What Is the Decimal Number System Definition Place Value and Solved Examples
On a number line, decimals are a set of numbers that lie between integers. They are simply another way to represent fractions. We can write more precise values of measurable quantities such as length, weight, distance, money, etc using decimals.
The numbers to the left of the decimal point are integers or whole numbers, while the numbers to the right are decimal fractions. In this article, we will learn about decimals.
Decimals Number System
The decimal number system is a positional notation that has a base of 10. It refers to numbers with a fractional part separated from an integer part by a decimal separator. Decimals allow us to write fractions without having to write a fraction with a numerator and denominator.
The above image Illustrates the Parts of a Decimal Number
Decimal Place Value Chart
The position of each digit is important when writing any number. When we go to the right in the below place value chart, the value of the digit becomes 10 times smaller, i.e., one-tenth, and when we move to the left, the value of the digit becomes ten times larger.
The above Decimals images Illustrate a Decimal Number with Corresponding Place Values
Types of Decimals
Decimals are categorised based on the type of digits that follow the decimal point. It depends on whether the digits are non-terminating or terminating.
Examples:
Non-terminating: 122.353535.... , 3.33333...., 13.66666…
Terminating: 85.9856, 2.5674, 7.5
Conclusion
The decimal numeral system is a standard system for showing integer and non-integer numbers. You can't learn about numbers completely unless you understand decimals. Hopefully, this article has offered you a good understanding of the significance of decimals.
To learn more mathematical concepts, explore our website.
FAQs on Understanding the Decimal Number System in Mathematics
1. What is the decimal number system?
The decimal number system is a base-10 number system that uses digits from 0 to 9 to represent numbers. It is called base-10 because each place value is a power of 10.
- Place values include ones (10⁰), tens (10¹), hundreds (10²), and so on.
- Each digit’s value depends on its position.
- Example: In 345, 3 represents 3 × 100 = 300.
2. Why is the decimal system called base 10?
The decimal system is called base 10 because it uses ten digits (0–9) and each place value is a power of 10. In this system:
- 10 ones = 1 ten
- 10 tens = 1 hundred
- 10 hundreds = 1 thousand
3. What are place values in the decimal number system?
In the decimal number system, place value refers to the value of a digit based on its position in the number. Each position represents a power of 10.
- Ones = 10⁰
- Tens = 10¹
- Hundreds = 10²
- Thousands = 10³
4. How do you write a number in expanded form in the decimal system?
A number is written in expanded form by expressing it as the sum of each digit multiplied by its place value.
- Example: 3,746 = (3 × 1000) + (7 × 100) + (4 × 10) + (6 × 1)
- This equals 3000 + 700 + 40 + 6.
5. How do decimal numbers work after the decimal point?
After the decimal point, each place value represents a negative power of 10.
- Tenths = 10⁻¹ = 1/10
- Hundredths = 10⁻² = 1/100
- Thousandths = 10⁻³ = 1/1000
6. How do you compare decimal numbers?
To compare decimal numbers, align them by place value and compare digits from left to right.
- Step 1: Write numbers with the same number of decimal places (add zeros if needed).
- Step 2: Compare whole numbers first.
- Step 3: Compare tenths, hundredths, etc.
7. What is the difference between a decimal number and a whole number?
A whole number has no decimal point, while a decimal number includes fractional parts separated by a decimal point.
- Whole numbers: 0, 1, 25, 300
- Decimal numbers: 2.5, 0.75, 10.01
8. How do you convert a fraction to a decimal?
To convert a fraction to a decimal, divide the numerator by the denominator.
- Example: 3/4 = 3 ÷ 4 = 0.75
- Example: 1/5 = 1 ÷ 5 = 0.2
9. What are the basic operations in the decimal number system?
The four basic operations in the decimal number system are addition, subtraction, multiplication, and division.
- Add/Subtract: Align decimal points before calculating.
- Multiply: Multiply as whole numbers, then place the decimal point correctly.
- Divide: Make the divisor a whole number by shifting the decimal.
10. What are common mistakes in the decimal number system?
Common mistakes in the decimal number system usually involve incorrect place value or misplacing the decimal point.
- Not aligning decimal points during addition or subtraction.
- Forgetting to count decimal places in multiplication.
- Comparing decimals without equalizing place values (e.g., thinking 0.5 < 0.45).
