How to Multiply or Divide Decimals
Read,4 minutes
In mathematics, a decimal can be defined as a number which has two parts: a whole part and a fractional part, and these two parts are separated by a decimal point. The whole part always represents a number greater than one, while the fractional part, i.e., the part after the decimal, always represents a number less than one.
For example, let’s take the number 11.3411.34. Now here the whole part is represented by 1111, whereas the fractional part (43100 )(43100 ) is represented by 4343. Here 4343 can also be denoted as the decimal part, as it lies after the decimal point.
Terminating and Non-Terminating Decimals
Terminating decimals are the one which have an end whereas non-terminating decimals don’t have an end. They are simply recurring digits that go on and on.
For example, 3.3333333.333333 , (103 )(103 ) is a recurring/non-terminating decimal, whereas 2.502.50 , (104 )(104 ) is a terminating decimal.
The Concept of Preceding Powers of 10
Now, there’s a very interesting concept linked to decimal numbers. This concept is known as the preceding powers of 1010. All decimal numbers are based on this concept. So, as we move from left to right in a decimal number, basically, the place value of every digit gets divided by 1010. So, the first digit after a decimal could be represented as 110110 , second as 11001100 and so on.
So, from this concept, we can easily find out the expanded form of a decimal.
For example, let’s take the decimal number 17.45717.457. The expanded form could be written as: 10+7+410+5100+7100010+7+410+5100+71000
Also, 17.45717.457 can be represented as 174571000174571000 in mixed fraction terms.
How to Multiply 2 Decimals
To multiply 2 decimals, use the following steps:
- First, line up the two numbers as you would do in case of normal multiplications.
- Now, just forget that they are decimal numbers and proceed with normal multiplication.
- Then add up the decimal points for both numbers. For example, in case of 2.89×3.742.89×3.74, the addition should be 44.
- Now, after normal multiplication, place the decimal point. So, if addition of decimal points is 44, add decimal after 4 digits starting from the extreme right to left.
How to Divide 2 Decimals
To divide 2 decimals, use the following steps:
- First, convert the divisor as well as the dividend into a whole number.
- Then divide as normal between two whole numbers.
For example, consider (34.75÷12.6)(34.75÷12.6). Now, multiply both the divisor and dividend by 100100 as the largest decimal point is that of hundredth. Now divide (3475÷1260)(3475÷1260) as you would normally do.
Free printable Worksheets
Related Topics
How to Compare Decimals
How to Multiply and Divide Decimals
How to Convert Between Fractions, Decimals, and Mixed Numbers
How to Compare Decimals
Exercises for Multiplying and Dividing Decimals
1) 12.8 ÷ 5.7 =12.8 ÷ 5.7 =
2) ×27.817.3×27.817.3
3) 88.8 ÷ 41.6 = 88.8 ÷ 41.6 =
4) ×76.624.2×76.624.2
5) 49.4 ÷ 21.2 = 49.4 ÷ 21.2 =
6) 27.8 ÷ 1.2 = 27.8 ÷ 1.2 =
7) 43.6 ÷ 34.2 = 43.6 ÷ 34.2 =
8) ×61.639.5×61.639.5
9) ×46.222.5×46.222.5
10) 29.6 ÷ 17.3 =29.6 ÷ 17.3 =
1) 12.8 ÷ 5.7 = 2.2456...12.8 ÷ 5.7 = 2.2456...
Solution
The divisor is not a whole number. Therefore, multiply it by 1010 to get 128128. Do the same for the dividend to get 5757 .
Now, divide: 128 ÷ 57 = 2.2456...128 ÷ 57 = 2.2456... . so the answer is 2.2456...2.2456... .
2) ×27.817.38.34194.60278.00480.94×27.817.38.34194.60278.00480.94
Solution
Set up and multiply the numbers as you do with whole numbers. 278 ×173 = 48094278 ×173 = 48094 . Count the total number of decimal places in both of the factors 1+1=21+1=2 . Then Place the decimal point in the product: 480.94480.94
3) 88.8 ÷ 41.6 = 2.1346...88.8 ÷ 41.6 = 2.1346...
Solution
The divisor is not a whole number. Therefore, multiply it by 1010 to get 888888. Do the same for the dividend to get 416416 .
Now, divide: 888 ÷ 416 = 2.1346...888 ÷ 416 = 2.1346... . so the answer is 2.1346...2.1346... .
4) ×76.624.215.32306.401532.001853.72×76.624.215.32306.401532.001853.72
Solution
Set up and multiply the numbers as you do with whole numbers. 766 ×242 = 185372766 ×242 = 185372 . Count the total number of decimal places in both of the factors 1+1=21+1=2 . Then Place the decimal point in the product: 1853.721853.72
5) 49.4 ÷ 21.2 = 2.3302...49.4 ÷ 21.2 = 2.3302...
6) 27.8 ÷ 1.2 = 23.1667...27.8 ÷ 1.2 = 23.1667...
7) 43.6 ÷ 34.2 = 1.2749...43.6 ÷ 34.2 = 1.2749...
8) ×61.639.530.80554.401848.002433.2×61.639.530.80554.401848.002433.2
9) ×46.222.523.1092.40924.001039.5×46.222.523.1092.40924.001039.5
10) 29.6 ÷ 17.3 = 1.711...29.6 ÷ 17.3 = 1.711...
Multiply and Divide Decimals Quiz