In this section we’re going to focus on two key principles when it comes to decimals. The first being rounding to a set number of decimal places, and the second being upper and lower boundaries.
So, rounding to decimal places – it’s very straightforward once you get the hang of it, and the best way to explain is with the use of examples!
In the exam you may be asked to round a number to one, two or three decimal places. We always look at the number one place to the right of where we’ve been asked to round to in order to decide if the decimal is rounded up or down.
For example, if we had to round 3.24 to one decimal place, 4 would be the deciding number. If the deciding number is five or above we round up (ie 3.3) or in this case as it is below five we would round down, so the correct answer would be 3.2.
Let’s do one more example just to make sure that is clear.
If we were asked to round 17.654 to one decimal place the answer would be 17.7. This is because the decider is the number one place to the right of where we’ve been asked to round to, in this case the 5.
As we know if it is five or above we round up! So the answer is 17.7. Nice and easy!
But what about if you’re asked to round to significant figures – well it follows a similar principal. Five or above round up, below five round down.
Here’s the example:
Round 10546 to three significant figures – the answer is 10500.
The third significant figure is the 5. The decider is a 4 so we don’t round up.
Here’s a more complicated example, pay close attention to where the significant figures are placed!
Round 0.0789823 to three significant figures – the answer is 0.079. Why? Because the third significant figure is the 9 (=0.0009). The decider is an 8 so we round up.
Now that you’ve got rounding nailed down, let’s take a look at boundaries.
Upper and lower boundaries follow the same rule of five being the decider, so let’s look at some examples to illustrate.
What is the upper bound of 0.34 (correct to two decimal places)?
The answer would be 0.345. Why? Because the maximum value for a number, x, to two decimal places is x + 0.005. In this case, it’s 0.34 + 0.005.
Final example, what is the minimum value for 1.38 to two decimal places?
The answer, 1.375. This is because the minimum for a number, x, to two decimal places is x – 0.005. In this case, it’s 1.38 – 0.005.