1.1. Measurements in Physics

The number of significant figures we present an answer to is hugely important in Physics. The precision we present an value to tells us something about the precision to which we know that value to be correct.

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For example, if I say my car is 4.4 m long, that means a very different thing to saying my car is 4.382461 m long. Am I really measuring the length of my car to the nearest micron?

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To take another example. Let's say I want to find the density of a block of wood of volume 20 cm3 with a mass of 30 grams. Your calculator may tell you the density is 0.6˙ g cmˉ³. However, a recurring number means an infinite degree of precision - such that we are confident that our value is exactly

 0.66666.... g cmˉ³. 

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What this means, for IB Physics we must never present our answers as the following:

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• No recurring decimals (e.g. ϱ = 0.6˙  g cmˉ³)

• No fractions (e.g. x = ⅖ m)

• No values in terms of π (e.g. θ = 2π radians)

• No trigonometric equations (e.g. F = 3 sin 45 N)

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Significant figures become especially important when performing calculations. It's important that our final answer is presented to same precision as the least precise value used to calculate it.

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Worked Example

 

Q. A student is trying to measure the density of a cylinder. They measure the diameter using a micrometer to 24.03 mm. The length is measured with a ruler to be 1.2 cm. The mass is measured as 6.02 g using a mass balance. What is the density of the cylinder?

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Here we have been using various pieces of measuring equipment with different amounts of precision. To calculate density we use the equation:

Density = mass / volume

 = m / πr²l

= 6.02 / (π × (2.403/ 2)² × 1.2)

= 1.1061923 ... gcmˉ³

≈ 1.1  gcmˉ³

We can only present our answer to the number of significant figures of our least precise measurements - i.e. 2 sig fig from our length measurement of 1.2 cm.

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Have a bit of practice with how to present your answers using these Isaac Physics gameboards.

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