Students should recognise and be able to use the symbol that indicates an…

The idea

In physics, measurements and calculated answers are rarely exact, so scientists show when a value is approximate. The symbol ̴ (a single wavy line, read as 'is approximately equal to' or 'approximately') can be placed between two quantities that are close in value, or used as a prefix before a number. For example, if a trolley of mass 0.50 kg is pushed with a force of 1.0 N, the acceleration is a = F ÷ m = 1.0 N ÷ 0.50 kg = 2.0 m/s² exactly. If the force is 1.1 N, then a = 1.1 N ÷ 0.50 kg = 2.2 m/s², but if the mass is only known to be about 0.5 kg, you would write a ̴ 2 m/s² or simply state the acceleration is ̴ 2 m/s². Use ̴ when rounding a calculated answer, reading a value from a graph, or when a measurement has uncertainty. Do not use it for exact definitions.

What earns the marks

• Recognises the symbol ̴ as meaning 'is approximately equal to' or 'approximately' and reads it correctly.
• Uses ̴ correctly, either between two numerical values or expressions, or as a prefix before a number, for example writing a ̴ 2 m/s² or ̴ 2 m/s² after rounding a calculated acceleration.
• Distinguishes between situations that need an equals sign, such as exact arithmetic like 1.0 N ÷ 0.50 kg = 2.0 m/s², and situations that need ̴, such as a rounded or measured value.
• Applies the symbol when reporting results from Newton's Second Law calculations where force, mass or acceleration have been measured to limited precision or read from a graph.
• Interprets a value written with ̴ as an approximation, so a later calculation using that value should also be treated as approximate.
• Uses the symbol consistently in written answers, tables and graph labels without confusing it with the equals sign or the 'proportional to' symbol.

Common mistakes and how to put them right

• Writing an equals sign for a rounded answer, for example 1.1 N ÷ 0.50 kg = 2 m/s².

  Put it right: Use ̴ because 2 m/s² is a rounded value, so write 1.1 N ÷ 0.50 kg ̴ 2 m/s².

• Confusing ̴ with the proportionality symbol ∝ or with a minus sign.

  Put it right: ̴ is a single wavy line meaning 'approximately equal to', while ∝ means 'is proportional to' and links quantities whose ratio is constant.

• Using ̴ instead of a decimal point.

  Put it right: ̴ must be used to indicate approximation, either between values or as a prefix before a complete value, for example ̴ 2 m/s², not 2̴ 0 m/s².

Exam tips

• When a question asks for an answer to a given number of significant figures, show the unrounded value first and then the rounded value with ̴, so the examiner can see both the calculation and the approximation.
• If you read a value from a graph, quote it with ̴ and state the precision you used, for example 'from the graph, a ̴ 2.2 m/s²'.
• Check every symbol in your final line: use = only when the two sides are exactly equal, and use ̴ when rounding, estimating or reporting a measurement with uncertainty.