Decimal Number
What is Decimal Number ?
A decimal number is a number represented using a base-10 numeral system, which uses the digits 0 through 9. In this system, each digit in a number represents a power of 10, with the rightmost digit representing 10^0, the next digit to the left representing 10^1, and so on. For example, the number 42 in decimal notation represents 410^1 + 210^0, or 40 + 2 = 42.
As a student, a decimal number is a way of expressing a number that includes a fractional component, such as 3.14 or 7.5. Decimal numbers are used in many areas of math, including arithmetic and algebra, and are commonly used in everyday situations such as measuring and pricing. Understanding how to work with decimal numbers, including how to add, subtract, multiply, and divide them, is an important part of a student's mathematical education. Additionally, many students will learn about converting decimal numbers to other forms of representation such as fractions and percentages.
Where Can We Use Decimal Number In Daily Life ?
Decimal numbers can be used in many everyday situations in life. Some examples include:
- Measuring: Decimal numbers are often used to express measurements, such as length, weight, and volume. For example, a person might weigh 150.5 pounds, or an object might measure 3.75 inches in length.
- Currency: Decimal numbers are used to express monetary amounts, such as the price of goods and services. For example, a cup of coffee might cost $3.50, and a shirt might cost $19.99.
- Science and technology: Decimal numbers are used in many areas of science and technology, such as physics, chemistry, and engineering. For example, scientists might use decimal numbers to express measurements of temperature in degrees Celsius, or engineers might use decimal numbers to express measurements of electrical current in amps.
- Cooking and Baking: Decimal numbers are used to express measurements of ingredients in cooking and baking recipes. For example, a recipe might call for 2.5 cups of flour, or 0.5 teaspoons of salt.
- Sports: Decimal numbers are used to express measurements in sports, such as time, distance and points. For example, a runner might run a mile in 4.5 minutes, or a basketball player might score 18.7 points in a game.
These are just a few examples of the many ways that decimal numbers are used in everyday life.
Common Questions And Answers About Decimal Numbers :
Are decimal numbers rational or irrational ?
A decimal number is either a rational number or an irrational number depending on whether it can be expressed as the ratio of two integers (a fraction) or not.
A rational number is a number that can be expressed as the ratio of two integers (a fraction), such as 1/2, 3/4, or 22/7. These numbers can also be expressed as terminating or repeating decimals. For example, 1/2 = 0.5, 3/4 = 0.75, 22/7 = 3.142857142857143.
An irrational number is a number that cannot be expressed as the ratio of two integers (a fraction), such as √2, π (pi) or e. These numbers can be expressed as non-repeating and non-terminating decimals. For example, √2 = 1.4142135623730951..., π = 3.141592653589793238... and e = 2.71828182845904523...
So, a decimal number is a rational number if it can be expressed as a ratio of integers and it can be expressed as a terminating decimal or a repeating decimal. On the other hand, a decimal number is irrational if it cannot be expressed as a ratio of integers, and it can be expressed as a non-repeating and non-terminating decimal.
Are decimal numbers real numbers ?
Yes, decimal numbers are considered to be real numbers. A real number is any number that can be represented on the number line, and decimal numbers can be represented on the number line just like integers, fractions, and irrational numbers. Decimal numbers include both rational numbers (numbers that can be expressed as a ratio of two integers) and irrational numbers (numbers that cannot be expressed as a ratio of two integers). Real numbers also include positive and negative numbers, zero and infinity.
A real number can be represented in different forms, such as a fraction, a decimal, a scientific notation, a surd or a complex number. Decimal representation is one of the most common forms of representation of real numbers in our daily life.
Are decimal numbers even or odd ?
Decimal numbers, by themselves, do not have the property of being even or odd as those properties are typically applied to integers (whole numbers). However, the integer part of a decimal number can be even or odd.
An even number is any integer that can be divided by 2 without leaving a remainder. For example, 2, 4, 6, and 8 are even numbers.
An odd number is any integer that cannot be divided by 2 without leaving a remainder. For example, 1, 3, 5, and 7 are odd numbers.
So, if the decimal number is a whole number, we can check whether it is even or odd by dividing it by 2 and see if there is a remainder or not. For example, 12.0 is an even number as it is a whole number and can be divided by 2 without leaving a remainder. On the other hand, 5.5 is not an even or odd number as it is not a whole number.
Are decimal numbers integers ?
A decimal number can be an integer, but it does not have to be. An integer is a whole number, including positive numbers, negative numbers and zero. Decimal numbers can include integers (such as 3.0 or -5.0) but can also include non-integers (such as 3.14 or -2.5). A decimal number is an integer if and only if it has no decimal component, that is, it has no digits after the decimal point. For example, 3.0 is an integer, but 3.14 is not.
In short, Decimal numbers are a subset of real numbers, which include integers and non-integers, while integers are a subset of decimal numbers which include only whole numbers.
Are decimal numbers rational ?
A decimal number can be a rational number or an irrational number depending on whether it can be expressed as the ratio of two integers (a fraction) or not.
A rational number is a number that can be expressed as the ratio of two integers (a fraction), such as 1/2, 3/4, or 22/7. These numbers can also be expressed as terminating or repeating decimals. For example, 1/2 = 0.5, 3/4 = 0.75, 22/7 = 3.142857142857143.
An irrational number is a number that cannot be expressed as the ratio of two integers (a fraction), such as √2, π (pi) or e. These numbers can be expressed as non-repeating and non-terminating decimals. For example, √2 = 1.4142135623730951..., π = 3.141592653589793238... and e = 2.71828182845904523...
So, a decimal number is a rational number if it can be expressed as a ratio of integers and it can be expressed as a terminating decimal or a repeating decimal. On the other hand, a decimal number is irrational if it cannot be expressed as a ratio of integers, and it can be expressed as a non-repeating and non-terminating decimal.
Are decimal numbers natural numbers ?
A decimal number can be a natural number, but it does not have to be. Natural numbers are the set of positive integers, which include the numbers 1, 2, 3, 4, 5, and so on. Decimal numbers can include natural numbers (such as 3.0 or 5.0) but can also include non-natural numbers (such as -2.5 or -3.14). A decimal number is a natural number if it has no decimal component and it is positive, that is, it has no digits after the decimal point and it is greater than zero. For example, 3.0 is a natural number, but -3.14 is not.
In short, natural numbers are a subset of integers, which are a subset of decimal numbers, but not all decimal numbers are natural numbers.
Are decimal numbers whole numbers ?
A decimal number can be a whole number, but it does not have to be. Whole numbers are the set of non-negative integers, which include the numbers 0, 1, 2, 3, 4, and so on. Decimal numbers can include whole numbers (such as 0.0 or 5.0) but can also include non-whole numbers (such as -2.5 or -3.14). A decimal number is a whole number if it has no decimal component, that is, it has no digits after the decimal point. For example, 3.0 and 0.0 are whole numbers, but -3.14 is not.
In short, whole numbers are a subset of integers, which are a subset of decimal numbers, but not all decimal numbers are whole numbers.
Can decimal numbers be negative ?
Yes, decimal numbers can be negative. A negative decimal number is a decimal number that is less than zero. Negative decimal numbers are represented by a minus sign (-) before the number. For example, -0.5, -1.23 and -3.14 are all examples of negative decimal numbers. Negative decimal numbers can also be rational or irrational, depending on whether they can be expressed as a ratio of integers or not.
It's worth mentioning that the concept of negative decimal numbers is used in mathematics and sciences as well as in everyday life in many areas such as accounting, economics, temperature and physics.
Decimal Numbers List :
Decimal numbers with tenths place.
Percent To Decimal Conversion
To convert a percentage to decimal form, follow these steps:
- Understand the Percentage: A percentage is a ratio expressed as a fraction of 100. For example, 20% is equivalent to 20/100.
- Write as a Fraction: Write the percentage as a fraction with a denominator of 100. For example, 20% becomes 20/100.
- Convert to Decimal: To convert the fraction to a decimal, divide the numerator (top number) by the denominator (bottom number). Using the example, 20/100 becomes 0.2 (20 ÷ 100 = 0.2).
- Express as Decimal: The result is the decimal form of the percentage. So, 20% as a decimal is 0.2.
Examples:
- 50% as a decimal: \( \frac{50}{100} = 0.5 \)
- 75% as a decimal: \( \frac{75}{100} = 0.75 \)
- 10% as a decimal: \( \frac{10}{100} = 0.1 \)
In general, to convert a percentage to a decimal, divide the percentage value by 100. This process is important when working with mathematical calculations or when comparing percentages to decimal values in various contexts.
Converting Fraction Number To Decimal Number
To convert a fraction to a decimal number, you simply divide the numerator (top number) by the denominator (bottom number). Here's a step-by-step guide:
- Identify the numerator and the denominator of the fraction.
- Divide the numerator by the denominator using a calculator or long division method.
- If the division results in a finite decimal, write down the result. If it results in a repeating decimal, you can either round the number to the desired decimal place or represent the repeating part with a bar over the repeating digits.
Example: Convert the fraction 3/4 to a decimal number.
- Numerator = 3, Denominator = 4
- Divide 3 by 4: 3 / 4 = 0.75
- The result is a finite decimal: 0.75
So, the fraction 3/4 can be represented as the decimal number 0.75.
Fraction to Decimal Converter
| Fraction Form : | Decimal Form : |
|---|---|
| Convert the fraction 22/44 to a decimal number | 0.5 |
| Convert the fraction 12/28 to a decimal number | 0.42857142857143 |
| Convert the fraction 5/13 to a decimal number | 0.38461538461538 |
| Convert the fraction 4/16 to a decimal number | 0.25 |
| Convert the fraction 33/58 to a decimal number | 0.56896551724138 |
| Convert the fraction 17/19 to a decimal number | 0.89473684210526 |