How to Multiply Decimal Numbers Without a Calculator
What Is a Decimal?
A decimal is a number consisting of two parts: a whole number to the left of the decimal point and a fractional part to the right. They are used to represent numbers lying in between the whole numbers (integers) as an alternative form to fractions.
For example, 0.5 is a decimal, with its fractional form being 1/2. 392.718 is also a decimal, this time lying between 392 and 393.
Multiplying two decimals together without a calculator can appear daunting, but in this how-to guide, we will break it down into simple steps to make it much more achievable.
For example, 0.5 is a decimal, with its fractional form being 1/2. 392.718 is also a decimal, this time lying between 392 and 393.
Multiplying two decimals together without a calculator can appear daunting, but in this how-to guide, we will break it down into simple steps to make it much more achievable.
Example 1: Multiply a Decimal by a Whole Number
To begin with, let's look at what happens when multiplying a decimal by a whole number.
The simplest way to start this is to remove the decimal point and complete the multiplication with the numbers you have now.
For example, let's solve 7 × 0.3.
We remove the decimal point and get 7 × 3 = 21.
We now need to put the decimal point back in, and there are a couple of ways of doing this. With simpler numbers like this one, we can look at the original sum and estimate an answer, then put the decimal point back in to create an answer near our estimate.
In our example, we know that 7 × 0.3 must be slightly smaller than 7 × 0.5, which is half of 7 = 3.5. Therefore, we can quickly see that the decimal point must go in between the 2 and the 1 to create 2.1 (0.21 is far too small compared to 3.5, and 21 is far too big).
This method is perfectly fine for simple sums, but sometimes another method is required. The second way is to count how many decimal places are in the original sum and ensure we have the same amount in the final answer.
7 × 0.3 has one decimal place (the 3), so the answer must also have 1 decimal place. We, therefore, get 7 × 0.3 = 2.1 as before.
The simplest way to start this is to remove the decimal point and complete the multiplication with the numbers you have now.
For example, let's solve 7 × 0.3.
We remove the decimal point and get 7 × 3 = 21.
We now need to put the decimal point back in, and there are a couple of ways of doing this. With simpler numbers like this one, we can look at the original sum and estimate an answer, then put the decimal point back in to create an answer near our estimate.
In our example, we know that 7 × 0.3 must be slightly smaller than 7 × 0.5, which is half of 7 = 3.5. Therefore, we can quickly see that the decimal point must go in between the 2 and the 1 to create 2.1 (0.21 is far too small compared to 3.5, and 21 is far too big).
This method is perfectly fine for simple sums, but sometimes another method is required. The second way is to count how many decimal places are in the original sum and ensure we have the same amount in the final answer.
7 × 0.3 has one decimal place (the 3), so the answer must also have 1 decimal place. We, therefore, get 7 × 0.3 = 2.1 as before.
Example 2: Multiplying a Decimal by a Whole Number
Let's try 0.46 × 6.
First we solve 46 × 6.
40 × 6 = 240 and 6 × 6 = 36, so 46 × 6 = 240 + 36 = 276.
By method 1, we need a number close to half of 6 = 3, and so we put the decimal point back between the 2 and 7 to get an answer of 2.76.
By method 2, the original sum has two decimal places (the 4 and 6 in 0.46), so our answer must have two decimal places. Again, we get the answer 2.76.
So 0.46 × 6 = 2.76.
First we solve 46 × 6.
40 × 6 = 240 and 6 × 6 = 36, so 46 × 6 = 240 + 36 = 276.
By method 1, we need a number close to half of 6 = 3, and so we put the decimal point back between the 2 and 7 to get an answer of 2.76.
By method 2, the original sum has two decimal places (the 4 and 6 in 0.46), so our answer must have two decimal places. Again, we get the answer 2.76.
So 0.46 × 6 = 2.76.
Example 3: Multiplying a Decimal by Another Decimal
We can multiply two decimals together by using the same tricks as before. Although method 1 of estimating the answer can be harder here, method 2 works in exactly the same way.
Let's try 0.08 × 0.03.
We start off in the same way by removing the decimal points.
8 × 3 = 24
Our original sum has four decimal places in it (0 and 8 in the first number and 0 and 3 in the second number), so the answer must also have four decimal places. The 24 we have so far only has two digits and so we need two zeros to make the four decimal places.
Therefore 0.08 × 0.03 = 0.0024.
Let's try 0.08 × 0.03.
We start off in the same way by removing the decimal points.
8 × 3 = 24
Our original sum has four decimal places in it (0 and 8 in the first number and 0 and 3 in the second number), so the answer must also have four decimal places. The 24 we have so far only has two digits and so we need two zeros to make the four decimal places.
Therefore 0.08 × 0.03 = 0.0024.
Example 4: Multiplying a Decimal by Another Decimal
In this example, we will look at a decimal with a whole number part being multiplied by another decimal.
63.52 × 0.4
First, convert into whole numbers.
6352 × 4
This isn't the easiest multiplication to do, but by using a written method such as the column method or grid method, we get:
6352 × 4 = 25 408
Our original question has two decimal places in the first number and one decimal place in the second number, so we need three decimal places altogether. Therefore
63.52 × 0.4 = 25.408
Note that this is one we could have solved by using our estimation method as well.
63.52 × 0.4
First, convert into whole numbers.
6352 × 4
This isn't the easiest multiplication to do, but by using a written method such as the column method or grid method, we get:
6352 × 4 = 25 408
Our original question has two decimal places in the first number and one decimal place in the second number, so we need three decimal places altogether. Therefore
63.52 × 0.4 = 25.408
Note that this is one we could have solved by using our estimation method as well.
Example 5: Being Careful With Extra Zeros
One thing to be wary of is when our answer has zeros on the end. Take a look at this example:
2.35 × 9.2
We first solve 235 × 92
90 × 235 = 21 150
2 × 235 = 470
235 × 92 = 21 620
As our original sum has three decimal places (two in the first number and one in the second), our new answer will need three decimal places too. We need to make sure we include the 0 at the end of these three, even though we won't need to write it in the final answer.
2.35 × 9.2 = 21.620
We don't write spare zeros at the end of decimals, so now we've counted it in our three, we can drop it from the answer to give us a final answer of 21.62.
2.35 × 9.2
We first solve 235 × 92
90 × 235 = 21 150
2 × 235 = 470
235 × 92 = 21 620
As our original sum has three decimal places (two in the first number and one in the second), our new answer will need three decimal places too. We need to make sure we include the 0 at the end of these three, even though we won't need to write it in the final answer.
2.35 × 9.2 = 21.620
We don't write spare zeros at the end of decimals, so now we've counted it in our three, we can drop it from the answer to give us a final answer of 21.62.
How to Multiply Decimals: A Summary
So, to summarise, when multiplying two decimals together without a calculator:
- Remove the decimal points.
- Multiply the two new numbers together.
- Reinsert the decimal point in the correct place in your answer by either estimating the answer or making sure your answer has the same number of decimal places as there are together in both original numbers.
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