Measuring Mass and Liquid Volume

Two different things

Mass is how much matter something holds. You measure it on a scale.

Volume is how much space something takes up. For liquids you measure it in a jug.

They are not the same. A big cushion takes up a lot of space and hardly weighs anything. A small stone takes up little space and is heavy.

The units

Measuring	Small unit	Big unit
mass	gram (g)	kilogram (kg)
liquid volume	milliliter (ml)	liter (L)

$$1 \text{ kg} = 1000 \text{ g} \qquad 1 \text{ L} = 1000 \text{ ml}$$

The prefixes are the same ones every time. Kilo means a thousand. Milli means a thousandth. Learn them once and they work for every unit.

Picking a sensible unit

Use the unit that gives a number you can say.

Thing	Sensible unit	About
an apple	grams	$150$ g
a bag of flour	kilograms	$1$ kg
a person	kilograms	$40$ kg
a spoonful of medicine	milliliters	$5$ ml
a bottle of water	milliliters	$500$ ml
a bucket	liters	$10$ L

Measuring a person in grams gives $40\,000$ g. That is correct and nobody says it. The right unit keeps the number small enough to be useful.

Reading a scale

Numbered marks tell you their own value. The small marks between them need one step first: figure out what one mark is worth.

Count the small marks between two numbers, then divide the gap.

A jug is marked $0$, $200$, $400$. There are $4$ small marks between each pair.

$$200 \div 4 = 50 \text{ ml per mark}$$

So a reading two marks past $200$ is:

$$200 + 2 \times 50 = 300 \text{ ml}$$

Never assume a mark is one unit. On this jug each one is fifty.

Why estimating first is worth the moment

An estimate is a sensible guess made before measuring. It is worth making, because it tells you whether the reading you get is believable.

Thing	Rough mass
a paperclip	$1$ g
an apple	$150$ g
a bag of sugar	$1$ kg
a cat	$4$ kg

If your scale says an apple is $2$ kg, the reading is wrong. Two kilograms is about the mass of a large bag of sugar, and an apple is nothing like that.

That check needs no arithmetic. You already know roughly how heavy an apple is, and the measurement has to agree with it.

Building a few of these reference masses is what makes estimating possible. A paperclip for a gram, a bag of sugar for a kilogram, a bottle of water for half a liter.

Adding and taking away

Amounts in the same unit add and subtract like ordinary numbers.

A jug holds $350$ ml. You pour in $200$ ml more.

$$350 + 200 = 550 \text{ ml}$$

Different units have to be made the same first:

A bag holds $2$ kg. You add $500$ g.

$$2 \text{ kg} = 2000 \text{ g} \quad\Rightarrow\quad 2000 + 500 = 2500 \text{ g}$$

That is $2.5$ kg. Adding $2$ and $500$ would have meant nothing, since they count different things.

Worked examples

Common mistakes

Practice problems