Coaching Centre
Measuring and recording
Why science uses standard SI units, the units and instruments for length, mass, volume, time and temperature, metric prefixes and conversions, reading scales and the meniscus without parallax error, and setting out a results table.
In 1999 NASA lost a $125 million spacecraft at Mars. One team had calculated the thruster forces in imperial units (pounds) and the other team assumed they were metric (newtons). Nobody noticed, the craft flew too low into Mars's atmosphere, and it was destroyed. Units matter.
Why standard units?
People used to measure with whatever was handy. Ancient Egyptians used the cubit, the length from elbow to fingertip (about 52 cm for the "royal cubit"). The trouble is obvious: whose elbow? A measurement only means something if everyone agrees what the unit is.
Today scientists everywhere use the International System of Units, called SI from its French name. A metre in Sydney is exactly the same as a metre in Tokyo, so scientists can repeat and check each other's experiments. Since 2019 every SI unit is defined from constants of nature, such as the speed of light, so the definitions can never wear out or be lost.
Five quantities you will measure
| Quantity | SI unit | Units you'll often use | Instrument |
|---|---|---|---|
| Length | metre (m) | km, cm, mm | Ruler, metre rule, tape measure |
| Mass | kilogram (kg) | g, mg, tonne | Electronic balance |
| Volume | cubic metre (m³) | L, mL, cm³ (1 mL = 1 cm³) | Measuring cylinder, pipette, burette |
| Time | second (s) | min, h | Stopwatch, data logger |
| Temperature | kelvin (K) | degrees Celsius (°C) | Thermometer, temperature probe |
Prefixes
Instead of inventing a new unit for big and small amounts, SI adds a prefix to the front of the unit. Each prefix means "multiply by" a fixed amount.
| Prefix | Symbol | Means | Example |
|---|---|---|---|
| kilo | k | × 1000 | 1 km = 1000 m |
| centi | c | ÷ 100 | 1 cm = 0.01 m |
| milli | m | ÷ 1000 | 1 mm = 0.001 m |
| micro | µ | ÷ 1 000 000 | a red blood cell is about 8 µm wide |
| nano | n | ÷ 1 000 000 000 | a virus is about 100 nm wide |
Convert (a) 2.5 kg to grams, (b) 450 mL to litres, (c) 36 mm to centimetres.
Quick check: when you change to a smaller unit, you need more of them, so the number gets bigger.
Reading a scale
Before you read any scale, work out the scale interval: the value of each small division. Count the divisions between two labelled numbers and divide. If the 10 and 20 mL marks have 10 small divisions between them, each division is 1 mL. If they have 5 divisions, each is 2 mL.
Liquids in narrow glass tubes have a curved surface called a meniscus. Water curves down in the middle, so you read the bottom of the curve. (Mercury curves up, so you'd read the top, but you'll rarely see mercury now.)
Always put your eye level with the reading. Look from above and the reading seems too high; look from below and it seems too low. This is parallax error. The same applies to rulers and thermometers. Also check for zero error: is the balance reading 0.00 g before you start? Is the end of the ruler worn, so you should start from the 1 cm mark?
- Read each instrument and type your answer. Work out the scale interval first.
- On the measuring cylinder, move your eye up and down. How far off does the reading look from above?
- Get five in a row right to finish the challenge.
Recording results
Results go into a table as you collect them, not on scraps of paper to copy later. A good results table:
- has a title that says what was measured;
- puts the independent variable in the first column, in order (smallest to largest);
- puts the units in the column heading, in brackets, so the cells hold only numbers;
- has a column for each repeat trial and one for the average;
- uses the same number of decimal places down each column.
| Ramp height (cm) | Trial 1 (cm) | Trial 2 (cm) | Trial 3 (cm) | Average (cm) |
|---|---|---|---|---|
| 10 | 62 | 58 | 63 | 61 |
| 20 | 121 | 125 | 117 | 121 |
| 30 | 178 | 183 | 182 | 181 |
| 40 | 240 | 236 | 244 | 240 |
Test yourself
The SI unit of mass is the
It's the only SI base unit with a prefix built into its name.
3.2 km is the same as
kilo = × 1000, so 3.2 × 1000 = 3200 m.
750 mL is the same as
750 ÷ 1000 = 0.75 L.
When reading the volume of water in a measuring cylinder you should read
Bottom of the curve, eye level.
A scale has 5 small divisions between the 10 °C and 20 °C marks. Each division is worth
(20 − 10) ÷ 5 = 2 °C per division.
In a results table, the units should go
Write them once in the heading so the cells contain only numbers.
Looking down at a measuring cylinder from above makes the reading seem
From above, your line of sight hits the scale above the meniscus. That's parallax error.
Which quantity does each unit or instrument measure?
Scientists use units so measurements mean the same everywhere. The prefix kilo means multiply by . The curved surface of water in a cylinder is the , and you read its . Reading a scale from an angle causes error, so keep your eye with the reading.
A student records these results for how long ice cubes take to melt at three temperatures: "20 degrees: 14 mins, 12 mins, 13. 30°: 9, 8 mins and 10. 10 °C - 22 min 19 min 21 min." Draw (describe) a properly set-out results table for this data and explain two improvements you made.
Title: Time for ice cubes to melt at different temperatures. Columns: Temperature (°C) | Trial 1 (min) | Trial 2 (min) | Trial 3 (min) | Average (min). Rows: 10 | 22 | 19 | 21 | 20.7; 20 | 14 | 12 | 13 | 13.0; 30 | 9 | 8 | 10 | 9.0. Improvements: I put the units once in the headings so every cell is just a number, and I put the temperatures in order from lowest to highest so the pattern is easy to see. I also added an average column.
Explain what parallax error is and how to avoid it when using a measuring cylinder.
Parallax error is when a reading looks higher or lower than it really is because you are looking at the scale from an angle. To avoid it, stand the cylinder on a flat bench and bend down so your eye is level with the bottom of the meniscus before you read it.