimal point separates the ones from the part smaller than 1. The places after it are tenths (0.1), hundredths (0.01) and thousandths (0.001).
Method. Write each part as a decimal, then add them together.
- Write 3 tens as a decimal. Each ten is worth 10.3 × 10 = 30
- Write 4 hundredths as a decimal. Each hundredth is worth 0.01.4 × 0.01 = 0.04
- Add the parts together. Each part goes in its own column, so the decimal points line up.30 + 0.04 = 30.04
Check. Read the answer back: 30.04 has the digits in the right places. ✓
Watch out. Use zeros to hold the places. 0.02 and 0.2 are different numbers.
Key words. The decimal point separates the ones from the part smaller than 1. The places after it are tenths (0.1), hundredths (0.01) and thousandths (0.001).
Method. Read the number carefully. Look at the digits in the question, and the order they are written in.
- Write the question as a decimal. Read the first digit of 0.407 and 0.470 in the same column.0.407 and 0.470
- Compare the tenths. Both have 4 tenths, so keep going.4 tenths = 4 tenths
- Compare the hundredths. Hundredths: 0 in 0.407, 7 in 0.470.0 hundredths < 7 hundredths
- Decide who is right. The number with 7 hundredths is bigger, so 0.47 is the bigger number.No. 0.47 is bigger.
Check. Ali looked at 407 and 47 without the decimal points. That does not compare the numbers. ✓
Watch out. Do not compare the digits without the decimal point. Compare each place from the left.
Key words. The decimal point separates the ones from the part smaller than 1. The places after it are tenths (0.1), hundredths (0.01) and thousandths (0.001).
Method. Zeros at the end of a decimal do not change its value. Check with place value.
- Write Mia's numbers with the same places. Add zeros to the end so both have three places.0.8 = 0.800; 0.08 = 0.080
- Compare the places. Both numbers have 8 tenths or 8 hundredths in the same places.0.800 and 0.8 have the same digits
- Decide. Adding zeros at the end does not change the value.No, she is wrong.
Check. 0.8 = 8/10 and 0.800 = 800/1000 = 8/10. ✓
Watch out. Zeros at the end of a decimal are free. Zeros at the start are not: 0.8 and 0.08 are not the same.