Most marks have no number
A kitchen scale, a measuring jug and a thermometer each have a scale: a row of marks, with numbers beside only some of them. To read one, first work out what the gap between two marks is worth, then count.
On this dial the numbered marks go 0, 20, 40, 60, 80, 100. The 5 equal gaps between them share 100, so each gap is worth 100 ÷ 5 = 20. The pointer sits 3 gaps along from 0, on the mark numbered 60: 3 × 20 = 60.
The numbered marks go up in 20s, and the pointer is on 60.
What one small step is worth
Between each pair of numbered marks there are 3 small marks. They cut the gap from 40 to 60 into 4 equal steps, so each step is worth 20 ÷ 4 = 5.
Now the pointer has moved. It is 2 steps past 40, so it reads 40 + 2 × 5 = 50.
Count the steps, not the marks. The 3 small marks make 4 steps, because the numbered marks at the two ends close off the first step and the last one. Dividing 20 by 3, the number of marks, gives the wrong size of step.
3 small marks cut each gap of 20 into 4 steps of 5. The pointer is 2 steps past 40: 50.
The same two moves on any scale
This kitchen scale is numbered every 100 g, up to 500 g. Each gap of 100 g is cut into 4 steps, so each step is worth 25 g, because 100 ÷ 4 = 25. The pointer is 2 steps past 200, so the reading is 200 + 2 × 25 = 250 g.
Every scale is read the same way. First find what one step is worth: divide the gap between two numbers by the number of steps in it. Then start at the last number the pointer has passed and count on the steps after it.
100 ÷ 4 = 25, so each step is worth 25 g. The pointer is 2 steps past 200: 250 g.
Four small marks make five steps
Scales do not all have the same number of small marks. This one has 4 small marks between the numbers, so each gap of 100 g is cut into 5 steps, and each step is worth 20 g, because 100 ÷ 5 = 20. The pointer is 3 steps past 200, so it reads 200 + 3 × 20 = 260 g.
4 small marks make 5 steps of 20 g in each gap of 100 g. The pointer is 3 steps past 200: 260 g.
Two ways to misread a dial
One mistake counts each small step as a whole gap. On the dial reading 50, that gives 40 + 2 × 20 = 80. But 4 steps share one gap of 20, so each step is only 5.
The other mistake stops at the last number and reads 40, leaving out the 2 steps past it. The pointer is past the 40, so those steps must be counted on.
Worked example: A Weighing Scale Read Between Its Labeled Marks
Question A weighing scale is labeled at every kilogram, and there are 4 small marks between each label and the next. When a basket of mangoes is placed on the scale, the pointer rests on the 3rd small mark after 2 kg. (a) What is the reading on the scale, in grams? (b) The empty basket has a mass of 450 g. What is the mass of the mangoes, in grams?
1.From one label to the next is 1 kg, which is 1000 g. The 4 small marks divide it into 5 equal spaces.
From one label to the next is 1000 g, and the 4 small marks make 5 equal spaces. 2.One small space stands for 1000 ÷ 5 = 200 g.
One small space stands for 1000 ÷ 5 = 200 g. 3.(a) The pointer is 3 spaces after 2 kg, so the reading is 2000 + 3 × 200 = 2600 g.
(a) The pointer is 3 spaces after 2 kg: 2000 + 3 × 200 = 2600 g. 4.(b) Take away the basket: the mass of the mangoes is 2600 − 450 = 2150 g, which is 2 kg 150 g.
(b) Without the 450 g basket, the mangoes are 2600 − 450 = 2150 g.
Answer: (a) 2600 g; (b) 2150 g
Common mistakes
- Dividing 1000 g by 4 because there are 4 small marks. Four marks make 5 spaces, so each space is 1000 ÷ 5 = 200 g, not 250 g.
- Reading the pointer as 2.3 kg because it is on the 3rd mark. Each space is 200 g, not 100 g, so the 3rd mark after 2 kg is 2 kg 600 g.