Decimal numbers are those that belong to the set of rational numbers (Q) and are written using a comma. These numbers are formed by an integer part and a decimal part, which appears to the right of the comma.
Example of a decimal number:
The basic mathematical operations – addition, subtraction, multiplication and division – are performed with the decimal numbers by applying some rules that we will see below.
1. Adding decimal numbers
In the sum of decimal numbers we must add the respective numbers of each decimal place, that is, tenths are added with tenths, hundredths with hundredths and thousandths with thousandths.
To make the calculations easier, write the numbers so that the commas are one below the other and the comma must also be aligned in the result.
Example 1: 0,6 + 1,2
Therefore, 0.6 + 1.2 = 1.8.
If one number has more decimal places than the other, you can add zeros to the number with fewer places after the decimal to equal the number of terms.
Example 2: 2,582 + 5,6 + 7,31
Therefore, 2.582 + 5.6 + 7.31 = 15.492.
2. Subtracting Decimal Numbers
As with addition, subtraction of decimal numbers must be done by lining up the commas.
Example 1: 3,57 – 1,45
Therefore, 3.57 – 1.45 = 2.12.
Example 2: 15,879 – 12,564
Therefore, 15,879 – 12,564 = 3,315.
Read too: What are decimal numbers?
3. division of decimal numbers
To perform the division, both the dividend and the divisor must have the same number of decimal places.
Example 1: Division of a decimal number by another decimal number
If, for example, the two division terms have a digit to the right of the comma, then we can multiply by 10 and eliminate it. Then we perform the division normally.
1st step:
2nd step:
Therefore, 3.5 0,5 = 7
Example 2: Division of a decimal number by a natural number
To perform this type of division we must rewrite the divisor so that it has the same number of decimal places as the dividend. After that, we eliminate the comma, multiplying the two terms by 10, 100, 1000… according to the number of decimal places, and perform the division.
1st step:
20,5 5 → 20,5
5,0
2nd step:
3rd step:
Note that an inexact division has occurred, that is, the operation has remainder. To continue, we must add a comma to the divisor and a zero to the rest.
4th step:
Therefore, 20.5 5 = 4,1.
Example 3: Division of a natural number by a decimal number
To perform the division we must add a comma to the dividend and then place zero digits to the right of the comma equal to the number of decimal places in the divisor.
If, for example, the divisor has a decimal place, then we add a comma followed by a 0 digit to the dividend. By multiplying the two terms by 10, we eliminate the comma and carry out the operation normally.
1st step:
14 0,7 → 14,0
0,7
2nd step:
3rd step:
Therefore, 14 0,7 = 20.
Learn more about division with decimal numbers.
4. Multiplication of decimal numbers
The multiplication operation with decimal numbers can be done by performing a multiplication normally and to the result add a comma so that the number of decimal places is equal to the sum of the decimal places of the numbers. multiplied.
Another way is to write the decimal numbers as a fraction and multiply numerator with numerator and denominator with denominator.
Example 1: Multiplication of a decimal number by a natural number
When multiplying a decimal number by a natural number we must repeat the number of decimal places in the result.
3.25 x 4
That would be the same as:
Example 2: Multiplication between decimal numbers
To multiply decimal numbers, we first carry out the multiplication normally, without taking the comma into account.
After that, in the result must be added the comma with the number of decimal places after it that corresponds to the sum of the decimal places of the multiplied numbers.
Method 1:
Method 2:
Example 3: Multiplication of a decimal number by 10, 100, 1000, …
When we multiply a decimal number by 10, 100, 1000, … we must “walk” with the decimal point to the right according to the number of zeros.
Example:
Therefore, by multiplying by:
- 10, “we walk” with the comma one space to the right;
- 100, “we walk” with the comma two spaces to the right;
- 1000, “we walk” with the decimal point three places to the right, and so on.
Read too: Rational Numbers
Exercises on operations with decimal numbers
question 1
Perform operations with the following decimal numbers.
a) 0.22 + 0.311
b) 1.58 - 0.4
c) 2.44 0,5
d) 5.35 x 1.3
Correct answers:
a) 0.22 + 0.311 = = 0.531
b) 1.58 - 0.4 = 1.18
c) 2.44 0,5 = 4,88
d) 5.35 x 1.3 = 6.955
a) 0.22 + 0.311 = 0.531
b) 1.58 - 0.4 = 1.18
c) 2.44: 0.5 = 4.88
2,44: 0,5 → 2,44: 0,50
d) 5.35 x 1.3 = 6.955
question 2
João lent his brother R$30.00. After a few days he received R$22.50 back, but his brother needed his help again and he gave him another R$15.00. Later, João's brother gave him R$19.50 back. How much does the brother still owe you?
a) BRL 2.00.
b) BRL 5.50.
c) BRL 4.50.
d) BRL 3.00.
Correct alternative: d) R$ 3.00.
- First loan: BRL 30.00
- First refund: BRL 22.50
- Second loan: BRL 15.00
- Second refund: BRL 19.50
- Debt: ?
Step 1: Subtract the amount that was returned from the first loan.
2nd step: add the second loan with the amount that the brother still owes.
3rd step: subtract the new amount returned.
Therefore, John's brother still owes him R$3.00.
question 3
Calculate:
a) Double 0.58
b) One third of 9.6
c) 10 times 13 hundredths
Right answer:
a) The double of 0.58 is 1.16.
b) One third of 9.6 is 3.2.
c) 10 times 13 hundredths is 1.3.
You may also be interested in: Decimal Numbering System
