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NSW Y11 Maths Standard NSW Y11 Maths Advanced NSW Y11 Maths Extension 1

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Earning and Managing Money Formulae and Equations Measurement And Energy Relative Frequency and Probability Perimeter, Area, Volume Classifying Data Linear Relationships Interest and Depreciation Exploring and Describing Data Time Budgeting

NSW Y11 Maths - Standard Measurement And Energy Standard Form, Significant Figures

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Standard Form, Significant Figures Theory

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Theory

Significant Figures

When ever we use numbers to talk about distances and amounts we often replace digits with zeroes or completely ignore numbers. Consider the following examples:

  1. A very rich man might have $76 301 080 980.43 (you might just say he has 76 billion dollars)
  2. A cell might weigh 0.0000350980230109 kilograms (you might just say 0.000035kg)

When we do this, we are choosing the most significant figures. In the two examples above we selected the 2 most significant numbers.

Scientific Notation

Some numbers are so big, it becomes difficult to write them down. This is when scientific notation comes in handy. Consider the following examples:

  1. the total weight of cellular protein is \(7 \times 10{−10}\text{ g}
  2. the distance from the Earth to the sun is \(1.496 \times 10{9}\,\text{ km}\)
  3. Perform the operation \(1200000^2\) on your calculator. If your calculator is restricted to 10-digit numbers, it should give you a solution in scientific notation (since it can’t fit on the screen).