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1.2 A) Rounding to Place Values
1.2 A) Rounding to Place Values
Approximations are quick ways to get answers to real world problems, such as how long you need to allocate for completing your maths homework or how much money you can make from selling tickets to a concert etc.
Throughout this section, we are going to be looking at many different approximation techniques. We will start by looking at rounding.
Throughout this section, we are going to be looking at many different approximation techniques. We will start by looking at rounding.
Approximation – Rounding
We can approximate numbers by rounding them. We can round numbers to the nearest 10, 100 1000 etc, or to a certain number of decimal places, such as 1 decimal place (the tenths), 2 decimal places (the hundredths), 3 decimal places (the thousandths) etc.
We can use the method below to round a number:
Let’s have a few different examples.
We can approximate numbers by rounding them. We can round numbers to the nearest 10, 100 1000 etc, or to a certain number of decimal places, such as 1 decimal place (the tenths), 2 decimal places (the hundredths), 3 decimal places (the thousandths) etc.
We can use the method below to round a number:
- Draw a line on the right of the place value that we are rounding to; if we are rounding to the nearest 10, we draw a line to the right of the ten place value; if we are rounding to the nearest million, we draw a line to the right of the million place value (it may be beneficial to draw the line in a different colour to the colour that you normally write in).
- The next step is to look at the first number that is on 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); this is known as rounding down.
B) If the number is 5 or greater, we increase the previous digit by 1; this is known as rounding up.
- The final step is to replace all of the numbers to the right of the line before the decimal place with zeros and remove any decimal numbers on the right of the line.
Let’s have a few different examples.
Example 1
Round the number below to the nearest 10.
Round the number below to the nearest 10.
The first step is to draw a line on the right of the place value that we are rounding to. We are rounding to the nearest ten, which means that our line will be to the right of the 2.
The next step is to look at the first number that is on the right of the line that we have just drawn, which is a 6. 6 is greater than 5 and this means that we are going to be rounding up. To round up, we increase the number to the left of the red line by 1; the 2 becomes a 3. The final step is to replace the 6 with a 0. Therefore, 7,926 rounded to the nearest ten is 7,930.
When learning about rounding, you may find it easier to understand it by using a number line. Example 1 is asking us to round 7,926 to the nearest ten, which is essentially saying “is 7,926 closer to 7,920 or 7,930”?
I have plotted these 3 numbers (7,920, 7,930 and 7,926) on a number line below.
I have plotted these 3 numbers (7,920, 7,930 and 7,926) on a number line below.
I have also plotted the crucial number for rounding this number, which is 7,925; any number that is less than 7,925 will be rounded down and any number that is 7,925 or greater will be rounded up.
7,926 is on the right of 6,925, which means that it is closer to 7,930 than 7,920, thus meaning that we round up.
7,926 is on the right of 6,925, which means that it is closer to 7,930 than 7,920, thus meaning that we round up.
Example 2
Round the number below to the nearest 100.
Round the number below to the nearest 100.
The first step is to draw a coloured line to the right of the place value that we are rounding to; we are rounding to the nearest 100, so we draw a line after the 3.
We now look to see whether the number to the right of the red line is less than 5, or equal to or greater than 5. The number to the right is 4 and this means that we round down; the number in the hundreds place value remains the same – it remains a 3. The final step is to replace all of the place values up to the decimal place with 0’s; we replace the tens (4) and the units (1) with zeros. Therefore, 78,341 to the nearest 100 is 78,300.
Example 3
Round the number below to 1 decimal place.
Round the number below to 1 decimal place.
This is our first decimal question, but the process is exactly the same except step 3 (which we will come onto later).
So, the first step in rounding is to draw a line on the right of the place value that we are rounding to; we are rounding to 1 decimal place, which means that the line will be on the right of the 3.
So, the first step in rounding is to draw a line on the right of the place value that we are rounding to; we are rounding to 1 decimal place, which means that the line will be on the right of the 3.
We now look at the value on the right of the line, which is 7. 7 is greater than 5, which means that we are rounding up. Therefore, we increase the first decimal place by 1; the 3 becomes a 4. We are rounding to a decimal place, which means that we get rid of all of the numbers that are on the right of the place value that we were rounding to (the right of the red line). Therefore, 42.376 to one decimal place is 42.4.
Example 4
Round the number below to the nearest thousand.
Round the number below to the nearest thousand.
Like the previous examples, the first step is draw a line on the right of the place value that we are rounding to; we are rounding to the nearest thousand, which means that we draw a line on the right of the 9 (I am going to get rid of the comma for this example, so that it is easier for you to see what is happening).
We now look at the number on the right of the red line, which is a 5. This means that we round our number up, which results in the number to the left of the red line being increased by 1. This results in the 39 thousand becoming 40 thousand. Also, all of the numbers on the right of the red line before the decimal place need to be replaced with 0’s and all of the numbers after the decimal place need to be ignored.
Therefore, 39,520.38 rounded to the nearest thousand is 40,000.
Therefore, 39,520.38 rounded to the nearest thousand is 40,000.