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# How do I find the minimum value of a number that has been rounded off?

By Grainne McLaughlin on the 11th of June, 2012

## Find the minimum and maximum values of a number that has been rounded off

There are two different ways of specifying where a number should be rounded off. They are:

• Decimal Places
• Significant Figures (see next Number Topic)

### Basic Method

1. IDENTIFY the position of the LAST DIGIT.
2. Then look at the next digit to the RIGHT - called the DECIDER.
3. If the DECIDER is 5 or more, then nROUND UP ther LAST DIGIT. If the DECIDER is 4 or less , then leave the LAST DIGIT as it is.

### Decimal Places (D.P.)

This is pretty easy:

1. To round off, lets say to 3 decimal places, the LAST DIGIT will be the 3rd one after the decimal point.
2. There must be no more digits after the last digit (not even zeros).

### Maximum and Minimum Values When Rounding

Wherever a measurement is rounded off to a given UNIT the actual measurement can be anything up top HALF A UNIT bigger or smaller.

Example: If we round 20.8cm to the nearest centimetre, it becomes 21cm.

If we are given the number 21cm and told it has been previously rounded to the nearest centimetre, we do not know what number it was originally. For example it could have been 21.2cm, or 20.9cm, or 20.756cm. What we do know, is the biggest (maximum) or smallest (minimum) number it could possibly have been.

• The minimum value it could have been, is 20.5cm (any smaller, even a tiny bit, and it would have rounded down to 20cm, not up to 21cm)
• The maximum value it could have been, is 21.499999999…cm. Because this looks messy, we tend to just say the maximum value it could have been before rounding is 21.5cm.

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