A thousand grams in a kilogram
The mass of an object is how heavy it is. Light things are measured in grams, written g: a paper clip has a mass of about 1 g. Heavier things are measured in kilograms, written kg.
Kilo means a thousand, so 1 kilogram is 1000 grams. Put a 1 kg weight on one side of a balance and 1000 g of weights on the other, and the balance stays level: 1 kg = 1000 g.
The balance stays level, because 1 kg and 1000 g are the same mass.
Every kilogram is another thousand grams
Each kilogram adds another 1000 grams. 2 kg is 2 × 1000 = 2000 g, and 3 kg is 3 × 1000 = 3000 g. To change kilograms to grams, multiply by 1000.
To change grams to kilograms, divide by 1000: 4000 g is 4000 ÷ 1000 = 4 kg. A gram is the smaller unit, so the same mass always takes a bigger number of grams than of kilograms.
Each step along the top line is 1 kg, and the same step along the bottom line is 1000 g.
Kilograms and grams together
A mass is often given in kilograms and grams together, such as 1 kg 500 g: one whole kilogram and 500 grams more. To write it in grams only, change the kilogram to 1000 g, then add the 500 g: 1000 + 500 = 1500 g.
The other way round, split off the full thousands. 2300 g holds two full thousands of grams, which are 2 kg, and 300 g are left over, so 2300 g = 2 kg 300 g.
1 kg 500 g balances 1500 g: the kilogram is 1000 g, and the 500 g joins it.
A kilogram as a decimal
A mass can also be written as a decimal of a kilogram. 5.3 kg means 5 kilograms and 3 tenths of a kilogram. A tenth of 1000 g is 100 g, so 3 tenths are 300 g, and 5.3 kg = 5000 + 300 = 5300 g.
Multiplying by 1000 gives the same answer in one step: it moves every digit three places to the left, so 5.3 × 1000 = 5300.
× 1 moves no digit, so the value is unchanged
Turn 5.3 into 5300
Multiplying by 1000 moves the 5 and the 3 three places to the left, and zeros fill the empty places: 5.3 kg is 5300 g.
Change the kilograms before adding
A kilogram is 1000 g, not 100 g. So 3 kg 400 g is 3000 + 400 = 3400 g, not 300 + 400 = 700 g.
The two numbers cannot simply be added either: 3 + 400 = 403 mixes kilograms with grams. Change the 3 kg to 3000 g first, and then add the 400 g.
Going back, only full thousands of grams make kilograms. 3400 g is 3 kg 400 g, not 34 kg: the 400 g left over is less than a kilogram.
Worked example: A Box of Identical Tins Weighed Before and After Some Are Removed
Question A box holding 12 identical tins of beans has a mass of 5.3 kg. After 5 of the tins are taken out, the box and the remaining tins have a mass of 3 kg 550 g. (a) What is the mass of one tin, in grams? (b) What is the mass of the empty box, in kilograms?
1.Write both masses in grams: 5.3 kg = 5300 g and 3 kg 550 g = 3550 g.
In grams the two weighings are 5300 g and 3550 g. The box is the same in both. 2.The box is the same in both weighings, so the difference is the mass of the 5 tins that were taken out: 5300 − 3550 = 1750 g.
The weighings differ by the 5 tins taken out: 5300 − 3550 = 1750 g. 3.(a) One tin has a mass of 1750 ÷ 5 = 350 g.
(a) One tin is 1750 ÷ 5 = 350 g. 4.The 12 tins together have a mass of 12 × 350 = 4200 g.
The 12 tins together are 12 × 350 = 4200 g. 5.(b) The empty box has a mass of 5300 − 4200 = 1100 g, which is 1.1 kg. Check: 1100 + 7 × 350 = 3550.
(b) The empty box is 5300 − 4200 = 1100 g, which is 1.1 kg.
Answer: (a) 350 g; (b) 1.1 kg
Common mistakes
- Writing 3 kg 550 g as 3.55 kg and 5.3 kg as 5 kg 3 g. The digit 3 in 5.3 kg is 3 tenths of a kilogram, which is 300 g.
- Dividing the difference of 1750 g by 7, the number of tins left in the box. The difference is the mass of the 5 tins that were taken out.