Module 5 (M5) – Geometry and measures - Reading scales on measuring instruments

Part ofMathsM5: Geometry and measures

This module builds on: M1 on metric units, fractions and decimals.

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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

An image of fruit on a weighing scale. The scale is magnified, showing that the scale is reading between 700g and 800g.

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

An image of fruit on a weighing scale. The scale is magnified, showing that the scale is reading between 2 kg and 3 kg.

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.

An image of a scale, with eight intervals between 0 and 1. The scale is reading on the 7th interval, indicating that the reading is 7/8.

Example

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

An image of a scale, with eight intervals between 0 and 1. The scale is reading on the 7th interval, indicating that the reading is 7/8.

The dial is pointing to \(\frac{7}{8}\).

Question

What speed is shown on the speedometer below?

An image of a speedometer, measuring in miles per hour (mph), with the scale rising from 10 to 120. The speedometer's needle sits between 60 and 70.

Question

What voltage is shown on the scale below.

An image of a voltmeter, with a scale rising from 0 to 15 volts, with 3 increments between each unit of volt. The dial reads the third increment between 5V and 6V.

Question

What weight will be shown on the scales when an extra 600g is added to them?

Scales showing 7 kg and 800 g

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