Websink Prep UKStep-by-step practice MathsLevel 5 chaptersMaths textbooksLevel 1Level 2Level 3Level 4Level 5Browse allPast papersFind a tutorBecome a tutor
Step-by-step practice: Maths · Level 5Chapter 1 · Place value to a million and decimals to tenths
Level 5 · Chapter 1

Place value to a million and decimals to tenths

By the end of this chapter you will be able to

  • Say the value of each digit in a number to 1,000,000
  • Read and write big numbers in numerals and words
  • Find 10,000 more or less, and round big numbers
  • Read and write tenths as decimals
  • Compare and order decimals to tenths

You should already know

  • Numbers to 10,000 and their place value (Level 4, chapter 1)
  • Rounding to the nearest 10, 100 and 1000 (Level 4, chapter 2)

Where this leads

  • Adding and subtracting whole numbers to a million (chapter 2)
  • Decimals to hundredths (chapter 7)

Step-by-step practice: maths (Level 5). Small steps, repeated until fluent. Content: Read, write, order and compare numbers to 1,000,000 and know the value of each digit (Y5 paraphrase), Round any whole number to the nearest 10, 100, 1000, 10000 or 100000 (Y5 paraphrase), Recognise and write decimals as tenths, and place them on a number line (Y4 paraphrase), Compare and order decimals to tenths (Y4 paraphrase).

Exercise P  Do you remember?

Non-calculator
1
FWhat is the value of the 6 in 2,645? (Hint: the 6 is in the hundreds column.)
2
FWrite 7,206 in words.
3
FWhat is 8 × 9?
4
FRound 4,736 to the nearest 100.
5
FWhat is 6,000 + 2,500 - 1,000?
1.1

Digits and place value to a million

Level 5
Know the value of each digit in a number to 1,000,000, Read, write and partition numbers to 1,000,000
Video lesson: Digits and place value to a millionComing soon

Each digit in a number has a value that depends on its column. In 472,893, the 4 is in the hundred thousands column, so it is worth 400,000. The 7 is in the ten thousands column, so it is worth 70,000.

Groups of three digits are separated by commas to make big numbers easier to read. Read the thousands, then the rest.

Hundred thousands4Ten thousands7Thousands2Hundreds8Tens9Ones3
The number 472,893 in a place value chart

Key ideas

  • Each column is ten times the column on its right.
  • The value of a digit = the digit × the value of its column.
  • Partitioning splits a number into the value of each digit.
Worked example 1.1.1
What is the value of the digit in the ten thousands column of 472,893?

Method. Read the column, then multiply the digit by the value of that column.

  1. Find the ten thousands column. Count the columns from the right: ones, tens, hundreds and so on.
    The digit is 7
  2. Multiply the digit by the value of its column. Each place in the ten thousands column is worth 10,000.
    7 × 10,000 = 70,000
  3. Write the value. This is the value of the digit in this number, not just the digit.
    70,000

Check. Check: 70,000 is 7 groups of 10,000.

Watch out. Say the value, such as 70,000, not only the digit 7.

Worked example 1.1.2
Write 472,893 in words.

Method. Read the thousands, then the last three digits, and join them with the word thousand.

  1. Split the number into thousands and the last three digits. Read the thousands first, then the rest.
    472 thousand and 893
  2. Say the thousands. Say the number before the thousand, then the word thousand.
    four hundred and seventy-two thousand
  3. Say the last three digits. Say them as a number up to 999.
    eight hundred and ninety-three
  4. Put the words together. Use a space between the two parts; use and before a number under 100.
    four hundred and seventy-two thousand eight hundred and ninety-three

Check. Check: count the words so that each part matches its digits.

Watch out. Do not write the digits in words one by one. Say the parts. Use and before the tens and ones.

Worked example 1.1.3
Write 472,893 as an addition of the value of each digit.

Method. Partition the number into the value of each digit.

  1. Find the value of each digit. Multiply each digit by the value of its column; leave out zeros.
    400,000, 70,000, 2,000, 800, 90, 3
  2. Write the parts as an addition. Add the parts together to make the number.
    400,000 + 70,000 + 2,000 + 800 + 90 + 3
  3. Check by adding. Adding the parts again must give the number we started with.
    400,000 + 70,000 + 2,000 + 800 + 90 + 3

Check. Check: the parts add to 472,893.

Watch out. Leave out any digit that is zero. Zero adds nothing.

Watch out

Watch out. The 7 in 472,893 is worth 70,000, not 7. Name the column first, then multiply.

Exam tip

Grown-up tip. Ask the child to read a big number in parts: “472 thousand, 893.” Practise saying the value of each digit aloud.

Exercise 1A  Practice: digits, words and partitioning

Non-calculator
1
FWrite 503,924 as an addition of the value of each digit.
2
FWrite 723,202 in words.
3
FWhat is the value of the digit in the hundreds column of 946,646?
4
FWrite 435,751 in words.
5
FWrite 672,537 in words.
6
FWrite 169,286 as an addition of the value of each digit.
7
FWhat is the value of the digit in the ten thousands column of 968,424?
8
FWrite 456,910 as an addition of the value of each digit.
9
FWrite 825,546 in words.
10
FWhat is the value of the digit in the hundred thousands column of 714,462?
11
FWhat is the value of the digit in the thousands column of 778,764?
12
FWhat is the value of the digit in the thousands column of 593,798?
13
FWrite 798,648 in words.
14
FWrite 594,527 in words.
15
FWrite 594,631 as an addition of the value of each digit.
16
FWhat is the value of the digit in the hundred thousands column of 533,255?
1.2

10,000 more or less; comparing and ordering

Level 5
Find 10,000 more and 10,000 less than a number, Compare and order numbers to 1,000,000
Video lesson: 10,000 more or less; comparing and orderingComing soon

10,000 more than a number changes the ten thousands digit by one. 10,000 less changes it the other way.

To compare two numbers with the same number of digits, start from the left. The first column where they differ decides.

Key ideas

  • Adding 10,000 changes only the ten thousands digit (carry if it is a 9).
  • Compare from the left, column by column.
  • Order from the smallest by comparing the digits from the left.
Worked example 1.2.1
What is 10,000 more than 295,000?

Method. Only the ten thousands digit changes when we add or take away 10,000.

  1. Look at the ten thousands digit. Adding or taking away 10,000 changes this digit by one.
    The ten thousands digit is 9
  2. Change that digit by one. Carry or borrow if the digit goes past 9 or below 0.
    9 + 1 = 10, so write 0 and carry 1 into the hundred thousands
  3. Write the answer. All the other digits stay the same.
    305,000

Check. Check: 305,000 take away 10,000 gives back 295,000.

Watch out. Do not change the thousands digit. 10,000 is not 1,000.

Worked example 1.2.2
What is 10,000 less than 640,000?

Method. Only the ten thousands digit changes when we add or take away 10,000.

  1. Look at the ten thousands digit. Adding or taking away 10,000 changes this digit by one.
    The ten thousands digit is 4
  2. Change that digit by one. Carry or borrow if the digit goes past 9 or below 0.
    4 - 1 = 3
  3. Write the answer. All the other digits stay the same.
    630,000

Check. Check: 630,000 add 10,000 gives back 640,000.

Watch out. Do not change the thousands digit. 10,000 is not 1,000.

Worked example 1.2.3
Which number is greater: 482,613 or 428,613?

Method. Compare the digits from the left. The first column where they differ decides.

  1. Compare the two numbers from the left. Look at the digits in the same column, starting with the largest.
    4 and 4 in the first column
  2. Find the first column where they differ. That column decides which number is greater.
    In the ten thousands column: 8 and 2
  3. Choose the greater number. The number with the greater digit in that column is greater.
    482,613

Check. Check: the other number is 428,613, which is smaller.

Watch out. Do not compare the last digits first. Start from the left.

Watch out

Watch out. 10,000 is not 1,000. Only the ten thousands digit changes, and it may carry into the hundred thousands.

Exam tip

Grown-up tip. Ask: “Which column changes?” before the child works out the answer.

Exercise 1B  Practice: 10,000 more or less, and comparing

Non-calculator
1
FWhich number is greater: 239,181 or 373,555?
2
FPut these numbers in order, smallest first: 652,205, 155,219, 770,401, 429,253.
3
FWhat is 10,000 less than 370,761?
4
FPut these numbers in order, smallest first: 737,897, 231,466, 926,988, 976,247.
5
FWhat is 10,000 more than 379,251?
6
FPut these numbers in order, smallest first: 278,344, 961,946, 159,358, 540,497.
7
FWhich number is greater: 183,696 or 726,162?
8
FWhat is 10,000 more than 335,794?
9
FPut these numbers in order, smallest first: 147,407, 714,563, 993,272, 161,173.
10
FWhat is 10,000 less than 165,825?
11
FPut these numbers in order, smallest first: 341,550, 731,589, 275,739, 289,999.
12
FWhat is 10,000 less than 148,018?
13
FWhat is 10,000 less than 383,161?
14
FPut these numbers in order, smallest first: 196,313, 298,764, 876,216, 654,369.
15
FPut these numbers in order, smallest first: 694,987, 971,828, 616,936, 842,660.
16
FPut these numbers in order, smallest first: 721,924, 657,061, 765,484, 208,820.
1.3

Rounding to the nearest 10, 100, 1000, 10000 and 100,000

Level 5
Round any whole number to the nearest 10, 100, 1000, 10000 or 100000
Video lesson: Rounding to the nearest 10, 100, 1000, 10000 and 100,000Coming soon

To round, look at the digit just to the right of the column you are rounding to. If it is 5 or more, round up. If it is 4 or less, round down.

Then replace all the digits to the right of that column with zeros.

Key ideas

  • Look one column to the right of the rounding column.
  • 5 or more: round up. 4 or less: round down.
  • Replace the digits after the rounding column with zeros.
Worked example 1.3.1
Round 472,893 to the nearest 1,000.

Method. Look at the digit to the right of the thousands column, then decide.

  1. Look at the hundreds digit. This digit decides whether to round up or down.
    The hundreds digit is 8
  2. Decide: round up or down. 5 or more: round up. 4 or less: round down.
    8 is 5 or more, so round up
  3. Write the rounded number. Replace the digits after the thousands column with zeros.
    473,000

Check. Check: 473,000 is a multiple of 1,000 and is the closest one to 472,893.

Watch out. Round up only when the next digit is 5 or more. Do not round up on a 4.

Worked example 1.3.2
Round 472,893 to the nearest 100,000.

Method. Look at the digit to the right of the hundred thousands column, then decide.

  1. Look at the ten thousands digit. This digit decides whether to round up or down.
    The ten thousands digit is 7
  2. Decide: round up or down. 5 or more: round up. 4 or less: round down.
    7 is 5 or more, so round up
  3. Write the rounded number. Replace the digits after the hundred thousands column with zeros.
    500,000

Check. Check: 500,000 is a multiple of 100,000 and is the closest one to 472,893.

Watch out. Round up only when the next digit is 5 or more. Do not round up on a 4.

Worked example 1.3.3
Round 296,458 to the nearest 10,000.

Method. Look at the digit to the right of the ten thousands column, then decide.

  1. Look at the thousands digit. This digit decides whether to round up or down.
    The thousands digit is 6
  2. Decide: round up or down. 5 or more: round up. 4 or less: round down.
    6 is 5 or more, so round up
  3. Write the rounded number. Replace the digits after the ten thousands column with zeros.
    300,000

Check. Check: 300,000 is a multiple of 10,000 and is the closest one to 296,458.

Watch out. Round up only when the next digit is 5 or more. Do not round up on a 4.

Watch out

Watch out. Round up only when the next digit is 5 or more. 472,893 to the nearest 1,000 is 473,000, not 472,000.

Exam tip

Grown-up tip. Ask the child to point to the digit that decides, and say “up” or “down” before writing the answer.

Exercise 1C  Practice: rounding

Non-calculator
1
FRound 394,653 to the nearest 100.
2
FRound 365,659 to the nearest 10.
3
FRound 358,135 to the nearest 10.
4
FRound 973,425 to the nearest 10.
5
FRound 307,682 to the nearest 100.
6
FRound 346,083 to the nearest 10.
7
FRound 357,569 to the nearest 10.
8
FRound 374,521 to the nearest 10.
9
FRound 789,603 to the nearest 1,000.
10
FRound 435,802 to the nearest 100.
11
FRound 828,908 to the nearest 1,000.
12
FRound 491,985 to the nearest 100.
13
FRound 822,128 to the nearest 10,000.
14
FRound 169,143 to the nearest 100,000.
15
FRound 285,029 to the nearest 100.
16
FRound 320,850 to the nearest 10,000.
1.4

Decimals to tenths

Level 5
Recognise and write decimals as tenths, and place them on a number line
Video lesson: Decimals to tenthsComing soon

A decimal point separates the whole number from the parts. The first digit after the point is the number of tenths.

3.4 means 3 whole ones and 4 tenths: 3 + 4/10. Between two whole numbers there are ten tenths.

Key ideas

  • The first digit after the decimal point is tenths.
  • A tenth is 0.1, and 4 tenths is 0.4.
  • Ten tenths make one whole.
Worked example 1.4.1
Write 3 + 4/10 as a decimal.

Method. Write the whole number, then a decimal point, then the tenths digit.

  1. Write the whole number first. This is the part before the decimal point.
    3
  2. Write the tenths after a decimal point. 4/10 is 4 tenths, so the digit 4 goes after the point.
    3.4
  3. Write the answer. A decimal point separates the whole number from the tenths.
    3.4

Check. Check: 4/10 is 0.4, and 3 + 0.4 = 3.4.

Watch out. The tenths digit is one place after the decimal point.

Worked example 1.4.2
What is the value of the tenths digit in 3.4?

Method. The first digit after the point is the number of tenths.

  1. Find the tenths digit. It is the first digit after the decimal point.
    The digit is 4
  2. Write its value. 4 tenths is 4/10.
    4/10 = 0.4
  3. Write the answer. The value of the digit is a decimal less than one.
    0.4

Check. Check: 0.4 + 3 = 3.4.

Watch out. Do not write the digit as a whole number. 4 in 3.4 is 0.4, not 4.

Worked example 1.4.3
The orange dot shows a decimal on the number line. Write the decimal.
22.12.22.32.42.52.62.72.82.93?

Method. Count the tenths from the lower whole number to the dot.

  1. Find the whole numbers either side. The dot is between 2 and 3.
    2 and 3
  2. Count the tenths from the lower whole number. Each small step between two whole numbers is one tenth.
    6 tenths after 2
  3. Write the decimal. Whole number first, then the point and the tenths.
    2.6

Check. Check: 2.6 is 6 steps past 2, and there are 10 steps to 3.

Watch out. There are ten tenths between two whole numbers. Count the small steps, not the big ones.

Watch out

Watch out. The 4 in 3.4 is worth 0.4, not 4. Read the digit after the point as tenths.

Exam tip

Grown-up tip. Use coins or a ruler marked in tenths. Ten 1p coins make 10p, which is one whole pound in tenths of pounds.

Exercise 1D  Practice: tenths

Non-calculator
1
FWrite 8 + 1/10 as a decimal.
2
FWhat is the value of the tenths digit in 4.8?
3
FWrite 6 + 1/10 as a decimal.
4
FWrite 2 + 6/10 as a decimal.
5
FThe orange dot shows a decimal on the number line. Write the decimal.
33.13.23.33.43.53.63.73.83.94?
6
FWrite 1 + 2/10 as a decimal.
7
FWrite 9 + 7/10 as a decimal.
8
FThe orange dot shows a decimal on the number line. Write the decimal.
99.19.29.39.49.59.69.79.89.910?
9
FThe orange dot shows a decimal on the number line. Write the decimal.
88.18.28.38.48.58.68.78.88.99?
10
FWhat is the value of the tenths digit in 8.7?
11
FWhat is the value of the tenths digit in 8.2?
12
FWrite 1 + 8/10 as a decimal.
13
FWrite 6 + 3/10 as a decimal.
14
FWrite 9 + 9/10 as a decimal.
15
FWhat is the value of the tenths digit in 4.5?
16
FWrite 2 + 8/10 as a decimal.
1.5

Comparing and ordering decimals to tenths

Level 5
Compare and order decimals to tenths, Find a decimal to tenths between two numbers
Video lesson: Comparing and ordering decimals to tenthsComing soon

Compare the whole numbers first. If they are the same, compare the tenths digits.

The number with more tenths is the greater one, even if it has fewer digits after the point.

Key ideas

  • Compare the whole numbers first.
  • If the whole numbers match, compare the tenths.
  • Write the list in order from the smallest.
Worked example 1.5.1
Which is greater: 3.7 or 3.4?

Method. Compare the whole numbers, then the tenths.

  1. Compare the whole numbers first. The bigger whole number is the bigger decimal.
    3 and 3
  2. If the whole numbers are the same, compare the tenths. The tenths digit decides when the whole numbers match.
    7 and 4 tenths
  3. Choose the greater decimal. This is the decimal with more of the bigger part.
    3.7

Check. Check: 3.7 is 37 tenths, and 3.4 is 34 tenths.

Watch out. 3.7 is greater than 3.4, not smaller. Compare the tenths: 7 tenths is more than 4 tenths.

Worked example 1.5.2
Put these in order, smallest first: 4.2, 3.9, 4.1, 3.6.

Method. Compare the whole numbers first, then the tenths.

  1. Compare the whole numbers. Put the numbers with the smallest whole number first.
    4, 3, 4, 3
  2. Compare the tenths when the whole numbers match. Use the tenths digit to break a tie.
    4.2, 3.9, 4.1, 3.6
  3. Write the list smallest first. Read the order from the smallest to the largest.
    3.6, 3.9, 4.1, 4.2

Check. Check: the first number is the smallest and the last is the greatest.

Watch out. Do not order by the number of digits after the point. 4.2 is greater than 3.9.

Worked example 1.5.3
Write a decimal to one place that is between 3.2 and 3.5.

Method. Turn both numbers into tenths, then choose any tenths number between them.

  1. Write both numbers in tenths. Count how many tenths each number has.
    3.2 = 32 tenths and 3.5 = 35 tenths
  2. Find the tenths in between. Any number of tenths strictly between them works.
    3.3 or 3.4
  3. Write an answer. Each is between the two numbers, so each is correct.
    Accept any of 3.3 or 3.4

Check. Check: each choice is greater than 3.2 and less than 3.5.

Watch out. Do not choose the same number as one of the two numbers in the question. It must be strictly between.

Watch out

Watch out. 3.7 is greater than 3.4. Do not think that 4 is bigger than 7 because the number is smaller.

Exam tip

Grown-up tip. Ask: “Which is bigger, 4.2 or 3.9? How do you know?” The whole number decides first.

Exercise 1E  Practice: comparing and ordering tenths

Non-calculator
1
FWhich is greater: 9.3 or 2.9?
2
RWrite a decimal to one place that is between 8.5 and 8.8.
3
FPut these in order, smallest first: 2.7, 2.1, 3.4, 2.4.
4
RWrite a decimal to one place that is between 4.2 and 4.7.
5
FPut these in order, smallest first: 2.0, 4.3, 4.1, 1.1.
6
FWhich is greater: 9.7 or 2.3?
7
FPut these in order, smallest first: 1.5, 5.4, 1.9, 5.3.
8
RWrite a decimal to one place that is between 1.5 and 2.1.
9
RWrite a decimal to one place that is between 1.2 and 1.4.
10
FWhich is greater: 1.1 or 4.4?
11
RWrite a decimal to one place that is between 4.9 and 5.2.
12
RWrite a decimal to one place that is between 4.5 and 4.7.
13
FPut these in order, smallest first: 5.2, 4.8, 7.5, 8.6.
14
RWrite a decimal to one place that is between 4.5 and 4.8.
15
RWrite a decimal to one place that is between 7.0 and 7.4.
16
FPut these in order, smallest first: 3.9, 3.8, 1.8, 1.2.

Chapter summary

SkillMethod
Value of a digitName the column, then digit × column value
Big numbers in wordsSay the thousands, then the rest; use and before tens and ones
10,000 more or lessChange the ten thousands digit by one; carry or borrow if needed
RoundingLook one column to the right: 5 or more round up; then zeros
TenthsThe digit after the point is the tenths; 3.4 = 3 + 4/10
Comparing decimalsWhole numbers first, then tenths

Can you…?

  • I can say the value of each digit in a number to 1,000,000
  • I can read and write big numbers in numerals and words
  • I can find 10,000 more and 10,000 less than a number
  • I can round to the nearest 10, 100, 1000, 10000 and 100,000
  • I can write and place decimals to tenths on a number line
  • I can compare and order decimals to tenths

Key terms

column
a place in a number, such as hundreds or tens
partition
split a number into the value of each digit
round
make a number simpler, by counting to the nearest 10, 100 and so on
tenths
parts when a whole is split into ten equal parts
decimal point
the dot that separates the whole number from the tenths

Exercise 1Z  Check-up

Non-calculator
1
Write a decimal to one place that is between 3.7 and 3.9.
2
Put these numbers in order, smallest first: 319,401, 338,787, 145,974, 516,230.
3
Write 537,447 in words.
4
What is the value of the digit in the thousands column of 138,006?
5
Write a decimal to one place that is between 1.4 and 1.6.
6
Round 820,237 to the nearest 10.
7
Write 922,084 as an addition of the value of each digit.
8
Put these in order, smallest first: 5.0, 6.8, 5.5, 9.3.
9
Which is greater: 8.0 or 7.4?
10
Round 285,067 to the nearest 1,000.

Total 19 marks. Allow about 19 minutes.

Exercise 1X  Practice test questions

Non-calculator
1
FWrite 8 + 5/10 as a decimal.[1 mark]
2
FRound 664,613 to the nearest 10.[1 mark]
3
FWrite 583,904 in words.[1 mark]
4
FWrite 682,719 as an addition of the value of each digit.[1 mark]
5
FRound 265,571 to the nearest 10,000.[2 marks]
6
FWrite 235,358 as an addition of the value of each digit.[2 marks]
7
FRound 282,376 to the nearest 1,000.[2 marks]
8
FWhich number is greater: 216,103 or 567,810?[3 marks]
9
FWrite 2 + 9/10 as a decimal.[3 marks]
10
FWrite 768,855 as an addition of the value of each digit.[3 marks]
Chapter 2: Adding and subtracting whole numbers to a million →

Websink Prep UK is an independent site. It is not affiliated with, endorsed by or sponsored by AQA, Pearson Edexcel, OCR, WJEC, Eduqas, CCEA, SQA, GL Assessment, CEM or the Department for Education. All exam board names and trademarks belong to their owners. Past papers are linked from the exam boards' own websites and are not hosted here.

About Websink Prep UK · Find a tutor · Privacy · Terms · Cookie settings