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Decimals in daily life have various applications including dealing with money, measuring weight, length, etc.
- Decimals are one of the types of numbers in Algebra that have a whole number and fractional parts separated by a decimal point.
- The decimal point is the dot that appears between the whole number and the fractions part.
- For example, 62.3 is a decimal number.
- The primary purpose of using decimal numbers is to achieve greater precision.
- For example, when we weigh ourselves on the scale, we do not always find that the weight is equal to a whole number.
- To know our actual weight, we need to understand what the decimal figure on the scale indicates.
| Table of Content |
Key Terms: Decimals, Terminating decimals, Non-terminating decimals, Recurring decimals, Non-recurring decimals, Whole number, Decimal point
What are Decimals?
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A decimal number is defined as a number that has a decimal point dividing the whole number from the fractional portions in algebra.
- A number smaller than one is represented by the digits following the decimal point.
- A dot (.) is used in decimal numbers to differentiate the whole number from the fractional number, which is known as the decimal point.
- The numbers to the right of the decimal point are known as decimal numbers.
- The numbers on the left of the decimal point are known as whole numbers or integers.
Also check:
| Important Topics | ||
|---|---|---|
| Degree of Polynomial | Complex numbers and Quadratic Equations | Trigonometric Functions |
| Polynomial Formula | Polynomial Important questions | Real-Valued Function |
Types of Decimals
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Decimal numbers are categorized into two types based on the number of digits and type of digits that appear after a decimal point:
- Terminating Decimal Numbers
- Non-Terminating Decimal Numbers
Terminating Decimal Numbers
Terminating decimals are numbers that have a fixed number of digits after the decimal point. Decimal numbers represent a whole in the same way that fractions indicate a portion of a whole.
For Example: 0.32. 0.124, 0.2456, and 0.651
Terminating decimals can be written in the form of \( \frac{p}{q}\)
Examples of terminating decimal numbersQues. Express 0.4 in the form of \( \frac{p}{q}\) Ans. 0.4 in the form of p/q can be represented as \(0.4=\frac{0.4 \times 10}{10}=\frac{0.4}{10}=\frac{2}{5}\) |
Non-Terminating Decimal Numbers
There are infinite decimal places in a non-terminating decimal.
- After the decimal point, the digits will not finish.
- A non-terminating, non-repeated decimal is a decimal number that continues forever with no repeating digits.
- Irrational numbers are non-terminating and non-recurring or non-repeating decimals.
- This decimal cannot be expressed as a fraction since it is an irrational number.
Non-terminating decimal numbers are further divided into two categories
- Recurring Decimal Numbers
- Non-Recurring Decimal Numbers
Recurring Decimal Numbers
After a decimal point, recurring decimal numbers keep repeating the same value. Repeating Decimals is another name for these numbers.
For Example:
- 0.128512851285…..
- 0.333333….
- 0.12121212….
Non-Recurring Decimal Numbers
Non-recurring Decimal Numbers are non-terminating and non-repeating Decimal Numbers. Non-recurring Decimal Numbers have an infinite number of digits at their decimal places, and their digits do not follow any particular order.
For Example:
- 43.89751…
- 87024.97658…
- 34.7789…
Uses of Decimals
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The following are the uses of decimals
- Decimals are used to examine whether numbers are logical or irrational.
- They are used to transform fractions, percentages, and ratios from one form to another.
- We use decimals to measure length, weight, area, and volume, among other things.
- For accurate calculations, decimals are commonly used.
- On a number line, we use decimals to represent some integers.
Application of Decimals in Everyday Life
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Some of the everyday applications of decimals in our daily lives are as follows.
Use of decimals when dealing with money
When dealing with money, dealing with decimal numbers is essential.
- In many instances such as when converting paisa to rupee.
- Assume we go to a local shop to buy 500 gm of rice, which costs Rs. 43 per kilogram.
- To calculate the price of 500 gm rice we divide Rs. 43 by 2, which equals 21.5.
To give the exact amount, we must first understand what 21.5 represents in rupees.
- 1 Re = 100 paise
- 0.5 Re = 50 paise
- 21.5 Rs = 21 Rs and 50 paise
ExamplesQues. Convert 145 paisa in Rupee. Ans. We know, 1 paisa = 1/100 Re Therefore, 145 paisa = 145 × (1/100) Re ⇒ 145 paisa = 145/100 ⇒ 145 paisa = Rs. 1.45, i.e. 1 Re and 45 paisa Ques. Convert 250 paisa in Rupee Ans. We know, 1 paisa = 1/100 Re Therefore, 250 paisa = 250 × (1/100) Re ⇒ 250 paisa = 250/100 ⇒ 250 paisa = Rs. 2.50, i.e. 2 Rs and 50 paisa |
Uses of decimals in weight measurement
When dealing with exact weight calculations, we commonly use decimals.
- The actual weight of an object is not always a whole number.
- In such circumstances, decimals are used to calculate the weight.
- For example, when we buy a papaya, it does not necessarily weigh in whole numbers; it may weigh less than 2 kg but more than 1 kg.
- In such cases, the shopkeeper must figure out how much to charge for a papaya depending on its weight.
As we all know,.
- 1 kg = 1000 gram
- 1 gram = 1000 milligram
Assume it is 1 kg and 250 grams. He will then charge the price of 1 kg + (250/1000) kg of papaya.
ExamplesQues. Convert 750 gm to kg Ans. We know, 1000 gm = 1 kg Therefore, 1 gm = 1/1000 kg 750 gm = 750 × (1/1000) kg ⇒ 750 gm = 750/1000 kg = 0.750 kg Ques. Represent 2 kg and 568 gm in decimal. Ans. We know, 1 gm = 1/1000 kg Therefore, 568 gm = 568/1000 kg So, 2 kg + 568/1000 kg = 2.568 kg |
Use of decimal to represent the length
It is not required that the length of an object be a multiple of the given graduation when measuring its length.
- For example, when measuring the length of a table using a meter scale, the length may not be a whole number.
- Instead, it can vary between two graduations on the meter scale.
- In such cases, decimal numerals are used.
From Unit conversion, we have
- 1 km = 1000 m
- 1 m = 100 cm
- 1 cm = 10 mm
Let the length of the table be 1 m and 25 cm, which can be expressed as (1 + 25/100) m.
ExamplesQues. Convert 553 cm into meters. Ans. We know, 100 cm = 1 m Therefore, 1 cm = 1/100 m ⇒ 553 cm = 553 × (1/100) m ⇒ 553 cm = 553/100 m = 5.53 m Ques. Convert 4 km and 25 m into decimal. Ans. We know, 1 km = 1000 m Therefore, 1 m = 1/1000 km ⇒ 4 km + 25 m = 4 + (25 × 1/1000) km = 4.025 km |
Also check:
| Mathematics Concepts | ||
|---|---|---|
Things to Remember
- Decimals are one of the types of numbers that have a whole number and fractional parts separated by a decimal point.
- The dot that appears between the whole number and the fractions part is known as the decimal point.
- A number smaller than one is represented by the digits following the decimal point.
- The numbers to the right of the decimal point are known as decimal numbers.
- The numbers on the left of the decimal point are known as whole numbers or integers.
Sample Questions
Ques. What are the mathematical applications of decimals? (2 Marks)
Ans. In the calculations, decimals are used everywhere. Decimals are used to calculate the length, height, weight, area, and volume of items in exact and accurate measures.
Ques. What are decimals? (2 Marks)
Ans. A decimal is a group of integers that are put together with a decimal point between them.
Ques. Convert 250 paise to rs? (2 Marks)
Ans. As known, 1 paisa = 1/100 rs
So, 250 paisa = 250x\(\frac{1}{100}\) =\(\frac{250}{100}\) rs = 2.30 rs.
= Rs 2 and 50 paisa
Ques. Convert 0.6 in the form of \(\frac{p}{q}\) . (2 Marks)
Ans. Let x= 0.666666............... (1)
As there is only one digit repeating, we will multiply by 10,
10x = 6.666666...........(2)
Subtract (1) from (2),
10x=6+ 0.66666....
10x = 6 + x
10x - x = 6
9x = 6
x=\(\frac{6}{9}\)= \(\frac{2}{3}\)
Ques. What do you mean by recurring decimals with examples? (2 Marks)
Ans. The repeating decimal numbers are decimal numbers that have an unlimited number of digits following the decimal point and are repeated at equal intervals. For examples,
0.22222…,5.5555….,6.12121212….,etc
Ques. Convert 15\(\frac{1}{8}\)into decimals. (2 Marks)
Ans. 15\(\frac{1}{8}\)= 15+ \(\frac{1}{8}\)
15+ \(\frac{1X125}{8X125}\) 125
15+ \(\frac{125}{1000}\)= 15+0.125
15.125
Ques. Express as rupees using decimals. (2 Marks)
a. 7 paisa
b. 9 rs 75 paisa
c. 8 rs 5 paisa
Ans. (1) 7 paisa = \(\frac{7}{100}\) rs
= 0.07 rs.
(2) 9 rs 75 paise = rs (9+\(\frac{75}{100}\))
9+0.75
Rs. 9.75
(3) 8 rs 5 paisa = rs (8+\(\frac{5}{100}\))
8+0.05
rs 8.05
Ques. A pen costs rs 32.50, what will be the cost of 24 pens? (2 Marks)
Ans. Cost of 1 pen= rs 32.50
The cost of 24 pens= rs 32.5024
Rs 780 is the cost of 24 pens.
Ques. Define terminating and non-terminating decimals. (2 Marks)
Ans. After a decimal point, terminating decimals have some digits. Non-terminating decimals, on the other hand, cannot have digits after the decimal point.
Ques. Express in km of the following using decimals. (2 Marks)
a. 65 m
b. 284 m
c. 3 km and 5 m
Ans. (1) 65m=\(\frac{65}{1000}\)km
0.065km
(2) 284m = \(\frac{284}{1000}\)km
0.284 km
(3) 3 km 5m = (3+\(\frac{5}{1000}\))
3+0.005km
3.005 km
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