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Primary Maths · Year 4Chapter 6 · Decimals and money
Year 4 · Tenths, Hundredths and Money · Lesson 6.4

Year 4: Dividing by 10 and 100

Part of the Year 4 tenths, hundredths and money chapter. Chapter overview · whole chapter on one page · Download worksheet (PDF) · Answers (PDF)

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6.4

Dividing by 10 and 100

Year 4
Divide 1- and 2-digit numbers by 10 and 100, Value of digits as ones, tenths and hundredths

When you divide by 10, the number gets 10 times smaller. Every digit moves one column to the right. When you divide by 100, every digit moves two columns to the right. The digits are the ones that move. The decimal point stays where it is.

TensOnestenthshundredthsStart÷ 105353
53 ÷ 10 = 5.3. The 5 moves from the tens column to the ones column and the 3 moves from the ones column to the tenths column.

Dividing by 100. Move the digits two columns.

TensOnestenthshundredthsStart÷ 10053053
53 ÷ 100 = 0.53. Each digit moves two columns to the right. The empty ones column gets a 0.

Fill the gaps with zeros. 7 ÷ 10 = 0.7 and 7 ÷ 100 = 0.07. In 0.07 there are 0 ones and 0 tenths, so both columns need a 0.

TensOnestenthshundredthsStart÷ 1007007
7 ÷ 100 = 0.07. The 7 moves two columns, to the hundredths column.

Tidying up. 40 ÷ 10 = 4.0, and 4.0 is just 4. And 30 ÷ 100 = 0.30, which is 0.3. The last 0 is not needed.

Why? Dividing by 100 is the same as dividing by 10 twice. 53 ÷ 10 = 5.3 and then 5.3 ÷ 10 = 0.53. The opposite is multiplying: 0.53 × 100 = 53. The digits move left.

Measures. There are 100 cm in 1 m. To change cm to m, divide by 100: 250 cm ÷ 100 = 2.5 m. There are 10 mm in 1 cm, so to change mm to cm, divide by 10: 36 mm ÷ 10 = 3.6 cm. Money. There are 100p in £1, so 450p ÷ 100 = £4.50.

Key words. To divide by 10 is to make a number 10 times smaller. The digits move to the right.

Key ideas

  • ÷ 10: every digit moves 1 column to the right.
  • ÷ 100: every digit moves 2 columns to the right.
  • Put a 0 in any empty column: 7 ÷ 100 = 0.07.
  • Dividing by 100 is the same as dividing by 10 twice.
  • The opposite of dividing is multiplying: the digits move left.
  • cm ÷ 100 = m, mm ÷ 10 = cm, p ÷ 100 = £.
Worked example 6.4.1
Work out 6 ÷ 10.

Key words. To divide by 10 is to make a number 10 times smaller. The digits move one column to the right. Dividing by 100 moves them two columns.

Method. Dividing by 10 moves each digit 1 place to the right in the place-value chart.

  1. Write the number in a place-value chart. Dividing by 10 makes every digit 10 times smaller.
    TensOnestenthshundredthsStart÷ 106
  2. Move every digit 1 column to the right. Each digit slides one column to the right, to a column that is worth 10 times less.
    TensOnestenthshundredthsStart÷ 10606
  3. Fill the empty ones column with a 0. A number like 0.53 starts with 0 ones. The 0 holds the place.
    0 ones
  4. Write the answer. Put the decimal point after the ones.
    6 ÷ 10 = 0.6

Check. Go the other way: 0.6 × 10 = 6. ✓

Watch out. The digits move to the right (they get smaller). Do not just add a 0 on the end.

Worked example 6.4.2
Work out 48 ÷ 10.

Key words. To divide by 10 is to make a number 10 times smaller. The digits move one column to the right. Dividing by 100 moves them two columns.

Method. Dividing by 10 moves each digit 1 place to the right in the place-value chart.

  1. Write the number in a place-value chart. Dividing by 10 makes every digit 10 times smaller.
    TensOnestenthshundredthsStart÷ 1048
  2. Move every digit 1 column to the right. Each digit slides one column to the right, to a column that is worth 10 times less.
    TensOnestenthshundredthsStart÷ 104848
  3. Write the answer. Put the decimal point after the ones.
    48 ÷ 10 = 4.8

Check. Go the other way: 4.8 × 10 = 48. ✓

Watch out. The digits move to the right (they get smaller). Do not just add a 0 on the end.

Worked example 6.4.3
Work out 48 ÷ 100.

Key words. To divide by 10 is to make a number 10 times smaller. The digits move one column to the right. Dividing by 100 moves them two columns.

Method. Dividing by 100 moves each digit 2 places to the right in the place-value chart.

  1. Write the number in a place-value chart. Dividing by 100 makes every digit 100 times smaller.
    TensOnestenthshundredthsStart÷ 10048
  2. Move every digit 2 columns to the right. Each digit slides two columns to the right, because dividing by 100 is dividing by 10 twice.
    TensOnestenthshundredthsStart÷ 10048048
  3. Fill the empty ones column with a 0. A number like 0.53 starts with 0 ones. The 0 holds the place.
    0 ones
  4. Write the answer. Put the decimal point after the ones.
    48 ÷ 100 = 0.48

Check. Go the other way: 0.48 × 100 = 48. ✓

Watch out. The digits move to the right (they get smaller). Do not just add a 0 on the end.

Worked example 6.4.4
Work out 7 ÷ 100.

Key words. To divide by 10 is to make a number 10 times smaller. The digits move one column to the right. Dividing by 100 moves them two columns.

Method. Dividing by 100 moves each digit 2 places to the right in the place-value chart.

  1. Write the number in a place-value chart. Dividing by 100 makes every digit 100 times smaller.
    TensOnestenthshundredthsStart÷ 1007
  2. Move every digit 2 columns to the right. Each digit slides two columns to the right, because dividing by 100 is dividing by 10 twice.
    TensOnestenthshundredthsStart÷ 1007007
  3. Fill the empty ones column with a 0. A number like 0.53 starts with 0 ones. The 0 holds the place.
    0 ones
  4. Write the answer. Put the decimal point after the ones.
    7 ÷ 100 = 0.07

Check. Go the other way: 0.07 × 100 = 7. ✓

Watch out. The digits move, not the decimal point. And 5 ÷ 100 is 0.05: you need a 0 in the tenths column as well as the ones column.

Worked example 6.4.5
Work out 30 ÷ 100.

Key words. To divide by 10 is to make a number 10 times smaller. The digits move one column to the right. Dividing by 100 moves them two columns.

Method. Dividing by 100 moves each digit 2 places to the right in the place-value chart.

  1. Write the number in a place-value chart. Dividing by 100 makes every digit 100 times smaller.
    TensOnestenthshundredthsStart÷ 10030
  2. Move every digit 2 columns to the right. Each digit slides two columns to the right, because dividing by 100 is dividing by 10 twice.
    TensOnestenthshundredthsStart÷ 10030030
  3. Fill the empty ones column with a 0. A number like 0.53 starts with 0 ones. The 0 holds the place.
    0 ones
  4. Write the answer. Put the decimal point after the ones. The last 0 is not needed: 4.0 is the same as 4, and 0.30 is the same as 0.3.
    30 ÷ 100 = 0.3

Check. Go the other way: 0.3 × 100 = 30. ✓

Watch out. The digits move to the right (they get smaller). Do not just add a 0 on the end.

Worked example 6.4.6
Find the missing number.   ? ÷ 10 = 3.6

Key words. To divide by 10 is to make a number 10 times smaller. The digits move one column to the right. Dividing by 100 moves them two columns.

Method. Use the opposite operation. The opposite of dividing is multiplying.

  1. Think about the opposite operation. The opposite of dividing by 10 is multiplying by 10.
    ? = 3.6 × 10
  2. Move every digit 1 column to the left. Multiplying makes each digit bigger, so the digits move left.
    3.6 × 10 = 36
  3. Write the answer.
    36 ÷ 10 = 3.6

Check. Check: 36 ÷ 10 = 3.6. ✓

Watch out. Dividing moves digits right. To undo it, move them left.

Worked example 6.4.7
Find the missing number.   52 ÷ ? = 0.52

Key words. To divide by 10 is to make a number 10 times smaller. The digits move one column to the right. Dividing by 100 moves them two columns.

Method. Count how many columns the digits moved to the right. One column is ÷ 10 and two columns is ÷ 100.

  1. Compare the two numbers. 52 became 0.52.
    52 → 0.52
  2. Count how many columns the digits moved. Each digit moved to the right.
    The digits moved 2 columns to the right.
  3. Decide what we divided by. 1 column means ÷ 10. 2 columns means ÷ 100.
    100

Check. Check: 52 ÷ 100 = 0.52. ✓

Watch out. Compare where the digits are, not how long the number looks.

Worked example 6.4.8
Change 340 cm into metres.

Key words. Convert means change from one unit to another. 1 m = 100 cm. 1 cm = 10 mm.

Method. There are 100 cm in 1 m. Divide by 100 to change cm into m.

  1. Find how many of the small unit make one of the big unit. We need this to change units.
    1 m = 100 cm
  2. Choose the operation. We are changing cm into m. A m is bigger, so we need fewer of them: divide by 100.
    340 ÷ 100
  3. Move the digits 2 columns to the right. Dividing by 100 makes each digit 100 times smaller.
    340 ÷ 100 = 3.4
  4. Write the answer with the unit.
    340 cm = 3.4 m

Check. Go back: 3.4 × 100 = 340. ✓

Watch out. Fewer m than cm: the number should get smaller. If it does not, you used the wrong operation.

Watch out

The digits move. You do not just add a point. 7 ÷ 100 is 0.07, not 0.7 and not 7.00. Also, dividing makes the number SMALLER, so the digits must move to the right. If the answer is bigger than what you started with, something has gone wrong.

Exercise 6D  Dividing by 10 and 100

Non-calculator
1
FQuick-fire! Divide each number by 10.
(a)3 ÷ 10 =
(b)9 ÷ 10 =
(c)20 ÷ 10 =
(d)45 ÷ 10 =
(e)70 ÷ 10 =
(f)86 ÷ 10 =
2
FQuick-fire! Divide each number by 100.
(a)4 ÷ 100 =
(b)8 ÷ 100 =
(c)60 ÷ 100 =
(d)37 ÷ 100 =
(e)90 ÷ 100 =
(f)52 ÷ 100 =
3
FUse the place-value charts. Write the answers.
(a)
TensOnestenthshundredthsStart÷ 105
5 ÷ 10 =
(b)
TensOnestenthshundredthsStart÷ 1034
34 ÷ 10 =
(c)
TensOnestenthshundredthsStart÷ 1007
7 ÷ 100 =
(d)
TensOnestenthshundredthsStart÷ 10026
26 ÷ 100 =
4
FFind each missing number.
(a)? ÷ 10 = 7
(b)? ÷ 100 = 0.9
(c)? ÷ 10 = 4.2
(d)? ÷ 100 = 0.35
5
FIs the missing number 10 or 100?
(a)8 ÷ ? = 0.8
(b)63 ÷ ? = 0.63
(c)95 ÷ ? = 9.5
(d)4 ÷ ? = 0.04
6
FEach number is divided by 10 to make the next one. Write the missing numbers.
(a)600,  60,  ?,  0.6,  ?
(b)90,  9,  ?,  ?
(c)70,  ?,  0.7,  ?
7
FChange each length into the bigger unit.
(a)300 cm = ? m
(b)450 cm = ? m
(c)36 mm = ? cm
(d)7 mm = ? cm
8
FThis time change metres into centimetres. Multiply by 100.
(a)3.5 m = ? cm
(b)0.72 m = ? cm
(c)6 m = ? cm
9
PSA rope is 6 m long.
??????????6 m
(a)The rope is cut into 10 equal pieces. How long is each piece?
(b)Another 6 m rope is cut into 100 equal pieces. How long is each piece?
10
PSWrite each stride length in metres.
(a)Tom’s stride is 75 cm long.
(b)Amira’s stride is 68 cm long.
11
RJack says, “5 ÷ 10 = 0.05.” What mistake has Jack made? What is the correct answer?
12
RAlways, sometimes or never?   When you divide a two-digit number by 100, the answer is less than 1.
13
RWhich two calculations have the answer 0.4? Tick two boxes.
A 4 ÷ 10    B 40 ÷ 100    C 40 ÷ 10    D 4 ÷ 100    E 400 ÷ 100
14
RAmira divides a number by 10 and then divides her answer by 10 again. What single number could she have divided by instead? Show it with 50.

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