Math // Fractions

Dividing by 10 and 100

Find the effect of dividing a one- or two-digit number by 10 and 100, identifying the value of the digits as ones, tenths, and hundredths

Ages
8 to 9
Type
Method
Builds on
2 topics
Leads to
2 topics
Standards
1 code

Quick check

If the learner starts with the number 48 and divides it by 10, can they tell you the answer — and explain what happened to each digit's place value?

Ask this to see whether the topic is secure.

Topic // Mastery

What mastery looks like

What a learner can do once this topic is secure.
  • Calculate 37 ÷ 10 = 3.7 and identify 3 as ones and 7 as tenths
  • Calculate 4 ÷ 100 = 0.04 and identify 4 as hundredths
  • Explain that dividing by 10 shifts each digit one place to the right

Topic // Map

Where this fits

What to learn first and what this topic opens up, with the reason for each link. Required links come first.
  • RequiredMust come first
  • HelpfulHelps, but not essential

Before this

2 topics

You are here

Dividing by 10 and 100

Ages 8 to 9 // Method

Leads to

2 topics
  • Multiplying and dividingRequired

    Multiplication & Division // Ages 9 to 10

    Dividing by 10/100 (Y4 fractions context) is prerequisite to ×÷ by 10/100/1000 with decimals

  • Using Mathematical StructureHelpful

    Mathematical Thinking // Ages 8 to 9

    Dividing by 10/100 exercises place-value structural patterns

Topic // Research-informed

Teaching notes

From the Marble Skill Taxonomy. These notes have not been validated in classrooms, so treat them as a starting point for your own judgement.

The approach

Dividing by 10 or 100 makes every digit ten or a hundred times smaller, so each digit slides one or two places to the RIGHT on a place-value chart while the digits and their order stay the same. 37 ÷ 10 = 3.7 (the 3 moves from tens to ones, the 7 from ones to tenths); 4 ÷ 100 = 0.04 (the 4 moves to hundredths and a 0 must hold the empty tenths place). The reliable idea is that digits shift and shrink. 'Add/remove a zero' fails for numbers like 37, which have no trailing zero, and 'move the decimal point' gives the same answer but hides why the values change and can lead to errors when a placeholder is needed.

Common misconceptions

  • Applies 'move the decimal point' by rote and gets the magnitude wrong (37 ÷ 10 → 0.37 or 370)
  • Omits the placeholder zero: 4 ÷ 100 → 0.4
  • Over-generalises 'divide by 10 = take a zero off', which fails on numbers without a trailing zero

Useful representations

  • Place-value chart with sliding/draggable digit cards
  • Gattegno (tenths/hundredths) chart
  • Base-ten blocks with exchange (a rod is a tenth of a flat)
  • Number line and money/metric contexts

Teaching practices

  • Use a place-value chart and physically slide digit cards one column right per division by 10 — the digits move, the point stays put
  • Forbid the 'just add/cross off a zero' shortcut; it only works for multiples of ten and breaks on 37 ÷ 10
  • Make the placeholder zero explicit: for 4 ÷ 100 the tenths column is empty, so a 0 must hold it to give 0.04, not 0.4
  • Anchor in money and metric (£4 ÷ 100 = 4p = £0.04; 37 cm ÷ 10) so the shrinking is meaningful
  • Read every result back by place value ('3 ones and 7 tenths') rather than as a digit string

Activities to try

  1. 1

    Slide the digits right on a place-value chart

    Why it works: Dividing by 10 (or 100) shifts every digit one (or two) places right and makes it ten (or a hundred) times smaller; a placeholder zero is needed whenever a column between the point and a digit is left empty.

    1. Set up a place-value chart with columns labelled hundreds, tens, ones, then a decimal point, then tenths and hundredths.
    2. Place digit cards for 37 (3 in tens, 7 in ones) and predict what dividing by 10 will do.
    3. Divide by 10 by sliding each digit card one column to the RIGHT: the 3 moves from tens to ones, the 7 moves from ones to tenths, giving 3.7. Notice the decimal point itself does not move.
    4. Read the result back by place value: '3 ones and 7 tenths'.
    5. Now place a single digit card for 4 in the ones column and divide by 100 by sliding it two columns right, so the 4 lands in hundredths.
  2. 2

    Confront the 'take a zero off' rule

    Why it works: 'Remove a zero' only works when there is a trailing zero to remove, and 'move the point' gives the right result only when it is applied carefully but does not explain why it works. Sliding each digit one place right and reading place value always works and shows why.

    1. Work out 40 ÷ 10 and notice that 'take a zero off' happens to give 4.
    2. Now try the same rule on 37 ÷ 10 and show it fails — there is no trailing zero to remove, and leaving 37 unchanged (or writing 370) is wrong.
    3. Redo 37 ÷ 10 on the place-value chart by sliding digits right to get 3.7, and state in your own words why the shortcut only worked for 40.
    4. Test 'move the decimal point' similarly and check it against the chart result. Notice that, done correctly, it agrees with the chart, but it does not show that each digit has become ten times smaller.
  3. 3

    Anchor the shrink in money and measurement

    Why it works: Dividing by 10 or 100 means a quantity becomes ten or a hundred times smaller, and the place-value result matches real money and metric amounts.

    1. Work out £4 ÷ 100 and connect it to 4p, writing it as £0.04; check the 4 sits in the hundredths (pence-of-a-pound) place.
    2. Work out 37 cm ÷ 10 and express the result as 3.7 cm, checking which column each digit lands in.
    3. For each context, say which digit moved and what it is now worth.

Topic // Standards

Curriculum standards

Codes for the curriculum statements this topic maps to. Each publisher owns its standard text.
The national curriculum in England: Key stages 1 and 2 framework document
Ma/KS2/Y4/F/7

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