3
Scales and the number ray
Textbook: Part 1, lesson 3, pp. 16–19
GoalFind the value of one scale division; convert units of mass; show numbers on the number ray.
New words
scale · shkaladivision (of a scale) · bo‘lmanumber ray · sonlar nuricoordinate · koordinata
Explanation
Measuring instruments (ruler, thermometer, scales, speedometer) have a scale. To find the value of one division, divide the difference between two neighbouring numbered marks by the number of divisions between them. Units of mass: 1 kg = 1000 g, 1 q = 100 kg, 1 t = 1000 kg. If we lay the unit segment again and again on a ray starting at O, we get the number ray. The number matching a point is called its coordinate and is written A(5).
Worked examples
A scale has 4 equal divisions between the marks 0 and 20. One division is worth 20 : 4 = 5. If the pointer is on the 3rd division after 20, it shows 20 + 3 × 5 = 35.
3 t 250 kg = 3 × 1000 kg + 250 kg = 3250 kg. On the number ray, point B(7) lies 7 unit segments to the right of O.
Class activity
“Read the scale”: draw a scale from 0 to 100 on the board. The teacher moves a pointer; pupils first say the value of one division and then the number shown.
Practice
1
Express in kilograms: 4 q 35 kg.
435
2
A scale has 6 equal divisions between 0 and 60. What is the value of one division?
10
3
One division is worth 5 and the pointer is on the 3rd division after 20. What number does it show?
35
4
Why can the number ray be called an endless scale?
Any natural number can be shown on it and the ray never ends.