Reading Scales and Measuring

What is a scale?

A scale is a line of marks that helps us read a measurement. Rulers, weighing scales, thermometers and measuring jugs all use scales. They turn a length, a mass or an amount of liquid into a number we can read.

The tricky part is that the marks are not always labelled with every number. Often only a few marks have numbers, and the small marks in between have none. So the first job is always the same: work out what one small step is worth.

The big idea: find one interval

The space between two neighbouring marks is called an interval. To find its value:

1. Look at two marks that do have numbers.
2. Find the gap between those numbers (subtract).
3. Count how many spaces are between them.
4. Divide the gap by the number of spaces.

That answer is the value of one small step. Once you know it, you can count along the scale.

Tip: count the spaces, not the marks. There is always one more mark than there are spaces.

Worked example 1: a number line scale

A scale shows 0 at one end and 20 at the other. Between them are 10 equal spaces.

1. Gap between the numbers: 20 − 0 = 20.
2. Number of spaces: 10.
3. Value of one space: 20 ÷ 10 = 2.

So the marks read 0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20. If a pointer sits on the third mark after 0, it shows 6.

Worked example 2: weighing scales

A kitchen scale is labelled 0, then 500, then 1000 grams. Between 0 and 500 there are 5 spaces.

1. Gap: 500 − 0 = 500.
2. Spaces: 5.
3. One space: 500 ÷ 5 = 100 g.

The pointer stops on the second small mark past 500. We count on in hundreds: 500, 600, 700. The mass is 700 g.

Reading a ruler

A ruler is a scale for length. Two rules keep your measuring accurate:

• Line up the zero. Put the 0 mark of the ruler against the start of the object, not the very edge of the ruler. The edge often has a little gap before zero.
• Read where the object ends. The number under the far end is the length.

On a centimetre ruler, the long marks are whole centimetres and the short marks are millimetres, with 10 mm in every centimetre. If a leaf ends on the 4th small mark past 7 cm, it is 7 cm and 4 mm, or 7.4 cm. You can revise these units in Units of Length, Mass and Capacity.

Reading a measuring jug

A measuring jug shows capacity. Hold it level and read at eye height. The surface of the liquid lines up with a mark on the scale.

Suppose a jug is marked 0, 200, 400, 600 millilitres, with 4 spaces between each pair of numbers.

1. Gap: 200 − 0 = 200.
2. Spaces: 4.
3. One space: 200 ÷ 4 = 50 ml.

If the water reaches the first small mark above 400, it shows 400 + 50 = 450 ml.

When the pointer is between marks

Sometimes the pointer or liquid does not land exactly on a mark. Then you have two choices:

• Round to the nearer mark if it is clearly closer to one side.
• Estimate a sensible in-between value if it sits roughly in the middle. Halfway between 30 and 40 is 35.

A good estimate is honest maths — it tells the reader the measurement is "about" that value.

Why finding the interval matters so much

Why not just read the nearest number? Because the labelled numbers can be far apart. Without knowing what each small step is worth, you cannot tell the difference between a mark meaning 600 and one meaning 650. Working out one interval first turns a confusing row of lines into a clear ladder of values you can climb.

Quick reference

Step	What to do
1	Find two labelled marks
2	Subtract to get the gap
3	Count the spaces between them
4	Divide: gap ÷ spaces = one interval
5	Count on from a labelled mark

Try it yourself

Find three scales in your home — a ruler, kitchen scales and a measuring jug work well.

1. For each one, point to two labelled marks and work out one interval.
2. Measure something and write down the value.
3. Ask someone to check your reading. Did you line up the zero on the ruler?

Well done!

You can now read rulers, scales and jugs by finding the value of one interval and counting on. Put your numbers to use in Reading Charts and Graphs, where the same idea of reading values from a scale appears again.