Chapter 6 · Prerequisite 2 of 2Basics for textbook pages 117–131Percentages · units · line graphs · nanometres

Percentages, Units & Reading Graphs ശതമാനം · ഗ്രാഫ്

The second half of this chapter uses a little arithmetic. You will need mass percentage (മാസ് പെർസെന്റേജ്, page 4) and parts per million, ppm, which counts in millions instead of hundreds. Pages 6 and 10 ask you to read solubility curves (ലേയത്വ കർവ്), which are line graphs. Page 7 measures particles in nanometres. This page builds each of these tools slowly, with labs to play with. If you are already confident, do the fill-in tables and the quiz, then go on.

📖 What you need

Multiplying and dividing, and simple fractions such as ½ and ¼.
A calculator is allowed for checking, but try the numbers in your head or notebook first.

1. Percent means “out of 100”

Per cent means “per hundred”. 34 % means 34 parts out of every 100 parts. Brass contains 34 % zinc (page 3): in every 100 g of brass there are 34 g of zinc and 66 g of copper. The two percentages add up to 100 %, because together they make the whole.

💯 A hundred squares – shade a percentage

shaded squares

2. What percentage is the part of the whole?

Usually the whole is not exactly 100. Then we work out what the part would be if the whole were 100:

percentage = (part ÷ whole) × 100

In this chapter the “whole” is often made of two parts added together, for example solute + solvent = solution. Then you must add first to find the whole, and only then divide.

⚖️ Part + rest = whole · find the percentage

part rest

🎬 Step by step · four kinds of percentage question

✍ Fill in – percentages (numbers only)

3. Ratios

A ratio compares two amounts. “Salt and water in the ratio 1 : 9” means 1 g of salt for every 9 g of water. The whole is 1 + 9 = 10 parts, so salt is 1 out of 10 parts = 10 % of the mixture, and water is 90 %. To turn a ratio into a percentage, add the parts to get the whole first.

Try it. Brass has copper and zinc in the ratio 66 : 34. What percentage of brass is copper?

The whole is 66 + 34 = 100 parts, so copper is 66 % and zinc 34 %. Here the ratio parts already add up to 100, so they are the percentages.

4. Units: grams, kilograms and millilitres

1 kg = 1000 g and 1 g = 1000 mg (milligrams). To change kg into g, multiply by 1000; to change g into kg, divide by 1000.
1 L = 1000 mL. Volume is measured in millilitres (mL) with a measuring cylinder.
Water is special: 1 mL of water has a mass of about 1 g (its density is 1 g/mL). So 100 mL of water weighs about 100 g, and 800 g of water takes up about 800 mL. The chapter uses this often (“100 mL of water” = 100 g of solvent).

🫙 Pour water onto a balance – mL and grams

water

The balance has been set to zero with the empty jug on it, so it shows only the mass of the water. Exactly 1 g per mL holds at 4 °C; at room temperature 1 mL of water is 0.997 g, which we round to 1 g.

✍ Fill in – unit changes (numbers only)

5. Reading a line graph

A line graph shows how one quantity changes when another changes. Before reading it, look at four things:

the horizontal axis (x-axis): what is measured along the bottom, and its unit (here: time in minutes);
the vertical axis (y-axis): what is measured up the side, and its unit (here: temperature in °C);
the scale: how much each small square stands for;
the shape of each line: rising (going up to the right), falling (going down) or flat (hardly changing). A steep line changes fast; a gentle one changes slowly.

To read a value: start at the number on the x-axis, go straight up to the line, then straight across to the y-axis and read the number there. On page 6 you will read solubility curves in exactly this way.

📈 Graph reader – move the time and read each line

time

✍ Fill in – read the graph above (numbers only)

Think. Which line is rising, which is falling, and which is almost flat? What does a flat line tell you?

The water line rises steeply (it heats up fast), then becomes flat at 100 °C while the water boils. The tea line falls, steeply at first and then more gently. The room line is almost flat: a flat line means the quantity hardly changes. On page 6, the solubility curve of common salt is almost flat like this, while potassium nitrate rises steeply.

6. Very small sizes: powers of ten and the nanometre

Scientists write very big and very small numbers with powers of ten. 10³ = 10 × 10 × 10 = 1000, and 10⁶ = 1 000 000 (one million, used in ppm on page 4). For small numbers the power is negative: 10⁻³ = 1 ÷ 1000 = 0.001.

1 millimetre (mm) = 10⁻³ m – the smallest division on your ruler.
1 micrometre (µm) = 10⁻⁶ m = one thousandth of a millimetre.
1 nanometre (nm) = 10⁻⁹ m = one millionth of a millimetre. So 1000 nm = 1 µm.

🔬 Zoom from a metre down to an atom

zoom

✍ Fill in – powers of ten (numbers only)

⭐ Key ideas

Percentage = (part ÷ whole) × 100. If the whole is “part + rest”, add them first.
A ratio 1 : 9 means 1 part out of 10 parts = 10 %.
1 kg = 1000 g · 1 L = 1000 mL · for water, 1 mL ≈ 1 g.
Read a graph: up from the x-value to the line, then across to the y-axis. Rising, falling, flat; steep means a fast change.
10⁶ = one million · 1 nm = 10⁻⁹ m · 1000 nm = 1 µm.

⚠️ Common mistakes

Dividing by the rest instead of the whole: 10 g in 90 g of water is not 10 ÷ 90; the whole is 100 g, so it is 10 %.
Forgetting the units on the axes: “30” on a solubility graph means 30 g per 100 g of water, not 30 °C.
Thinking a bigger negative power means a bigger size: 10⁻⁹ m is much smaller than 10⁻⁶ m.

7. Check yourself

Next: Solutions, solutes and solvents ▶