3 significant figures and standard form

• Standard form is very useful for writing very large or small numbers
• Stabdard form is written in the form A×10n where A is a number between 1 and 10
• n represents the number of places the decimal point is moved (for +n values the decimal point has been moved to the left, for -n values the decimal point has been moved tot he right)
• 3435 in standard form is 3.435×10³
• 1029000 in standard form is 1.029×10⁶
• 0.025 in standard form is 2.5×10-²
• 23.2 in standard form is 2.32×10¹
• 0.0000278 in standard form is 2.78×10-⁵
• To find the value of n

  • For numbers greater than 1, n = number of places between first number and decimal place
  • For numbers less than 1, n = number of places from the decimal place to the first number (including that number)
• 9.37865 to 1 significant figure is 9. To 2 significant figures is 9.4. To 3 significant figures is 9.38. To 4 significant figures is 9.379. To 5 significant figures is 9.3787.
• 4204274 to 1 significant figures is 4000000. To 2 significant figures is 4200000. To 3 significant figures is is 4200000. To 4 significant figures is 4204000. To 5 significant figure is 4204300
• 0.903521 to 1 significant figure is 0.9. To 2 significant figures is 0.90. To 3 significant figures is 0.904. To 4 significant is 0.9035. To 5 significant figures is 0.90353
• 0.00239482 to 1 significant figures is 0.002. To 2 significant figures is 0.0024. To 3 significant figures 0.00239. To 4 significant figures is 0.002395. To 5 significant figures is 0.0023948
• Significant figures for calculations involving multiplication/division:

  - My final answer should be given to the same number of significant figures as the least number of significant figures in the data used

  e.g calculate the average speed of a car that travels 1557m in 95 seconds

  Average speed = 1557÷95 = 16m/s -1 (answer given to 2 significant figures as lowest significant figures in data is 2 significant figures for time)
• Significant figures for calculations involving addiction/subtraction ONLY:

  • Here the number of significant figures is irrelevant - it is about the place value of the data. For example
  • Calculate the total energy released when 263KJ and 1282KJ of the energy released
  • Energy released = 263 + 1282 = 1545KJ (answer is to nearest unit as both values are to nearest unit)