Scientific Notation & Metric Multipliers
Scientific Notation
- In physics, measured quantities cover a large range from the very large to the very small
- Scientific notation is a form that is based on powers of 10
- The scientific form must have one digit in front of the decimal place
- Any remaining digits remain behind the decimal place
- The magnitude of the value comes from multiplying by 10n where n is called 'the power'
- This power is positive when representing large numbers or negative when representing small numbers
Worked example
Express 4 600 000 in scientific notation.
Step 1: Write the convention for scientific notation
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- To convert into scientific notation, only one digit may remain in front of the decimal point
- Therefore, the scientific notation must be 4.6 × 10n
- The value of n is determined by the number of decimal places that must be moved to return to the original number (i.e. 4 600 000)
- To convert into scientific notation, only one digit may remain in front of the decimal point
Step 2: Identify the number of digits after the 4
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- In this case, that number is +6
Step 3: Write the final answer in scientific notation
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- The solution is: 4.6 × 106
Metric Multipliers
- When dealing with magnitudes of 10, there are metric names for many common quantities
- These are known as metric multipliers and they change the size of the quantity they are applied to
- They are represented by prefixes that go in front of the measurement
- Some common examples that are well-known include
- kilometres, km (× 103)
- centimetres, cm (× 10–2)
- milligrams, mg (× 10–3)
- Metric multipliers are represented by a single letter symbol such as centi- (c) or Giga- (G)
- These letters go in front of the quantity of interest
- For example, centimetres (cm) or Gigawatts (GW)
Common Metric Multipliers Table
Worked example
What is the answer to the addition of 3.6 Mm + 2700 km in metres?
Step 1: Check which metric multipliers are in this problem
- M represents Mega- which is × 106 (not milli- which is small m!)
- k represents kilo- which is a multiplier of × 103
Step 2: Apply these multipliers to get both quantities to be metres
3.6 × 106 m + 2.7 × 106 m
Step 3: Write the final answer in units of metres
6.3 × 106 m
Examiner Tip
You are expected to know metric multipliers for your exams. Make sure you become familiar with them in order to avoid any mistakes.