Weight units, estimating and reading scales
A shopkeeper weighs rice in kg, a goldsmith weighs a ring in g and a pharmacist weighs medicine in mg. A truck carries sand in tonnes. Choosing the right unit tells us how heavy a thing is.
Weight tells how heavy something is. Units, from small to big: milligram (mg), gram (g), kilogram (kg), quintal, tonne. A scale shows weight with a needle or a number; first find what one small mark stands for.
Formula: Value of one mark = (difference between two marked numbers) ÷ (number of gaps between them). Reading = marks counted × value of one mark.
In the figure: The scale has marks at 0, 250 g, 500 g, 750 g and 1 kg. The needle is on the third mark: 3 × 250 g = 750 g.
Rule 1: Pick the sensible unit — Think of a familiar object for each unit: a sugar sachet is about 5 g, a school bag about 3 kg, a loaded truck about tonnes.
- Easy: An ant: mg. A pencil: about 5 g.
- Medium: A bed: about 60 kg (not 60 g).
- Exam-type: A refrigerator: about 50 kg (not 50 g).
Rule 2: Read a scale — Find the value of one mark first, then count the marks from 0.
- Easy: Marks every 250 g, needle on the 3rd mark: 750 g.
- Medium: Marks every 100 g, needle on the 7th mark: 700 g.
- Exam-type: Marks every 500 g, needle on the 5th mark: 2,500 g = 2 kg 500 g.
Every scale starts at 0; always check where the needle starts and what one small mark means.
Reading the nearest number instead of counting marks, or writing a heavy object in g (a bed as 60 g).
Mark value × number of marks. Check the answer against a familiar object. Memory clue: "Small things in g, people and bags in kg, trucks in tonnes."
Spot the difference
| Object | Sensible unit | About |
|---|---|---|
| Ant | mg | 2 mg |
| Pencil | g | 5 g |
| School bag | kg | 3 kg |
| Truck load | tonne | 5 tonnes |
Practice questions
- 1Which is sensible for a school bag: 3 g, 3 kg or 300 kg?
- 2Which unit is best to weigh a gold ring?
- 3Is "iron almirah – 40 g" correct? What should it be?
- 4A scale has marks every 250 g. The needle is on the 3rd mark. Weight?
- 5Marks every 500 g, needle on the 5th mark. Weight in kg and g?
- 6Which unit would you use for the weight of an ant?
- 7A scale reads between 1 kg and 2 kg with 4 equal gaps. What does one mark stand for?
- 8Name one thing you would weigh in g, one in kg and one in tonnes.
Show answers (try them yourself first)
- 13 kg
- 2gram
- 3No, about 40 kg
- 4750 g
- 52 kg 500 g
- 6milligram
- 71,000 g ÷ 4 = 250 g
- 8For example: a pencil, a rice bag, a truck of sand
Converting units: kg, g, mg, quintal, tonne
Shrenu needs 3 kg 500 g of flour but her kitchen scale shows only grams. She must change 3 kg 500 g into grams: 3,500 g.
1 kg = 1,000 g; 1 g = 1,000 mg; 100 kg = 1 quintal; 1,000 kg = 1 tonne. To go from a big unit to a small unit, multiply; from small to big, divide.
Formula: a kg b g = (a × 1,000 + b) g. N g = (N ÷ 1,000) kg, with the remainder in g.
In the figure: Top: the ladder of units and what to multiply by. Bottom: a double number line puts kg above and g below, 1 kg = 1,000 g, so 3 kg 500 g = 3,500 g.
Rule 1: kg and g — Multiply the kg by 1,000 and add the grams. To go back, divide by 1,000: quotient = kg, remainder = g.
Converting units: kg, g, mg, quintal, tonne
In the app you can move this figure with your finger.
Open in the app- Easy: 7 kg 67 g = 7,000 + 67 = 7,067 g.
- Medium: 10,760 g = 10 kg 760 g.
- Exam-type: 4,080 g = 4 kg 80 g (not 4 kg 8 g).
Rule 2: g and mg, quintal and tonne — Same idea: 1 g = 1,000 mg; 1 quintal = 100 kg; 1 tonne = 1,000 kg = 10 quintals.
- Easy: 4 g 100 mg = 4,000 + 100 = 4,100 mg.
- Medium: 5,000 kg = 50 quintals = 5 tonnes.
- Exam-type: 8 tonnes = 8 × 1,000 = 8,000 kg.
The small part (g) is added after multiplying; it never gets multiplied by 1,000.
Writing 5 kg 50 g as 5,500 g. 50 g is only 50, so 5,000 + 50 = 5,050 g. Also 1 l 400 ml is 1,400 ml, not 1,040 ml.
Think of three-digit grams: the part after the comma is always grams. 5,050 g = 5 kg 050 g. Memory clue: "Big to small: times 1,000; small to big: divide by 1,000."
Spot the difference
| Unit pair | Relation | Example |
|---|---|---|
| kg – g | 1 kg = 1,000 g | 3 kg 500 g = 3,500 g |
| g – mg | 1 g = 1,000 mg | 4 g 100 mg = 4,100 mg |
| quintal – kg | 1 quintal = 100 kg | 5,000 kg = 50 quintals |
| tonne – kg | 1 tonne = 1,000 kg | 8 tonnes = 8,000 kg |
Practice questions
- 1Convert 3 kg 500 g into grams.
- 2Convert 2 kg 250 g into grams.
- 3Convert 10,760 g into kg and g.
- 4Convert 7 kg 67 g and 8 kg 69 g into grams.
- 5A sugar sachet weighs 5 g. How many milligrams?
- 6Convert 4,080 g and 12,042 g into kg and g.
- 75,000 kg = ___ quintals = ___ tonnes. Fill in.
- 8Shamim says 5 kg 50 g = 5,050 g; Rehan says 5,500 g. Who is right and why?
Show answers (try them yourself first)
- 13,500 g
- 22,250 g
- 310 kg 760 g
- 47,067 g and 8,069 g
- 55,000 mg
- 64 kg 80 g and 12 kg 42 g
- 750 quintals, 5 tonnes
- 8Shamim: 5 × 1,000 + 50 = 5,050 g
Comparing weights
Harpreet packs watermelon 3 kg, mangoes 2 kg, pineapple 1 kg 750 g and apples 1 kg 250 g for a picnic. Which is the heaviest? Which is the lightest? To compare, we first make the units the same.
To compare two weights, change both to the same unit (usually grams), then compare the numbers. Use <, = or >. For ordering, list from the greatest (descending) or the least (ascending).
Formula: Compare in grams: 1 kg 600 g = 1,600 g. If a number of kg is different, the bigger kg wins; if kg are equal, compare the g.
In the figure: The longer the bar, the heavier the fruit: 3,000 g > 2,000 g > 1,750 g > 1,250 g.
Rule 1: Same unit, then compare — Convert both weights to grams and compare digit by digit from the left.
- Easy: 1 kg 600 g (1,600 g) < 1,700 g.
- Medium: 10 kg 35 g = 10,035 g.
- Exam-type: 5 kg 50 g (5,050 g) > 4 kg 500 g (4,500 g).
Rule 2: With milligrams and sums — Change everything to the smallest unit; for sums, add first and then compare.
- Easy: 20 g = 20,000 mg > 200 mg.
- Medium: 9,000 mg = 9 g < 90 g.
- Exam-type: 800 mg + 88 mg = 888 mg = 880 mg + 8 mg.
You cannot compare 1 kg 600 g with 1,700 until both are in the same unit.
Looking only at the biggest-looking number: 1 kg 600 g vs 1 kg 60 g — 600 is not 60, so 1,600 > 1,060.
First compare the kg; only if the kg are equal compare the grams. Memory clue: "Same unit first, then < = >."
Spot the difference
| Left | Right | Sign |
|---|---|---|
| 1 kg 600 g | 1,700 g | < |
| 1 kg 600 g | 1 kg 60 g | > |
| 10 kg 35 g | 10,035 g | = |
| 5 kg 50 g | 4 kg 500 g | > |
Practice questions
- 1Which is heavier: 3 kg or 1 kg 750 g?
- 2Compare 1 kg 600 g and 1,700 g.
- 3Compare 10 kg 35 g and 10,035 g.
- 4Compare 5 kg 50 g and 4 kg 500 g.
- 5Arrange in descending order: 3 kg, 1 kg 750 g, 1 kg 250 g, 2 kg.
- 6Compare 20 g and 200 mg.
- 7Compare 800 mg + 88 mg and 880 mg + 8 mg.
- 8Compare 900 g + 7,000 g and 7 kg + 900 g.
Show answers (try them yourself first)
- 13 kg
- 21,600 g < 1,700 g
- 310,035 g = 10,035 g
- 45,050 g > 4,500 g
- 53 kg, 2 kg, 1 kg 750 g, 1 kg 250 g
- 620,000 mg > 200 mg
- 7888 mg = 888 mg
- 87,900 g = 7,900 g
Adding and subtracting weights
Rathna buys 2 kg 500 g rice for daily use and 1 kg 750 g more for a festival. How much rice does she have? We add like quantities: kg with kg, g with g.
Add grams to grams and kg to kg; if the grams reach 1,000 or more, carry 1 kg. Subtract the same way; if grams are not enough, borrow 1 kg = 1,000 g. Or change both to grams, calculate, and change back.
Formula: (a kg b g) ± (c kg d g): g first (carry or borrow 1,000 g), then kg.
In the figure: 500 g + 750 g = 1,250 g = 1 kg 250 g. Write 250 under g and carry the 1 kg: 2 + 1 + 1 = 4 kg. Total 4 kg 250 g.
Rule 1: Add like quantities — Add the grams first. If you get 1,000 g or more, change 1,000 g into 1 kg and add it to the kg.
Adding and subtracting weights
In the app you can move this figure with your finger.
Open in the app- Easy: 2 kg 500 g + 1 kg 750 g = 4 kg 250 g.
- Medium: 17 kg 900 g + 12 kg 700 g = 30 kg 600 g.
- Exam-type: 5 kg 200 g + 8 kg 900 g + 12 kg 600 g = 26 kg 700 g.
Rule 2: Subtract like quantities — If the grams on top are fewer, borrow 1 kg (1,000 g) from the kg first. Or subtract in grams.
- Easy: 10 kg − 4 kg 500 g = 5 kg 500 g.
- Medium: 2 kg 500 g − 1 kg 750 g = 750 g.
- Exam-type: 9 kg 750 g − 3 kg 700 g = 6 kg 50 g.
Check subtraction by adding back: answer + the smaller weight must give the bigger weight.
Forgetting to carry 1 kg: 500 g + 750 g = 1,250 g, so write 250 g and add 1 kg, not "1,250 g" in the g column.
With friendly numbers (250, 500, 750) add and subtract in your head: 500 + 500 = 1 kg. Memory clue: "Grams first, carry or borrow 1,000, then kilograms."
Spot the difference
| Step | Add | Subtract |
|---|---|---|
| g column | may reach 1,000 → carry 1 kg | may be short → borrow 1 kg |
| Example | 2 kg 500 g + 1 kg 750 g = 4 kg 250 g | 2 kg 500 g − 1 kg 750 g = 750 g |
Practice questions
- 1Find 2 kg 500 g + 1 kg 750 g.
- 2Find 2 kg 100 g + 3 kg 950 g.
- 3A sack of 10 kg has 4 kg 500 g of sand used. How much is left?
- 4A rice sack weighs 9 kg 750 g; later 3 kg 700 g. How much rice was used?
- 5A truck delivers 17 kg 900 g in the morning and 12 kg 700 g in the afternoon. Total?
- 6A box of books weighs 14 kg 750 g. After taking some out it weighs 10 kg 500 g. Weight removed?
- 7A Gurdwara kitchen has 65 kg of flour, uses 42 kg 275 g, then buys 52 kg 500 g. How much flour is there now?
- 8Show 6 kg 300 g + 2 kg 450 g in grams and in kg and g.
Show answers (try them yourself first)
- 14 kg 250 g
- 26 kg 50 g
- 35 kg 500 g
- 46 kg 50 g
- 530 kg 600 g
- 64 kg 250 g
- 765 kg − 42 kg 275 g = 22 kg 725 g; + 52 kg 500 g = 75 kg 225 g
- 86,300 + 2,450 = 8,750 g = 8 kg 750 g
Multiplying, dividing and rates
A farmer has 4 sacks of 10 kg 500 g each. A shopkeeper sells rice at ₹60 for 1 kg. 5 kg of tomatoes cost ₹73, so 10 kg cost double. Weight problems use multiplication, division and rates.
To multiply a weight, multiply the kg and the g separately (or change to grams) and add. To divide, divide the kg and the g separately (or in grams). A rate is the cost of 1 unit; if the weight doubles, the cost doubles.
Formula: Cost = weight in kg × rate per kg. If weight × n, then cost × n.
In the figure: Both lines are multiplied by the same number (× 2): 5 kg → 10 kg and ₹73 → ₹146.
Rule 1: Multiply and divide weights — Work with kg and g separately, or change to grams, calculate, and change back.
- Easy: 4 × 10 kg 500 g = 40 kg + 2,000 g = 42 kg.
- Medium: 4 kg 800 g ÷ 4 = 1 kg 200 g (4,800 ÷ 4 = 1,200 g).
- Exam-type: 3 × 2 kg 250 g = 6 kg + 750 g = 6 kg 750 g.
Rule 2: Cost and rate — Find the cost of 1 unit (rate) or use a double number line: multiply or divide both lines by the same number.
- Easy: Rice ₹60 per kg, 12 kg 500 g: 12.5 × 60 = ₹750.
- Medium: 4 people need 500 g; 8 people need 2 × 500 g = 1,000 g.
- Exam-type: ₹200 for 10 kg iron: 20 kg costs ₹400.
Multiply the SAME number on both lines of a double number line (weight and cost).
Multiplying only the kg and forgetting the grams: 4 × 10 kg 500 g is not 40 kg 500 g.
Turn 250 g, 500 g, 750 g into ¼, ½, ¾ kg to multiply quickly. Memory clue: "Same factor on both lines — weight and money."
Spot the difference
| Problem | Method | Answer |
|---|---|---|
| 4 × 10 kg 500 g | 40 kg + 2,000 g | 42 kg |
| 4 kg 800 g ÷ 4 | 4,800 g ÷ 4 | 1 kg 200 g |
| 5 kg ₹73 → 10 kg | × 2 | ₹146 |
Practice questions
- 1Find 4 × 10 kg 500 g.
- 2Share 4 kg 800 g equally into 4 boxes. Weight of each?
- 34 people need 500 g rice. How much for 8 people?
- 45 kg of tomatoes cost ₹73. Cost of 10 kg?
- 5A scrap dealer pays ₹8 per kg. What does he pay for 16 kg?
- 6He pays ₹200 for every 10 kg of iron. Cost for 20 kg?
- 7Cost of 12 kg 500 g rice at ₹60 per kg?
- 8A king donates 10 times his weight in wheat: 800 kg this year, 780 kg last year. How much weight did he gain?
Show answers (try them yourself first)
- 142 kg
- 21 kg 200 g
- 31,000 g (1 kg)
- 4₹146
- 5₹128
- 6₹400
- 7₹750
- 880 − 78 = 2 kg
Capacity: litres and millilitres
Milk, petrol and juice are measured in litres (l) and millilitres (ml). A tea cup holds about 100 ml, a water bottle 500 ml, a milk packet 1 l. Capacity tells how much a container can hold.
1 l = 1,000 ml. Everything you learned for kg and g works the same for l and ml: convert, compare, add, subtract, multiply and divide.
Formula: a l b ml = (a × 1,000 + b) ml. Number of glasses = total ml ÷ ml of one glass.
In the figure: 1 l = 500 ml + 500 ml = 4 × 250 ml = 1,000 ml.
Rule 1: Convert and compare — Convert l to ml by multiplying by 1,000 and adding the ml; compare in ml.
Capacity: litres and millilitres
In the app you can move this figure with your finger.
Open in the app- Easy: 3 l 8 ml = 3,008 ml; 9 l 90 ml = 9,090 ml.
- Medium: 14,075 ml = 14 l 75 ml.
- Exam-type: 5 l 600 ml > 5,400 ml, because 5,600 > 5,400.
Rule 2: Operations on capacity — Add and subtract like quantities (l with l, ml with ml, carry or borrow 1,000 ml). For equal sharing, divide in ml.
- Easy: 2 l 500 ml + 2 l 800 ml = 5 l 300 ml.
- Medium: 9 l − 5 l 300 ml = 3 l 700 ml.
- Exam-type: 5 l juice ÷ 250 ml = 5,000 ÷ 250 = 20 glasses.
Make the units the same before comparing, adding or dividing: all in ml, or all in l.
Writing 1 l 400 ml as 1,040 ml. The ml part is three digits: 1,000 + 400 = 1,400 ml.
Use 500 ml, 250 ml, 100 ml chunks: 4 × 250 ml = 1 l, 2 × 500 ml = 1 l, 10 × 100 ml = 1 l. Memory clue: "Litre has 1,000 millilitres — just like a kilo has 1,000 grams."
Spot the difference
| Weight | Capacity | Relation |
|---|---|---|
| kg – g | l – ml | 1 : 1,000 |
| 3 kg 500 g = 3,500 g | 3 l 500 ml = 3,500 ml | same method |
| 2 × 500 g = 1 kg | 2 × 500 ml = 1 l | same idea |
Practice questions
- 1Convert 3 l 8 ml into ml.
- 2Muskaan drinks 3 l a day. How many 500 ml bottles is that?
- 3Convert 14,075 ml into l and ml.
- 4Compare 5 l 600 ml and 5,400 ml.
- 5Tina bought 2 l 500 ml petrol, Sam bought 2 l 800 ml more than Tina. How much did Sam buy?
- 6After refuelling Sam's fuel gauge shows 9 l, and he added 5 l 300 ml. How much was there before?
- 7A juice vendor has 5 l of juice and 250 ml glasses. How many full glasses? If a glass costs ₹25, what does he earn?
- 88 l 400 ml oil is poured equally into 7 containers. How much in each?
Show answers (try them yourself first)
- 13,008 ml
- 26
- 314 l 75 ml
- 45,600 ml > 5,400 ml
- 55 l 300 ml
- 63 l 700 ml
- 720 glasses; 20 × ₹25 = ₹500
- 88,400 ÷ 7 = 1,200 ml = 1 l 200 ml