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1.2 C) Truncating Numbers
1.2 C) Truncating Numbers
Another method for approximation is to truncate numbers. We can truncate numbers to a specific place value or to a certain number of significant figures. There is no rounding involved in truncating. An example of where truncation is used is age; you are 15 until your 16th birthday. If we were to round ages, as soon as you are 15 and a half years old, we would say that you are 16. Another example is the time on your phone where we truncate to the minutes and never round the seconds.
We follow the steps below to truncate a number:
Let’s have a few examples:
We follow the steps below to truncate a number:
- Find the place value that we are truncating to and place a line to the right of this number (in the same way that we did with rounding to a specific place value or significant figure).
- We then replace all of the numbers to the right of the line and before the decimal place with a 0, and get rid of all of the numbers in the decimal place positions on the right of the line.
Let’s have a few examples:
Example 1
Truncate the number below to 2 significant figures.
Truncate the number below to 2 significant figures.
The first step is to find the place value that we a truncating to. We are truncating to 2 significant figures, which means that we are looking for the second non-zero number from the left, which is 2. We then place a line to the right of this number (I have ignored the comma so that it is easier to read). I have also labelled the significance of each of the figures in the number below.
We now replace any numbers between the line that we have just drawn and the decimal place with a 0 and ignore all of the decimal places. Therefore, 72,399.21 truncated to 2 significant figures is 72,000.
Example 2
Truncate the number below to 1 decimal place.
Truncate the number below to 1 decimal place.
We are truncating the number above to 1 decimal place. Therefore, our line is going to be on the right of the first decimal place, which is the 2.
The next step is to replace the numbers to the right of the line and before the decimal place with a 0 (there are none of these to replace with a zero), and to get rid of all of the numbers in the decimal place positions on the right of the line. Therefore, 93.2341 truncated to 1 decimal place is 93.2.
Final Note
Questions about truncation often catch people out in the exam because they forget what the technique is. Therefore, it is probably a good idea to write down what truncating is on a revision card.
Questions about truncation often catch people out in the exam because they forget what the technique is. Therefore, it is probably a good idea to write down what truncating is on a revision card.