What are Fractions and Decimals?
Introduction
Fractions, decimals, and even fractions constitute key mathematical concepts essential in our daily lives and across diverse research areas. Knowing these representations of numbers is necessary to perform tasks like measuring, calculating proportions, and understanding information. This article examines the definitions and characteristics of decimals and fractions, reviewing their applications, uses, and conversion methods.
(Read More: Want to Study a Mathematics Course abroad?)
Suppose you're a college pupil looking to improve the mathematical abilities of your students or someone who is looking to gain an understanding of these concepts. In that case, this blog thoroughly describes the difference between decimals and fractions and what they do.
What are Decimals?
Decimals are numbers that contain dots (called"the decimal point") to indicate portions of the whole. They represent values smaller than one, as with fractions; however, they are more easily described. In this case, 0.5 is a decimal, similar to 1/2.
However, while decimals are considered integers without numbers after the decimal number (5.0 or 10.00), most decimals have non-integer values. For example, 3.75 means three whole parts and 75 hundredths. In this case, the number 7 is in the tenth position, and the number 5 is in the hundredth place.
For instance, decimals can be used in everyday life when dealing with cash. When you purchase a chocolate item for $1.50, that equals 1 dollar plus 50 cents.
Examples:
- 2.0 (a decimal that also doubles as an integer)
- 4.25 (4 and 25 hundredths)
- 7.99 (almost 8)
(Note: How do you use BODMAS while practicing math questions? Know More!)
Decimals allow us to write numbers more accurately, specifically in cases where the numbers are between the whole numbers. And Yes, decimals are integers if nothing is to be gained after the decimal mark.
What are Fractions?
Fractions are a method for displaying the parts of a larger object. When an object is divided into equal parts, a number indicates what percentage of each part is there. A fraction is composed of two numbers; the top number is known as the numerator, while the lower number is known as the denominator. For example, 1/2, 1 represents the numerator (parts we own), and 2 is the denominator (total parts).
Fractions can be very helpful in everyday life. If you cut the pizza into 4 equal pieces and then eat one, you eat 1/4 of the pizza. If you consume half of the glass of water, this is 1/2.
And sometimes, fractions and decimals could have the exact values. For example, 1/2 = 0.5 and 3/4 = 0.75.
(Note: Completed your 12th? Don't know how to calculate the percentage of marks, check this! )
Fractions may also be more significant than 1. For example, 5/4 means that you are more than the whole number, which is an improper fraction.
Examples:
- 1/2 (one out of two equal parts)
- 3/4 (three out of four equal parts)
- 5/5 (a whole)
Fractions help us comprehend and communicate the details of things clearly, as decimals help us do.
Visualizing Decimal Numbers
Understanding decimal numbers requires knowing how they appear and the significance they provide in a straightforward method. Decimals refer to numbers that employ the dot (decimal punctuation) to distinguish entire numbers from the parts of the total. The decimal points are calculated using tenths, hundredths, and thousandths. As an example, for the figure 3.6, the digit. 6 is located in tenth place, 6 of the 10 parts.
(You may also like: Mensuration: Properties and Formulas)
Decimals are integers only if zero digits, such as 4.0 or 7.00, follow the decimal point. If we find digits following the decimal point, it is a case of not-whole numbers.
To make decimal numbers simpler to understand, we can use visual aids such as grids, numbers lines, or actual objects like money or measuring tools.
What is the Relationship Between Fractions and Decimals?
Their relationship is based on the fact that every fraction can be transformed into decimal form, and every decimal is expressed as an arbitrary fraction.
To convert a fraction to decimal, split by the numerator (top value) with the denominator (bottom number). For example, 1/4 becomes 0.25 because 1 / 4 = 0.25. Similarly, 3/5 becomes 0.6. It makes decimals a practical way to write fractions while doing calculations.
In contrast, converting a decimal into a fraction requires setting the decimal to the power of 10 and then simplifying. In this case, 0.75 becomes 75/100 and then simplifies to 3/4.
This connection can help compare figures, perform operations, and tackle real-world problems measuring money or time. These two types are merely two different ways to express the same concept.
(Explore Now: What Are the Best Career Paths After Commerce Without Maths?)
Decimals and Fractions
Decimals and fractions may look different, but they represent the same idea—parts of a whole. The main difference is in how they are written. Decimals use a dot, while fractions use a slash. For example, 0.25 and ¼ mean the same: 25 out of 100, or one part of four equal pieces.
One important thing to remember is that every decimal can be written as a fraction and vice versa. This makes it easier to switch between forms depending on the situation. Decimals are more common in money and measurements, while fractions are often used in cooking and dividing objects.
Decimals and Percentages
Just like fractions, each decimal number can be expressed as a percent. It is essential to convert decimals into percentages when comparing two or more. For example, which would score higher when Sandra scored 20.5 from 40 marks, and Kim scored 22.25 out of 45? Changing a decimal number to an amount takes two easy steps. To begin, you must multiply the decimal by 100, which moves the decimal two positions toward the right. Also, add a % symbol (%).
Example: 0.67 = 0.67 x 100% = 67%
In the same way, we can convert a percentage into a decimal. First, divide the percent number by 100, then eliminate the decimal sign. We then reduce the number by 100 to convert it into a decimal.
(Discover More: Bachelor of Science in Applied Math: Is It Worth It?)
Decimals in Everyday Life
Decimals are everywhere and play an essential part in daily life. Whether we are aware of this or not, people use decimals to measure money, weight, distance, and time, as well as when making purchases or cooking.
If, for instance, you purchase something at $2.50, the ".50" is a decimal, equivalent to 50 cents or a half dollar. Regarding measurements, a bottle can hold 1.5 Liters, 1 and 1/2 Liters. If you're baking a dessert and the recipe requires 0.75 cups of sugar, then the recipe uses exact decimals.
Decimals help us be precise. Instead of "a little more than 1," we could say 1.2 or 1.75, depending on the extra amount.
Real-Life Examples:
- Pricing: $3.99 (three dollars and ninety-nine cents)
- Height: 1.75 meters
- Duration: 1.5 hours = 1 hour 30 minutes
- The fuel: 2.3 liters of gasoline
Decimals allow us to communicate tiny quantities clearly and effectively.
(Find Out More: After 10th, What’s Next? Find the Right Exam for You!)
Frequently Asked Questions
1. What are fractions in mathematics?
Fractions represent a part of a whole. They are written in the form a/b, where a is the numerator (part) and b is the denominator (whole). For example, ½ means one out of two equal parts.
2. What are decimals in mathematics?
Decimals are another way to represent parts of a whole using a decimal point. For example, 0.5 is the decimal equivalent of the fraction ½. Decimals are based on powers of 10.
3. How are fractions and decimals related?
Fractions can be converted into decimals and vice versa. For example, ¾ is equal to 0.75. Both are used to represent non-whole numbers or values between whole numbers.
4. What are proper and improper fractions?
A proper fraction has a numerator smaller than the denominator (e.g., 3/4). An improper fraction has a numerator equal to or greater than the denominator (e.g., 5/3). Improper fractions can also be written as mixed numbers (e.g., 5/3 = 1 2/3).
5. How do you convert a fraction to a decimal?
To convert a fraction to a decimal, divide the numerator by the denominator. For example, 1 ÷ 4 = 0.25. You can use long division or a calculator for this.
6. How do you convert a decimal to a fraction?
Write the decimal over a power of 10 (depending on the number of decimal places) and simplify. For example, 0.75 = 75/100 = 3/4. Always reduce the fraction to its simplest form.
7. Why do we use fractions and decimals in real life?
Fractions and decimals are used in measurements, money, time, cooking, and data analysis. For example, you might need ¾ cup of flour in a recipe or pay $1.50 for a snack. They help in accurate and precise communication of values.
8. What is a recurring or repeating decimal?
A repeating decimal has digits that repeat forever after the decimal point. For example, 1/3 = 0.333... (where 3 repeats indefinitely). These decimals can be converted into fractions.
9. What is a terminating decimal?
A terminating decimal ends after a finite number of digits. For example, 1/2 = 0.5 is a terminating decimal. Only fractions with denominators having prime factors of 2 and/or 5 terminate.
10. Are decimals easier to use than fractions?
It depends on the context. Decimals are easier for calculations, especially in money and science, while fractions are useful in measurements, dividing things, and understanding ratios. Both are essential tools in math.
11. How do you compare fractions and decimals?
Convert either fractions to decimals or decimals to fractions for easy comparison. For instance, to compare 0.6 and 2/3, convert 2/3 to decimal (≈0.666), and now you can see that 2/3 is greater. Number lines are also helpful.
12. What is the decimal system based on?
The decimal system is base-10, meaning each place value is 10 times the value of the one to its right. It includes tenths, hundredths, thousandths, etc. This system is used worldwide in everyday math.
13. Can fractions and decimals be negative?
Yes, both fractions and decimals can be positive or negative. For example, -3/4 or -0.75 both indicate a negative value. The negative sign shows direction on a number line or loss in quantity.
14. What are mixed numbers in fractions?
A mixed number consists of a whole number and a proper fraction. For example, 1 ½ means one whole and one-half. It’s useful when dealing with quantities more than one but not whole.
15. How are percentages related to fractions and decimals?
Percentages are a way to express numbers out of 100, which can be written as fractions or decimals. For example, 50% = 50/100 = 0.5. Understanding this relationship helps in solving many real-life math problems.
