Use significant figures and standard form where appropriate

The idea

Standard form writes a number as A × 10ⁿ, where A is at least 1 and less than 10 and n is a whole-number index. For example, 0.00045 = 4.5 × 10⁻⁴ and 62 000 = 6.2 × 10⁴. A positive index means a large number and a negative index means a value below 1. Significant figures show how precisely a value is known: 3.14159 rounds to 3.14 to three significant figures, and 0.00567 rounds to 0.0057 to two significant figures because leading zeros do not count. Use standard form for very large or very small quantities and round final answers to a sensible number of significant figures, usually matching the least precise data given.

What earns the marks

• Writes a number in the form A × 10ⁿ with A between 1 and 10.
• Uses a negative index for a value smaller than 1 and a positive index for a large value.
• Rounds a value to a stated number of significant figures correctly.
• Ignores leading zeros when counting significant figures.
• Chooses standard form or a sensible number of significant figures for very large or very small data.

Common mistakes and how to put them right

• Writes the coefficient as 45 × 10⁻⁵ instead of 4.5 × 10⁻⁴.

  Put it right: Keep the coefficient between 1 and 10.

• Counts leading zeros as significant figures.

  Put it right: Start counting from the first non-zero digit.

• Gives a final answer to more significant figures than the data justify.

  Put it right: Round to match the least precise value.

Exam tips

• Check the coefficient lies between 1 and 10 before finalising a standard-form answer.
• Count significant figures from the first non-zero digit, moving left to right.
• State the number of significant figures or the power of ten you have used so the rounding is clear.