Uncertainties rules

1. How to write uncertainties with the data
Uncertainties are written with the symbol of “±”
For example: 10.5 ±0.1 cm
5.2 ± 0.3 s
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2. Reminder
•There are two types of uncertainties
1. Absolute uncertainty
• Given or otherwise this is equal to Lease Count of Measuring Instruments
1. Fractional uncertainty
𝑓𝑟𝑎𝑐𝑡𝑖𝑜𝑛𝑎𝑙 𝑢𝑛𝑐𝑒𝑟𝑡𝑎𝑖𝑛𝑖𝑡𝑦 =
𝐿𝑒𝑎𝑠𝑡 𝐶𝑜𝑢𝑛𝑡
𝑀𝑒𝑎𝑠𝑢𝑟𝑒𝑑 𝑉𝑎𝑙𝑢𝑒
𝑃𝑒𝑟𝑐𝑒𝑛𝑡𝑎𝑔𝑒 𝑢𝑛𝑐𝑒𝑟𝑡𝑎𝑖𝑛𝑖𝑡𝑦 =
𝐿𝑒𝑎𝑠𝑡 𝐶𝑜𝑢𝑛𝑡
𝑀𝑒𝑎𝑠𝑢𝑟𝑒𝑑 𝑉𝑎𝑙𝑢𝑒
𝑋100 and is given in “%”
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3. Rule # 1: Addition and Subtraction rule
• Whenever we ADD or SUBTRACT any quantities , we ALWAYS add
Absolute uncertainties ( ALWAYS )
• We are given with two distances measured by meter rod
(recall LC of meter rod = 0.1 cm )
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4. Rule # 2: Multiplication and Division rule
• Whenever we MULTIPLY or DIVIDE any quantities , we ALWAYS
add Fractional uncertainties ( ALWAYS )
• For that we first have to convert Absolute uncertainty to fractional
uncertainty.
• Recall 𝑃𝑒𝑟𝑐𝑒𝑛𝑡𝑎𝑔𝑒 𝑢𝑛𝑐𝑒𝑟𝑡𝑎𝑖𝑛𝑖𝑡𝑦 =
𝐿𝑒𝑎𝑠𝑡 𝐶𝑜𝑢𝑛𝑡(𝐴𝑈)
𝑀𝑒𝑎𝑠𝑢𝑟𝑒𝑑 𝑉𝑎𝑙𝑢𝑒
𝑋100
• i.e. we Divide the AU with the measured value and Multiply by 100
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5. • For example, we determine maximum uncertainty in the value of the
resistance R of a conductor determined by given formula and data
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6. • First of all we convert absolute uncertainties in voltage and current
into their respective percentage uncertainty
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7. Applying the rule
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8. Final part
• We convert back the % age uncertainty into AU.
• For that we reverse the order, divide by 100, multiply by measured
value
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