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1.2 B) Round to Significant Figures
1.2 B) Round to Significant Figures
There are two different ways to round number; rounding to a certain place value (this was explored in the previous section) and rounding to significant figures.
We are able to round numbers to significant figures regardless of how large or small they are. Often you will be asked to round numbers to either 1, 2 or 3 significant figures.
To round a number to a significant number of figures, we follow the following steps:
Let’s have a few examples:
We are able to round numbers to significant figures regardless of how large or small they are. Often you will be asked to round numbers to either 1, 2 or 3 significant figures.
To round a number to a significant number of figures, we follow the following steps:
- The first step is to find the significant number that we are rounding to. If we are rounding to 1 significant figure, we are looking for the first non-zero figure in the number from the left. If we are rounding to 2 significant figures, we are looking for the second non-zero figure starting from the left. When we have found the significant figure, we are place a line to the right of it (in the same way that we did when we were rounding to a particular place value).
- The next step is to look at the number that is to the right of the line that we have just drawn. There are now two options depending on the value of this number to the right of the line:
A) If this number is less than 5, we will keep the previous digit the same (the one to the left of the line).
B) If the number is 5 or greater, we increase the previous digit by 1. - The final step is to replace any of the numbers to the right of the line with a 0 up to the decimal point and remove any decimal numbers on the right of the line.
Let’s have a few examples:
Example 1
Round the number below to 1 significant figure.
Round the number below to 1 significant figure.
When we are working with significant figures, we start counting from the first non-zero figure from the left. In 189.573, the first significant figure is 1, the second is 8, the third is 9, the fourth is 5, the fifth is 7 and the sixth is 3. You may find it easier to write these significant numbers above the number, like what I have done below.
We are rounding this number to 1 significant figure and the first significant figure in 189.573 is 1. Therefore, we draw a line after the 1.
The next step is to look at the number to the right of the line. This number is 8, which is greater than 5, which means that we round up. Therefore, we increase the number on the left of the red line by 1. Also, we replace all of the numbers on the right of the line and before the decimal place with a 0, and ignore all of the numbers after the decimal place.
Therefore, 189.573 to 1 significant figure is 200.
Therefore, 189.573 to 1 significant figure is 200.
Example 2
Round the number below to 2 significant figures.
Round the number below to 2 significant figures.
Like the question before, I am going to label the significance of each of the figures in the number. We start counting from the first non-zero from the left. This means that the first significant figure is the 7 (we do not count the 0’s to the left of the 7). The second significant figure is 9, third is 4 and fourth is 3.
The next step is to draw a line on the right of the significant figure that we are rounding to. We are round to 2 significant figures, which means that we are going to draw a line on the right of the second most significant figure, which is the 9.
We now look at the number to the right of the red line. This number is a 4, which means that we round down. Therefore, we keep the number on the left of the red line as it is (the 9 stays as a 9) and as the numbers to the right of the line are decimals, we get rid of them.
Therefore, 0.007943 rounded to 2 significant figures is 0.0079.
Therefore, 0.007943 rounded to 2 significant figures is 0.0079.
Example 3
Round the number below to 3 significant figures.
Round the number below to 3 significant figures.
Like with the previous two examples, I am going to label the significance of the numbers. We start counting significant number from the first non-zero from the left. Therefore, we start counting from the 6. This means that the 6 is the first significant figure, the 0 is the second significant figure (it is a significant number despite being a 0 because we have started counting from the 6), the 3 is the third significant figure, the 9 is the fourth significant figure and the 1 is the fifth significant figure.
We are rounding to 3 significant figures. Therefore, we are going to draw a line on the right of the third significant figure; we draw a line after the 3.
The next step is to look at the number that is on the right of the line that we have just drawn. This number is a 9, which means that we are going to round up. Rounding up causes the 3 on the left of the line to become a 4, and all of the number to the right of the red line up to the decimal place get replaced with 0’s. Therefore, 60,391 rounded to 3 significant figures is 60,400.
