This module builds on: M1 on metric units, fractions and decimals.
Scales
Scales are number lines which can be straight or circular. The number line is split into intervals with divisions marked.
You will see scales on measuring jugs, car speedometers, oven dials and many other measuring instruments.
Reading scales
When reading scales on any sort of measuring instrument, it is important to look at the divisions and intervals and work out what each interval is worth.
Example

The larger intervals on this kitchen scale go up in hundreds. You can also see there is a smaller interval in between each hundred.
This must be worth 50 g since it is the halfway point between hundreds.
The arrow on the dial is pointing at the smaller division between 700 g and 800 g, so the mass of the fruit must be 750 g.
Example

The large intervals on this scale go up in 1 kg. Between each large division there are 10 small intervals. Each small interval is worth 0.1 kg or 100 g.
The arrow is between 2 kg and 3 kg, on the third division after 2 kg, so the dial is showing 2.3 kg.

Example
On this scale, there are 8 intervals between 0 and 1. Each interval is worth \(\frac{1}{8}\).

The dial is pointing to \(\frac{7}{8}\).
Question
What speed is shown on the speedometer below?

Answer
The large intervals are worth 10 mph. The dial points to halfway between 60 and 70 mph. The speed shown is 65 mph.
Question
What voltage is shown on the scale below.

The large intervals are worth 1 volt. There are 4 intervals between each large division, so each smaller interval is worth one quarter of a volt.
The dial points to 3 divisions after 5 V. The voltage shown is 5.75 V.
Question
What weight will be shown on the scales when an extra 600g is added to them?

Answer
The large intervals are worth 1 kg. There are 10 intervals between each kg so each interval will be worth 0.1 kg or 100 g.
The dial shows 7.8 kg.
\(7.8 \text{kg} + 0.6 \text{kg} = 7.8 + 0.6 = 8.4 \text{kg}\)
The answer is 8.4 kg.
More on M5: Geometry and measures
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