Significant figures

How do I know what degree of accuracy to give my answer to?

• If a question requires your answer to be an exact value

  • You can leave it as a simplified fraction

    • E.g. $\frac{5}{6}$

  • You can leave it in terms of format(‘truetype’)%3Bfont-weight%3Anormal%3Bfont-style%3Anormal%3B%7Dtext%7Bfill%3A%23000000%3B%3C%2Fstyle%3E%3C%2Fdefs%3E%3Ctext%20font-family%3D%22math1437d7d1d97917cd627a34a6a0f%22%20font-size%3D%2216%22%20font-style%3D%22italic%22%20text-anchor%3D%22middle%22%20x%3D%226.5%22%20y%3D%2216%22%3E%26%23x3C0%3B%3C%2Ftext%3E%3C%2Fsvg%3E) or a square root

    • E.g. format(‘truetype’)%3Bfont-weight%3Anormal%3Bfont-style%3Anormal%3B%7Dtext%7Bfill%3A%23000000%3B%3C%2Fstyle%3E%3C%2Fdefs%3E%3Ctext%20font-family%3D%22Times%20New%20Roman%22%20font-size%3D%2218%22%20text-anchor%3D%22middle%22%20x%3D%224.5%22%20y%3D%2216%22%3E4%3C%2Ftext%3E%3Ctext%20font-family%3D%22math1437d7d1d97917cd627a34a6a0f%22%20font-size%3D%2216%22%20font-style%3D%22italic%22%20text-anchor%3D%22middle%22%20x%3D%2215.5%22%20y%3D%2216%22%3E%26%23x3C0%3B%3C%2Ftext%3E%3C%2Fsvg%3E), or %22%2F%3E%3Cpolyline%20fill%3D%22none%22%20points%3D%226%2C0%202%2C-7%201%2C-6%22%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20transform%3D%22translate(0.5%2C23.5)%22%2F%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%2214.5%22%20x2%3D%2226.5%22%20y1%3D%224.5%22%20y2%3D%224.5%22%2F%3E%3Ctext%20font-family%3D%22Times%20New%20Roman%22%20font-size%3D%2218%22%20text-anchor%3D%22middle%22%20x%3D%2220.5%22%20y%3D%2220%22%3E3%3C%2Ftext%3E%3C%2Fsvg%3E)

  • If it is an exact decimal up to and including 5 s.f., you can write it out without rounding it

    • E.g. 0.9375, or 850.25

• If the answer is not exact, an exam question will often state the required degree of accuracy for an answer

  • E.g. Give your answer to 2 significant figures

• If the degree of accuracy is not asked for, use 3 significant figures

  • All working and the final answer should show values correct to at least 4 significant figures
  • The final answer should then be rounded to 3 significant figures

• In money calculations, unless the required degree of accuracy is stated in the question, you can look at the context

  • Round to 2 decimal places
    • E.g. $64.749214 will round to $64.75
  • Or to the nearest whole number, if this seems sensible (for example, other values are whole numbers)
    • $246 029.8567 rounds to $246 030

• When calculating angles, all values should be given correctly to 1 decimal place

  • An angle of 43.5789format(‘truetype’)%3Bfont-weight%3Anormal%3Bfont-style%3Anormal%3B%7Dtext%7Bfill%3A%23000000%3B%3C%2Fstyle%3E%3C%2Fdefs%3E%3Ctext%20font-family%3D%22math138af86134b65d0f10fe33d30dd%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%224.5%22%20y%3D%2216%22%3E%26%23xB0%3B%3C%2Ftext%3E%3C%2Fsvg%3E) will round to 43.6format(‘truetype’)%3Bfont-weight%3Anormal%3Bfont-style%3Anormal%3B%7Dtext%7Bfill%3A%23000000%3B%3C%2Fstyle%3E%3C%2Fdefs%3E%3Ctext%20font-family%3D%22math138af86134b65d0f10fe33d30dd%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%224.5%22%20y%3D%2216%22%3E%26%23xB0%3B%3C%2Ftext%3E%3C%2Fsvg%3E)
  • An angle of 135.211…format(‘truetype’)%3Bfont-weight%3Anormal%3Bfont-style%3Anormal%3B%7Dtext%7Bfill%3A%23000000%3B%3C%2Fstyle%3E%3C%2Fdefs%3E%3Ctext%20font-family%3D%22math138af86134b65d0f10fe33d30dd%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%224.5%22%20y%3D%2216%22%3E%26%23xB0%3B%3C%2Ftext%3E%3C%2Fsvg%3E) will round  to 135.2°

[!Conclusion]
3 s.f. for normal
2 d.p. for money
1 d.p. for angle in degree