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Rounding off the measurements

Rounding off

When we measure an object, we can measure it up to a larger or smaller level of accuracy. This level of accuracy is expressed in decimal points. For example, we can measure the length of a piece of wood as 5.2563 cms.  However, we may choose to express this length in 1, 2 or 3 decimal points, in which case we will need to round up or round down the numbers. How does that work?

We round up to the next higher number if the measurement is past or equal to the half way point between the readings (here it is 0.5, or 0.05, or 0.005, or 0.0005, and so on). Otherwise we round down.

In the example above, if we have to express the length of the piece of wood in 3 decimal points, we look at the fourth decimal point, and round it up or down depending on the number in the fourth decimal position. Here it is 3, and it is less than the half way point of measurement, so we will round it down, and express the length as 5.256 cms.

If we have to express it in 2 decimal places, then the number in the hundredth position (6 here) is more than half way between the readings, so we will round the length up to 5.26 cms.

 

Accuracy of measurements

While measuring any object, there is invariably an error of reading (depending on the type of instrument used to measure the object). The accuracy of measurement refers to how close the reading is to the exact value of the quantity being measured. We always allow a small margin of error – called the precision error – and this is the smallest unit marked on the instrument.

As a general rule, all measurements are accurate to within pm{1/2} of the smallest unit marked on the instrument.

Examples:

  1. If we are using a tape measure or a metre ruler to find the height of a person, and the height of the person is say 94 cms. The error allowed in measuring this person’s height is¬†pm{1/2}cm. Hence the person’s actual height must be in the range of 93.5 cms to 94.5 cms (Remember, 94.5 will not be included because it will round up to 95 when measuring in the nearest centimetre).

  2. The length of a driveway is 5m, the smaller unit is centimetre, so we are allowed a margin or error of pm{1/2}m, i.e. 50 cms. Hence the exact length lies within the range of 5pm{1/2}m i.e. between 4.5m and 5.5m or 4m 50 cms and 5m 50 cms.