Improve Tuition · Foundation Maths · Year 3–6 · GCSE Grade 1–3 support
Diagnostic practice paper
Multiplying and Dividing by 10, 100 and 1000
A diagnostic ladder from tens facts to decimal fluency.
42 questions · four year-band sections · visual place-value walkthroughs · no time pressure
For the tutor
Where the pupil stops tells you the year-band gap
AStops in A → ten-times-table facts weakYear 3
BStops in B → whole-number place value weakYear 4
CStops in C → decimals not secureYear 5
DStruggles in D → GCSE application & reasoning weakYear 6+
Tutor view Diagnostic notes for each section▸
Section A · Tens facts only
If a pupil cannot do these, the gap is basic times-table fluency, not place value. Go back to the 10× table and the inverse relationship before any place-value teaching.
Section B · Tens and hundreds, whole answers
Watch for pupils who say “just add a zero”. It works here by coincidence, so the misconception hides. Introduce digit-movement language NOW, before decimals arrive in Section C.
Section C · Decimals enter
This is the most common failure point in Year 5–7 catch-up. The “add a zero” shortcut breaks the moment decimals appear (3.5 × 10 ≠ 3.50). If a pupil stops here, decimals and place value are not secure.
Section D · Full decimal fluency
A pupil who can calculate but cannot explain (Q41, Q42) is not yet GCSE-ready — their skill is fragile and rote. The reasoning questions are the real test of understanding.
This paper checks whether a pupil truly understands place value when multiplying and dividing by 10, 100 and 1000. It starts with Year 3 tens facts, builds through Year 4 whole-number place value, introduces decimals in Year 5, and finishes with Year 6 / GCSE-style decimal fluency.
The big idea: it is the digits that move — not zeros that get added, and not the decimal point. Here is exactly what that looks like.
Drive it yourself · whole numbers first4Start at 4. Multiply up first — × 10, × 100, × 1000 — then divide back down to undo it.
Th1000s
H100s
T10s
Oones
4
This is the whole-number stage: multiply to send the digit left, divide to bring it back. A button switches off when a move would overflow or slip past the ones into decimals — decimals are the next step. The grey 0s are placeholders holding the empty columns.
Worked scaffold · build up, then bring back down
Step 1 — multiply up (gets bigger)
4 × 10 = 40digit jumps 1 place left
4 × 100 = 400jumps 2 places left
4 × 1000 = 4000jumps 3 places left
Step 2 — divide back down (gets smaller)
4000 ÷ 10 = 400digit jumps 1 place right
4000 ÷ 100 = 40jumps 2 places right
4000 ÷ 1000 = 4jumps 3 places right — back to the start
Check ✓every answer stays a whole number: dividing simply undoes the multiplying.
Next stepOnce this is secure, dividing past the ones is where decimals begin — for example 4 ÷ 10 = 0.4. The diagrams below show exactly how a digit slides into the tenths and hundredths.
Example 1 — multiplying
3.5 × 10 = 35× 10 — every digit moves 1 place left
The 3 slides from ones to tens; the 5 slides from tenths to ones. Both move one place left.
What the arrows show: multiplying by 10 makes the number ten times bigger, so every digit slides one place to the left (towards the bigger place values). Multiplying by 100 slides them two places; by 1000, three places. The empty ones place is filled with a 0 placeholder — that is where “add a zero” comes from, but it is the result of the move, not the rule.
Dividing works the same way, but in the opposite direction — the number gets smaller, so the digits slide right.
Example 2 — dividing
6 ÷ 100 = 0.06÷ 100 — every digit moves 2 places right
The 6 slides two places right, from ones to hundredths. The ones and tenths are filled with placeholder zeros so we can read it: 0.06.
The decimal point never moves. It sits between the ones and the tenths and stays put. What moves is the digits, sliding past it. Watch out for “3.5 × 10 = 3.50” — that is wrong, because 3.50 is the same as 3.5. The digits must actually move: 3.5 × 10 = 35.
How to read the boxes: a dashed box shows where a digit started; a solid box shows where it lands; a gold dotted box is a placeholder zero. Every worked answer further down uses the same boxes, with Watch it move and Hear it buttons.
Section A · Year 3 — Tens facts only
Multiply and divide by 10 using whole-number facts.
Learning objective 1 · Grade 1 foundation
Multiply and divide by 10 using whole-number facts.
Success criteria — I can:
recall the ten-times table (10, 20, 30, …, 120)
use × 10 to find a multiple of ten
divide a multiple of ten by 10 to get back to the start
use the inverse: if 6 × 10 = 60, then 60 ÷ 10 = 6
MethodTo × 10 move every digit one place left; to ÷ 10 move it one place right. (10 has one zero → one place.)
Q1.Work out 4 × 10.
Your answer:(1 mark)
Watch each digit move:
4 times 10 equals 40. Each digit moves 1 place to the left. Before: 4 in the ones. After: 4 in the tens, 0 in the ones.
4 × 10 = 40◀ × 10 — each digit moves 1 place left
5 faded = where the digit started5 boxed = where the digit lands
7 times 10 equals 70. Each digit moves 1 place to the left. Before: 7 in the ones. After: 7 in the tens, 0 in the ones.
7 × 10 = 70◀ × 10 — each digit moves 1 place left
5 faded = where the digit started5 boxed = where the digit lands
T
O
before
7
after
7
0
Q3.Work out 9 × 10.
Your answer:(1 mark)
Watch each digit move:
9 times 10 equals 90. Each digit moves 1 place to the left. Before: 9 in the ones. After: 9 in the tens, 0 in the ones.
9 × 10 = 90◀ × 10 — each digit moves 1 place left
5 faded = where the digit started5 boxed = where the digit lands
T
O
before
9
after
9
0
Q4.Work out 12 × 10.
Your answer:(1 mark)
Watch each digit move:
12 times 10 equals 120. Each digit moves 1 place to the left. Before: 1 in the tens, 2 in the ones. After: 1 in the hundreds, 2 in the tens, 0 in the ones.
12 × 10 = 120◀ × 10 — each digit moves 1 place left
5 faded = where the digit started5 boxed = where the digit lands
H
T
O
before
1
2
after
1
2
0
Q5.Work out 6 × 10.
Your answer:(1 mark)
Watch each digit move:
6 times 10 equals 60. Each digit moves 1 place to the left. Before: 6 in the ones. After: 6 in the tens, 0 in the ones.
6 × 10 = 60◀ × 10 — each digit moves 1 place left
5 faded = where the digit started5 boxed = where the digit lands
T
O
before
6
after
6
0
Q6.You just found 6 × 10 = 60. Dividing undoes multiplying, so work out 60 ÷ 10.
Your answer:(1 mark)
Watch each digit move:
60 divided by 10 equals 6. Each digit moves 1 place to the right. Before: 6 in the tens, 0 in the ones. After: 6 in the ones.
60 ÷ 10 = 6▶ ÷ 10 — each digit moves 1 place right
5 faded = where the digit started5 boxed = where the digit lands
T
O
before
6
0
after
6
Dividing is the inverse of multiplying: if 6 × 10 = 60, then 60 ÷ 10 takes you straight back to 6. The digits simply move back the other way.
Q7.Work out 30 ÷ 10.
Your answer:(1 mark)
Watch each digit move:
30 divided by 10 equals 3. Each digit moves 1 place to the right. Before: 3 in the tens, 0 in the ones. After: 3 in the ones.
30 ÷ 10 = 3▶ ÷ 10 — each digit moves 1 place right
5 faded = where the digit started5 boxed = where the digit lands
T
O
before
3
0
after
3
Think: what × 10 = 30? So 30 ÷ 10 = 3.
Q8.Work out 80 ÷ 10.
Your answer:(1 mark)
Watch each digit move:
80 divided by 10 equals 8. Each digit moves 1 place to the right. Before: 8 in the tens, 0 in the ones. After: 8 in the ones.
80 ÷ 10 = 8▶ ÷ 10 — each digit moves 1 place right
5 faded = where the digit started5 boxed = where the digit lands
T
O
before
8
0
after
8
Q9.Work out 50 ÷ 10.
Your answer:(1 mark)
Watch each digit move:
50 divided by 10 equals 5. Each digit moves 1 place to the right. Before: 5 in the tens, 0 in the ones. After: 5 in the ones.
50 ÷ 10 = 5▶ ÷ 10 — each digit moves 1 place right
5 faded = where the digit started5 boxed = where the digit lands
T
O
before
5
0
after
5
Q10.Work out 120 ÷ 10.
Your answer:(1 mark)
Watch each digit move:
120 divided by 10 equals 12. Each digit moves 1 place to the right. Before: 1 in the hundreds, 2 in the tens, 0 in the ones. After: 1 in the tens, 2 in the ones.
120 ÷ 10 = 12▶ ÷ 10 — each digit moves 1 place right
5 faded = where the digit started5 boxed = where the digit lands
H
T
O
before
1
2
0
after
1
2
Section B · Year 4 — Tens and hundreds, whole answers
Multiply and divide whole numbers by 10 and 100, where the answer stays whole.
Learning objective 2 · Grade 1 foundation
Multiply and divide whole numbers by 10 and 100.
Success criteria — I can:
multiply a 2- or 3-digit whole number by 10 and by 100
divide a multiple of 10 or 100 to a whole-number answer
explain that × 10 moves each digit one place left, × 100 moves it two
recognise that zeros are placeholders, not the real rule
MethodCount the zeros — 10 has one, 100 has two. Move every digit that many places: left for ×, right for ÷. A 0 fills any column the digits leave empty.
Q11.Work out 23 × 10.
Your answer:(1 mark)
Watch each digit move:
23 times 10 equals 230. Each digit moves 1 place to the left. Before: 2 in the tens, 3 in the ones. After: 2 in the hundreds, 3 in the tens, 0 in the ones.
23 × 10 = 230◀ × 10 — each digit moves 1 place left
5 faded = where the digit started5 boxed = where the digit lands
The 0 in the ones column is a placeholder — it is not “adding a zero”, it is the empty ones place after the digits moved.
Q12.Work out 23 × 100.
Your answer:(1 mark)
Watch each digit move:
23 times 100 equals 2300. Each digit moves 2 places to the left. Before: 2 in the tens, 3 in the ones. After: 2 in the thousands, 3 in the hundreds, 0 in the tens, 0 in the ones.
23 × 100 = 2300◀◀ × 100 — each digit moves 2 places left
5 faded = where the digit started5 boxed = where the digit lands
Th
H
T
O
before
2
3
after
2
3
0
0
Q13.Work out 45 × 10.
Your answer:(1 mark)
Watch each digit move:
45 times 10 equals 450. Each digit moves 1 place to the left. Before: 4 in the tens, 5 in the ones. After: 4 in the hundreds, 5 in the tens, 0 in the ones.
45 × 10 = 450◀ × 10 — each digit moves 1 place left
5 faded = where the digit started5 boxed = where the digit lands
H
T
O
before
4
5
after
4
5
0
Q14.Work out 45 × 100.
Your answer:(1 mark)
Watch each digit move:
45 times 100 equals 4500. Each digit moves 2 places to the left. Before: 4 in the tens, 5 in the ones. After: 4 in the thousands, 5 in the hundreds, 0 in the tens, 0 in the ones.
45 × 100 = 4500◀◀ × 100 — each digit moves 2 places left
5 faded = where the digit started5 boxed = where the digit lands
Th
H
T
O
before
4
5
after
4
5
0
0
Q15.Work out 8 × 100.
Your answer:(1 mark)
Watch each digit move:
8 times 100 equals 800. Each digit moves 2 places to the left. Before: 8 in the ones. After: 8 in the hundreds, 0 in the tens, 0 in the ones.
8 × 100 = 800◀◀ × 100 — each digit moves 2 places left
5 faded = where the digit started5 boxed = where the digit lands
H
T
O
before
8
after
8
0
0
Q16.Now the other way round — work out 450 ÷ 10.
Your answer:(1 mark)
Watch each digit move:
450 divided by 10 equals 45. Each digit moves 1 place to the right. Before: 4 in the hundreds, 5 in the tens, 0 in the ones. After: 4 in the tens, 5 in the ones.
450 ÷ 10 = 45▶ ÷ 10 — each digit moves 1 place right
5 faded = where the digit started5 boxed = where the digit lands
H
T
O
before
4
5
0
after
4
5
Dividing undoes multiplying. × 10 moved the digits left, so ÷ 10 moves them one place right.
Q17.Work out 2300 ÷ 100.
Your answer:(1 mark)
Watch each digit move:
2300 divided by 100 equals 23. Each digit moves 2 places to the right. Before: 2 in the thousands, 3 in the hundreds, 0 in the tens, 0 in the ones. After: 2 in the tens, 3 in the ones.
2300 ÷ 100 = 23▶▶ ÷ 100 — each digit moves 2 places right
5 faded = where the digit started5 boxed = where the digit lands
Th
H
T
O
before
2
3
0
0
after
2
3
Q18.Work out 700 ÷ 100.
Your answer:(1 mark)
Watch each digit move:
700 divided by 100 equals 7. Each digit moves 2 places to the right. Before: 7 in the hundreds, 0 in the tens, 0 in the ones. After: 7 in the ones.
700 ÷ 100 = 7▶▶ ÷ 100 — each digit moves 2 places right
5 faded = where the digit started5 boxed = where the digit lands
H
T
O
before
7
0
0
after
7
Q19.Work out 3600 ÷ 10.
Your answer:(1 mark)
Watch each digit move:
3600 divided by 10 equals 360. Each digit moves 1 place to the right. Before: 3 in the thousands, 6 in the hundreds, 0 in the tens, 0 in the ones. After: 3 in the hundreds, 6 in the tens, 0 in the ones.
3600 ÷ 10 = 360▶ ÷ 10 — each digit moves 1 place right
5 faded = where the digit started5 boxed = where the digit lands
Th
H
T
O
before
3
6
0
0
after
3
6
0
Q20.Work out 5000 ÷ 100.
Your answer:(1 mark)
Watch each digit move:
5000 divided by 100 equals 50. Each digit moves 2 places to the right. Before: 5 in the thousands, 0 in the hundreds, 0 in the tens, 0 in the ones. After: 5 in the tens, 0 in the ones.
5000 ÷ 100 = 50▶▶ ÷ 100 — each digit moves 2 places right
5 faded = where the digit started5 boxed = where the digit lands
Th
H
T
O
before
5
0
0
0
after
5
0
Section C · Year 5 — Decimals enter
Begin multiplying and dividing whole numbers and decimals by 10, 100 and 1000.
Learning objective 3 · Grade 1–2
Begin multiplying and dividing whole numbers and decimals by 10, 100 and 1000.
Success criteria — I can:
multiply a decimal by 10, 100 or 1000 (e.g. 3.5 × 10 = 35)
divide a whole number to give a decimal (e.g. 6 ÷ 100 = 0.06)
recognise that × 1000 moves each digit three places left
use place-value language: tens, ones, tenths, hundredths, thousandths
MethodSame rule, but the digit can now cross the decimal point. The point never moves — the digits do. Count the zeros = places to move.
Drive it yourself · now into decimals6Start at 6. Divide to send the digit past the ones into the decimals — multiply to bring it back up to whole.
Th1000s
H100s
T10s
Oones
·
ttenths
h100ths
th1000ths
6
Now the digit can move right of the ones — into tenths, hundredths and thousandths. The point still never moves; the digit does. A button switches off at the edges (past the thousands, or past the thousandths). The grey 0s are placeholders, including the 0 before the point that lets you read a number like 0.06.
Worked scaffold · into decimals, then back to whole
Step 1 — divide into the decimals (gets smaller)
6 ÷ 10 = 0.6digit jumps 1 place right — into the tenths
6 ÷ 100 = 0.06jumps 2 places right — into the hundredths
6 ÷ 1000 = 0.006jumps 3 places right — into the thousandths
Step 2 — multiply back up (gets bigger)
0.006 × 10 = 0.06digit jumps 1 place left
0.006 × 100 = 0.6jumps 2 places left
0.006 × 1000 = 6jumps 3 places left — back to a whole number
Check ✓the point never moved — only the digit did, and ÷ then × returns you to 6.
Q21.Work out 3.5 × 10.
Your answer:(1 mark)
Watch each digit move:
3.5 times 10 equals 35. Each digit moves 1 place to the left. Before: 3 in the ones, 5 in the tenths. After: 3 in the tens, 5 in the ones.
3.5 × 10 = 35◀ × 10 — each digit moves 1 place left
5 faded = where the digit started5 boxed = where the digit lands
T
O
·
t
before
3
·
5
after
3
5
·
Check: 35 ÷ 10 = 3.5 ✓ — dividing undoes the multiplying and lands back on the start.
NOT 3.50 — that is still 3.5. The digits move; the decimal point stays put.
Q22.Work out 2.7 × 100.
Your answer:(1 mark)
Watch each digit move:
2.7 times 100 equals 270. Each digit moves 2 places to the left. Before: 2 in the ones, 7 in the tenths. After: 2 in the hundreds, 7 in the tens, 0 in the ones.
2.7 × 100 = 270◀◀ × 100 — each digit moves 2 places left
5 faded = where the digit started5 boxed = where the digit lands
H
T
O
·
t
before
2
·
7
after
2
7
0
·
Q23.Work out 4.7 × 1000.
Your answer:(1 mark)
Watch each digit move:
4.7 times 1000 equals 4700. Each digit moves 3 places to the left. Before: 4 in the ones, 7 in the tenths. After: 4 in the thousands, 7 in the hundreds, 0 in the tens, 0 in the ones.
4.7 × 1000 = 4700◀◀◀ × 1000 — each digit moves 3 places left
5 faded = where the digit started5 boxed = where the digit lands
Th
H
T
O
·
t
before
4
·
7
after
4
7
0
0
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Q24.Work out 0.06 × 100.
Your answer:(1 mark)
Watch each digit move:
0.06 times 100 equals 6. Each digit moves 2 places to the left. Before: 0 in the ones, 0 in the tenths, 6 in the hundredths. After: 6 in the ones.
0.06 × 100 = 6◀◀ × 100 — each digit moves 2 places left
5 faded = where the digit started5 boxed = where the digit lands
O
·
t
h
before
0
·
0
6
after
6
·
First time the starting number has two decimal places. Read 0.06 as “six hundredths”; × 100 sends that 6 two places left into the ones, so the answer is the whole number 6.
Q25.Work out 0.075 × 1000.
Your answer:(1 mark)
Watch each digit move:
0.075 times 1000 equals 75. Each digit moves 3 places to the left. Before: 0 in the ones, 0 in the tenths, 7 in the hundredths, 5 in the thousandths. After: 7 in the tens, 5 in the ones.
0.075 × 1000 = 75◀◀◀ × 1000 — each digit moves 3 places left
5 faded = where the digit started5 boxed = where the digit lands
T
O
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t
h
th
before
0
·
0
7
5
after
7
5
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Q26.Now divide — work out 35 ÷ 10.
Your answer:(1 mark)
Watch each digit move:
35 divided by 10 equals 3.5. Each digit moves 1 place to the right. Before: 3 in the tens, 5 in the ones. After: 3 in the ones, 5 in the tenths.
35 ÷ 10 = 3.5▶ ÷ 10 — each digit moves 1 place right
5 faded = where the digit started5 boxed = where the digit lands
T
O
·
t
before
3
5
·
after
3
·
5
You saw 3.5 × 10 = 35. Dividing undoes that: 35 ÷ 10 sends the digits one place right, straight back to 3.5.
Q27.Work out 90 ÷ 100.
Your answer:(1 mark)
Watch each digit move:
90 divided by 100 equals 0.9. Each digit moves 2 places to the right. Before: 9 in the tens, 0 in the ones. After: 0 in the ones, 9 in the tenths.
90 ÷ 100 = 0.9▶▶ ÷ 100 — each digit moves 2 places right
5 faded = where the digit started5 boxed = where the digit lands
T
O
·
t
before
9
0
·
after
0
·
9
Q28.Work out 6 ÷ 100.
Your answer:(1 mark)
Watch each digit move:
6 divided by 100 equals 0.06. Each digit moves 2 places to the right. Before: 6 in the ones. After: 0 in the ones, 0 in the tenths, 6 in the hundredths.
6 ÷ 100 = 0.06▶▶ ÷ 100 — each digit moves 2 places right
5 faded = where the digit started5 boxed = where the digit lands
O
·
t
h
before
6
·
after
0
·
0
6
The 0 in the ones and tenths columns are placeholders so we can read the 6 in the hundredths place.
Q29.Work out 450 ÷ 1000.
Your answer:(1 mark)
Watch each digit move:
450 divided by 1000 equals 0.45. Each digit moves 3 places to the right. Before: 4 in the hundreds, 5 in the tens, 0 in the ones. After: 0 in the ones, 4 in the tenths, 5 in the hundredths.
450 ÷ 1000 = 0.45▶▶▶ ÷ 1000 — each digit moves 3 places right
5 faded = where the digit started5 boxed = where the digit lands
H
T
O
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t
h
before
4
5
0
·
after
0
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4
5
Q30.Work out 8 ÷ 1000.
Your answer:(1 mark)
Watch each digit move:
8 divided by 1000 equals 0.008. Each digit moves 3 places to the right. Before: 8 in the ones. After: 0 in the ones, 0 in the tenths, 0 in the hundredths, 8 in the thousandths.
8 ÷ 1000 = 0.008▶▶▶ ÷ 1000 — each digit moves 3 places right
5 faded = where the digit started5 boxed = where the digit lands
O
·
t
h
th
before
8
·
after
0
·
0
0
8
The hardest case: the 8 moves three places right, into the thousandths. The ones, tenths and hundredths are all empty, so each gets a placeholder 0 — with a 0 before the point too — giving 0.008.
Section D · Year 6 / GCSE entry — Full decimal fluency
Secure fluency with decimals to 3 decimal places, plus conversions, money, and reasoning.
Learning objective 4 · Grade 1–3
Secure fluency with decimals up to 3 decimal places, applied and explained.
Success criteria — I can:
multiply and divide decimals to 3 dp by 10, 100 and 1000
apply this to metric-conversion and money word problems
explain why “the decimal point moves” is wrong — the digits move
check answers using estimation
MethodCount the zeros, move every digit that many places, keep the point fixed, then check with the inverse (× undoes ÷).
Q31.Work out 3.056 × 10.
Your answer:(1 mark)
Watch each digit move:
3.056 times 10 equals 30.56. Each digit moves 1 place to the left. Before: 3 in the ones, 0 in the tenths, 5 in the hundredths, 6 in the thousandths. After: 3 in the tens, 0 in the ones, 5 in the tenths, 6 in the hundredths.
3.056 × 10 = 30.56◀ × 10 — each digit moves 1 place left
5 faded = where the digit started5 boxed = where the digit lands
3.056 times 1000 equals 3056. Each digit moves 3 places to the left. Before: 3 in the ones, 0 in the tenths, 5 in the hundredths, 6 in the thousandths. After: 3 in the thousands, 0 in the hundreds, 5 in the tens, 6 in the ones.
3.056 × 1000 = 3056◀◀◀ × 1000 — each digit moves 3 places left
5 faded = where the digit started5 boxed = where the digit lands
Th
H
T
O
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t
h
th
before
3
·
0
5
6
after
3
0
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Q33.Work out 45.8 ÷ 10.
Your answer:(1 mark)
Watch each digit move:
45.8 divided by 10 equals 4.58. Each digit moves 1 place to the right. Before: 4 in the tens, 5 in the ones, 8 in the tenths. After: 4 in the ones, 5 in the tenths, 8 in the hundredths.
45.8 ÷ 10 = 4.58▶ ÷ 10 — each digit moves 1 place right
5 faded = where the digit started5 boxed = where the digit lands
T
O
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t
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before
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5
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8
after
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8
Q34.Work out 45.8 ÷ 100.
Your answer:(1 mark)
Watch each digit move:
45.8 divided by 100 equals 0.458. Each digit moves 2 places to the right. Before: 4 in the tens, 5 in the ones, 8 in the tenths. After: 0 in the ones, 4 in the tenths, 5 in the hundredths, 8 in the thousandths.
45.8 ÷ 100 = 0.458▶▶ ÷ 100 — each digit moves 2 places right
5 faded = where the digit started5 boxed = where the digit lands
T
O
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h
th
before
4
5
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8
after
0
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4
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8
Q35.Work out 45.8 ÷ 1000.
Your answer:(1 mark)
Watch each digit move:
45.8 divided by 1000 equals 0.0458. Each digit moves 3 places to the right. Before: 4 in the tens, 5 in the ones, 8 in the tenths. After: 0 in the ones, 0 in the tenths, 4 in the hundredths, 5 in the thousandths, 8 in the ten-thousandths.
45.8 ÷ 1000 = 0.0458▶▶▶ ÷ 1000 — each digit moves 3 places right
5 faded = where the digit started5 boxed = where the digit lands
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O
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th
tth
before
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8
after
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Q36.A ribbon is 4.5 metres long. How many millimetres is that? (1 m = 1000 mm.)
Your answer:(1 mark)
Watch each digit move:
4.5 times 1000 equals 4500. Each digit moves 3 places to the left. Before: 4 in the ones, 5 in the tenths. After: 4 in the thousands, 5 in the hundreds, 0 in the tens, 0 in the ones.
4.5 × 1000 = 4500◀◀◀ × 1000 — each digit moves 3 places left
5 faded = where the digit started5 boxed = where the digit lands
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metres → millimetres means × 1000.
Q37.A coin weighs 7.5 g. What do 100 identical coins weigh, in grams?
Your answer:(1 mark)
Watch each digit move:
7.5 times 100 equals 750. Each digit moves 2 places to the left. Before: 7 in the ones, 5 in the tenths. After: 7 in the hundreds, 5 in the tens, 0 in the ones.
7.5 × 100 = 750◀◀ × 100 — each digit moves 2 places left
5 faded = where the digit started5 boxed = where the digit lands
H
T
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before
7
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after
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0
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Q38.£36.50 is shared equally between 10 people. How much does each get, in pounds?
Your answer:(1 mark)
Watch each digit move:
36.5 divided by 10 equals 3.65. Each digit moves 1 place to the right. Before: 3 in the tens, 6 in the ones, 5 in the tenths. After: 3 in the ones, 6 in the tenths, 5 in the hundredths.
36.5 ÷ 10 = 3.65▶ ÷ 10 — each digit moves 1 place right
5 faded = where the digit started5 boxed = where the digit lands
T
O
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before
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6
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after
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£36.50 is the same number as 36.5. Each digit moves one place right: £36.50 ÷ 10 = £3.65.
Q39.A wire is 2300 mm long. How many metres is that? (1000 mm = 1 m.)
Your answer:(1 mark)
Watch each digit move:
2300 divided by 1000 equals 2.3. Each digit moves 3 places to the right. Before: 2 in the thousands, 3 in the hundreds, 0 in the tens, 0 in the ones. After: 2 in the ones, 3 in the tenths.
2300 ÷ 1000 = 2.3▶▶▶ ÷ 1000 — each digit moves 3 places right
5 faded = where the digit started5 boxed = where the digit lands
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before
2
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after
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millimetres → metres means ÷ 1000.
Q40.A jug holds 1.25 litres. How many millilitres is that? (1 litre = 1000 ml.)
Your answer:(1 mark)
Watch each digit move:
1.25 times 1000 equals 1250. Each digit moves 3 places to the left. Before: 1 in the ones, 2 in the tenths, 5 in the hundredths. After: 1 in the thousands, 2 in the hundreds, 5 in the tens, 0 in the ones.
1.25 × 1000 = 1250◀◀◀ × 1000 — each digit moves 3 places left
5 faded = where the digit started5 boxed = where the digit lands
Th
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before
1
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2
5
after
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0
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litres → millilitres means × 1000.
Q41.A pupil says: “3.5 × 10 = 3.50.” Explain why this is wrong, and give the correct answer.
Your explanation:
(2 marks)
Compare with the model answer, then mark yourself:
Model answer
Multiplying by 10 must make a number bigger, but 3.50 is exactly the same as 3.5 — the extra zero changes nothing. The mistake is “add a zero”. The real rule: every digit moves one place left.
3.5 times 10 equals 35. Each digit moves 1 place to the left. Before: 3 in the ones, 5 in the tenths. After: 3 in the tens, 5 in the ones.
3.5 × 10 = 35◀ × 10 — each digit moves 1 place left
5 faded = where the digit started5 boxed = where the digit lands
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O
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t
before
3
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5
after
3
5
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Q42.A pupil says: “When you divide by 100, you add two zeros.” Explain why this does not work for 6 ÷ 100.
Your explanation:
(2 marks)
Compare with the model answer, then mark yourself:
Model answer
Adding two zeros gives 600 — but that is bigger, and dividing should make a number smaller. Dividing by 100 moves each digit two places right: the 6 slides from ones to hundredths.
6 divided by 100 equals 0.06. Each digit moves 2 places to the right. Before: 6 in the ones. After: 0 in the ones, 0 in the tenths, 6 in the hundredths.
6 ÷ 100 = 0.06▶▶ ÷ 100 — each digit moves 2 places right
5 faded = where the digit started5 boxed = where the digit lands