What you need to know
A decimal is any number with a decimal point. They are the numbers that fall between the integers.
The diagram below shows how the value of each digit changes depending on its position. You can find more info on place value here Place Value Revision
To add decimals, you should be familiar with the column method for addition and subtraction, click here Addition and Subtraction Worksheets and Revision to learn all about them. The good news is that these methods work exactly the same way for decimals, all you have to do is make sure you line up the decimal points when you write your numbers above one another.
Subtracting decimals is easy if you know how to add. Make sure you are confident with the column method, click here Addition and Subtraction Worksheets and Revision.
The easiest way to multiply decimals is to move the decimal place on each value to turn them into a whole number. Remember how many decimal places your have moved in total. Complete the column or grid method for multiplication and then move the decimal place back the same amount at the end.
When dividing decimals we use a similar method as multiplying in that you move the decimal place of the number you are dividing by, to make it a whole number, note down how many places you have moved in total. Perform long division and then move the decimal place back the same number of times to get your final answer.
Example 1: Adding Decimals
Use the column method as shown below
Example 2: Subtracting Decimals
Evaluate 62.059 - 1.118
Use the column method as shown below
Example 3: Multiplying Decimals
Evaluate 5.7\times 6.32.
In this example we use the column method. The decimal place is moved once on 5.7 to make 57 and twice on 6.32 to make 632. Therefore in total the decimal place has moved 3 times.
Now we need to move the decimal place back the same number of times, so we move it 3 times to the left to get:
Answer = 36.024
Example 4: Dividing Decimals
Evaluate 7.488 \div 1.2.
Similar to multiplying decimals, when dividing decimals we want to make it easy for us by moving the decimal place so that we can use long division. We do this by moving the decimal place of the number we are dividing by.
Remember to move the decimal place back to get the final answer. In this example we only moved it one place, so we move it back once place:
Answer = 6.24
1) Evaluate 82.07 + 31.865
By means of column addition or otherwise, we can add together the values that hold the same respective place. When the sum of two values is greater or equal to 10, we have to carry the tens unit value over to the next column,
Therefore we find,
2) Evaluate 18.63 \div 2.3
We can make the calculation easier by converting the divisor to a whole number. We can do this and still have the same calculation by multiplying both 2.3 and 18.63 by 10, so now we have,
Hence the answer is,
18.63\div 2.3 = 8.1
3) Evaluate 3.566\times 14
The latter number is already whole, so we just need to make the first number whole:
3.566\times 1,000 = 3,566
Thus the column multiplication is,
Adding the the two parts,
We multiplied one of our numbers by 1,000, which means our result is 1,000 times too big. Therefore, the final answer is,
3.566 \times 14 = 49,924\div 1,000 = 49.924
4) Evaluate 0.89+0.113
We can add together the values in each of the columns. When the sum of two values is greater or equal to 10, we have to carry the tens unit value over to the next column,
5) Evaluate 0.002\times 0.043
We can make the calculation easier by converting the decimals to a whole numbers.
If we multiply 0.002 and 0.043 by 1000, we have a simple integer multiplication,
However this value is 1000\times1000=1,000,000 times to big, so we have to divide the result by this,
Worksheets and Exam Questions
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