Choosing units and the millimetre
You measure a pencil in cm, a classroom in m and the road to another town in km. A sprout or a coin is so small that even cm is too big — we use millimetres.
We measure length in mm, cm, m and km. Pick the unit that gives a small, easy number. 1 cm = 10 mm: one centimetre is divided into 10 equal parts, each 1 millimetre.
Formula: mm = cm × 10; cm = mm ÷ 10. a cm b mm = (a × 10 + b) mm.
In the figure: Each cm on the ruler has 10 small marks. The red line goes 3 cm and 6 more marks, so it is 3 cm 6 mm = 36 mm long.
Rule 1: Pick a sensible unit — Tiny things: mm. Small things: cm. Rooms and playgrounds: m. Roads and cities: km.
Choosing units and the millimetre
In the app you can move this figure with your finger.
Open in the app- Easy: The thickness of a coin: about 2 mm.
- Medium: The length of a notebook: about 24 cm.
- Exam-type: The distance between two cities: hundreds of km.
Rule 2: Millimetres and centimetres — Multiply the cm by 10 and add the extra mm. To go back, divide mm by 10: the quotient is cm and the remainder is mm.
- Easy: 5 cm 8 mm = 5 × 10 + 8 = 58 mm.
- Medium: 83 mm = 80 mm + 3 mm = 8 cm 3 mm.
- Exam-type: 126 mm = 12 cm 6 mm.
A mm is the smallest unit on a school ruler: 10 mm make 1 cm, so the marks between two centimetre numbers are millimetres.
Writing 3 cm 6 mm as 3.6 mm or 306 mm. It is 36 mm: 3 cm = 30 mm, plus 6 mm.
mm → cm: cut off the last digit as the mm part. 126 mm → 12 cm | 6 mm. Memory clue: "Ten small mm make one cm."
Spot the difference
| Point | cm to mm | mm to cm |
|---|---|---|
| Operation | × 10 | ÷ 10 |
| Example | 7 cm = 70 mm | 90 mm = 9 cm |
Practice questions
- 1Which unit would you use for the thickness of a coin?
- 21 cm = ___ mm
- 3Convert 9 cm into mm.
- 4Convert 4 cm 7 mm into mm.
- 5Write 83 mm in cm and mm.
- 6Write 205 mm in cm and mm.
- 7A sprout is 5 cm 3 mm long. How many mm is that?
- 8Draw a line of 58 mm using a scale. Write its length in cm and mm.
Show answers (try them yourself first)
- 1mm
- 210
- 390 mm
- 447 mm
- 58 cm 3 mm
- 620 cm 5 mm
- 753 mm
- 85 cm 8 mm
Converting between mm, cm, m and km
A tailor says a cloth is 7 m 25 cm long, while the shop sheet says 725 cm. Both are the same length written in different units.
10 mm = 1 cm, 100 cm = 1 m, 1,000 m = 1 km. From a big unit to a small unit we multiply; from a small unit to a big unit we divide. Kilo means thousand.
Formula: m → cm: × 100. cm → m: ÷ 100. km → m: × 1,000. m → km: ÷ 1,000.
In the figure: Going right (to smaller units) multiply by 1,000, then 100, then 10. Going left, divide.
Rule 1: Mixed form to one unit — Change the big part to the small unit and add the small part. Keep zeros in the right places.
Converting between mm, cm, m and km
In the app you can move this figure with your finger.
Open in the app- Easy: 7 m 25 cm = 700 cm + 25 cm = 725 cm.
- Medium: 9 m 5 cm = 900 cm + 5 cm = 905 cm (not 95 cm).
- Exam-type: 12 km 80 m = 12,000 m + 80 m = 12,080 m.
Rule 2: One unit to mixed form — Split off the last 2 digits for cm (or the last 3 digits for m in km).
- Easy: 460 cm = 4 m 60 cm.
- Medium: 1,275 cm = 12 m 75 cm.
- Exam-type: 7,005 m = 7 km 5 m.
The size of the length does not change when the unit changes: only the number and the unit name change.
Treating 9 m 5 cm as 95 cm. The cm part needs 2 digits: 5 cm is 05 cm, so 9 m 5 cm = 905 cm.
Use the double number line: 1 m is 100 cm, so 4 m is 400 cm, 7 m is 700 cm and so on. Memory clue: "Kilo = 1,000; centi = 100 in a metre; milli = 10 in a centimetre."
Spot the difference
| Point | Big → small | Small → big |
|---|---|---|
| Operation | multiply | divide |
| Example | 6 km = 6,000 m | 4,000 m = 4 km |
Practice questions
- 1How many metres are in 18 km?
- 2Convert 7 m 25 cm into cm.
- 3Write 460 cm in m and cm.
- 4Convert 4,350 m into km and m.
- 5Convert 9 m 5 cm into cm.
- 6Convert 12 km 80 m into metres.
- 7How many millimetres are in 3 m?
- 8Write 3,908 cm in m and cm, then in mm.
Show answers (try them yourself first)
- 118,000 m
- 2725 cm
- 34 m 60 cm
- 44 km 350 m
- 5905 cm
- 612,080 m
- 73,000 mm
- 839 m 8 cm; 39,080 mm
Comparing lengths
A rope is 4 m 20 cm and a ribbon is 410 cm. Which is longer? We cannot just compare the numbers 4, 20 and 410: first we must write both in the same unit.
To compare lengths, write them in the same unit. Then compare the numbers: bigger number = longer length. Use <, = or >.
Formula: Convert both → same unit → compare the numbers.
In the figure: 4 m 20 cm = 420 cm, which is 10 cm more than 410 cm, so the rope is longer.
Rule 1: Same unit first — Change every length to the smallest unit used (or to the unit that makes the work easiest).
Comparing lengths
In the app you can move this figure with your finger.
Open in the app- Easy: 3 km 50 m = 3,050 m < 3,500 m.
- Medium: 250 mm = 25 cm > 2 cm 60 mm = 8 cm.
- Exam-type: 380 cm = 3 m 80 cm (equal).
Rule 2: Order and difference — To order several lengths, convert all to one unit and arrange. To find how much longer, subtract.
- Easy: 420 cm, 4 m 5 cm, 4,100 mm = 420 cm, 405 cm, 410 cm. Shortest: 4 m 5 cm.
- Medium: Ribbon 650 cm and rope 6 m 40 cm = 640 cm: the ribbon is 10 cm longer.
- Exam-type: 950 m < 1 km because 1 km = 1,000 m.
7 m 5 cm and 7 m 50 cm are different: 705 cm and 750 cm. The cm part has 2 digits, so 5 cm is 05 cm.
Comparing the numbers without changing units: thinking 410 cm > 4 m 20 cm because 410 > 4 and 410 > 20.
Convert to the smaller unit — then you only have whole numbers to compare. Memory clue: "Same unit, then size."
Spot the difference
| Point | 4 m 20 cm | 410 cm |
|---|---|---|
| In cm | 420 cm | 410 cm |
| Longer? | Yes | No |
Practice questions
- 1Which is longer: 3 km 50 m or 3,500 m?
- 2Put <, = or >: 380 cm ___ 3 m 80 cm
- 3Put <, = or >: 950 m ___ 1 km
- 4Which is longer: 7 m 5 cm or 7 m 50 cm?
- 5Put <, = or >: 65 mm ___ 6 cm 5 mm
- 6Which is shortest: 420 cm, 4 m 5 cm or 4,100 mm?
- 7A rope is 6 m 40 cm and a ribbon is 650 cm. How much longer is the ribbon?
- 8Arrange in increasing order: 2 m 75 cm, 257 cm, 2,800 mm.
Show answers (try them yourself first)
- 13,500 m
- 2=
- 3<
- 47 m 50 cm
- 5=
- 64 m 5 cm (= 405 cm)
- 710 cm
- 8257 cm, 2 m 75 cm, 2,800 mm (257, 275, 280 cm)
Adding and subtracting lengths
Saji walked 2 km 650 m in the morning and 1 km 480 m in the evening. How far did he walk in all? We add like units: km with km, m with m — and regroup 1,000 m as 1 km.
Add or subtract like units (km with km, m with m, cm with cm). Regroup when needed: 1,000 m = 1 km and 100 cm = 1 m. Or change everything to the small unit, calculate, and change back.
Formula: Method 1: add small units → regroup → add big units. Method 2: convert all to the small unit → calculate → convert back.
In the figure: 650 m + 480 m = 1,130 m = 1 km 130 m. Then 2 km + 1 km + 1 km = 4 km. Total 4 km 130 m.
Rule 1: Add lengths — Add the small unit parts first. If they reach the next unit, regroup.
Adding and subtracting lengths
In the app you can move this figure with your finger.
Open in the app- Easy: 5 m 40 cm + 3 m 75 cm: 40 + 75 = 115 cm = 1 m 15 cm → 9 m 15 cm.
- Medium: 7 km 900 m + 6 km 350 m = 14 km 250 m.
- Exam-type: 3 km 200 m × 2 (round trip) = 6 km 400 m.
Rule 2: Subtract lengths — If the small unit part is smaller, borrow 1 big unit (1 m = 100 cm, 1 km = 1,000 m).
- Easy: 9 m 20 cm − 4 m 65 cm: 920 − 465 = 455 cm = 4 m 55 cm.
- Medium: 7 km 100 m − 2 km 450 m: 7,100 − 2,450 = 4,650 m = 4 km 650 m.
- Exam-type: 8 km − 3 km 750 m: 8,000 − 3,750 = 4,250 m = 4 km 250 m.
You can only add or subtract numbers that have the same unit. Write the unit in every step.
Writing 6 km 1,105 m as an answer. 1,105 m has more than 1,000 m, so regroup: 7 km 105 m.
Convert both to the small unit and use ordinary column addition or subtraction. Memory clue: "Like with like, then regroup at 100 or 1,000."
Spot the difference
| Point | Method 1 | Method 2 |
|---|---|---|
| 4 km 125 m + 2 km 980 m | 125 + 980 = 1,105 m → 7 km 105 m | 4,125 + 2,980 = 7,105 m → 7 km 105 m |
| Answer | 7 km 105 m | 7 km 105 m |
Practice questions
- 1Add 2 km 650 m + 1 km 480 m.
- 2Add 5 m 40 cm + 3 m 75 cm.
- 3Subtract 9 m 20 cm − 4 m 65 cm.
- 4A ribbon is 12 m long. 4 m 35 cm is cut off. How much is left?
- 5Add 4 km 125 m + 2 km 980 m.
- 6Subtract 7 km 100 m − 2 km 450 m.
- 7A road is 8 km long. 3 km 750 m is paved. How much is left to pave?
- 8A cyclist rides 2 km 500 m every day. How far in 4 days? Give the answer in km.
Show answers (try them yourself first)
- 14 km 130 m
- 29 m 15 cm
- 34 m 55 cm
- 47 m 65 cm
- 57 km 105 m
- 64 km 650 m
- 74 km 250 m
- 810 km
Distances and intervals
For a 3-km race the organisers put a flag every 500 m. Planning a race, a bus route or a rope length means dividing a total distance into equal steps.
Number of equal steps = total distance ÷ step length (in the same unit). The distance between two stops = the difference of their distances from the start.
Formula: steps = total ÷ step. distance between stops = bigger distance − smaller distance.
In the figure: 3 km = 3,000 m. A flag every 500 m gives flags at 500, 1,000, 1,500, 2,000, 2,500 and 3,000 m: 3,000 ÷ 500 = 6 flags.
Rule 1: Equal steps in a distance — Change the total to the same unit as the step, then divide.
Distances and intervals
In the app you can move this figure with your finger.
Open in the app- Easy: How many 250 m ropes make 1 km? 1,000 ÷ 250 = 4.
- Medium: A 2 km 400 m track with a child every 300 m: 2,400 ÷ 300 = 8 children.
- Exam-type: Steps of 50 cm to cover 10 m: 1,000 ÷ 50 = 20 steps.
Rule 2: Distance between stops — Subtract the smaller distance from the bigger distance (both measured from the same start).
- Easy: P at 120 km, Q at 475 km: P to Q = 475 − 120 = 355 km.
- Medium: Q at 475 km, R at 1,030 km: Q to R = 555 km.
- Exam-type: Gap P–Q (355) vs gap Q–R (555): Q–R is farther apart.
The first flag at 500 m and the last at the finish line: count = total ÷ step. If a flag is also at the start, add 1.
Dividing without matching units: 3 km ÷ 500 m. Write 3 km as 3,000 m first.
Draw the distance as a line and mark the stops; then count them. Memory clue: "Same unit, then divide to count the steps."
Spot the difference
| Point | Number of steps | Distance between stops |
|---|---|---|
| Method | total ÷ step | bigger − smaller |
| Example | 3,000 ÷ 500 = 6 | 475 − 120 = 355 km |
Practice questions
- 1How many 250 m ropes make 1 km?
- 2A 3-km race has a flag every 500 m (first at 500 m, last at the finish). How many flags?
- 3How many steps of 50 cm make 10 m?
- 4Station P is 120 km and Q is 475 km from the start. How far is P from Q?
- 5A 2 km 400 m track has a child every 300 m (first at 300 m, last at the end). How many children?
- 6A cyclist rides 2 km 500 m daily. How far in 4 days?
- 7Q is 475 km and R is 1,030 km from the start. P is 120 km. Which gap is bigger: P–Q or Q–R? By how much?
- 8A 4-km race has a flag every 800 m. How many flags?
Show answers (try them yourself first)
- 14
- 26
- 320
- 4355 km
- 58
- 610 km
- 7Q–R is bigger: 555 − 355 = 200 km more.
- 85