A Basic Guide to Decimals

Decimals are numbers that show both whole numbers and parts of a whole. They are written with a decimal point. For example, if a cake costs 5 dollars and 25 cents, we write it as $5.25 where 5 is the whole number and 25 is the fractional part.
 

Decimals are another way to write fractions. You can easily change a decimal to a fraction or a fraction to a decimal. For example, \(\frac{3}{8}\) as a decimal is 0.375, and \(\frac{1}{8}\) as a decimal is 0.125. Learning how to convert decimals to fractions helps in solving problems faster.
 

Decimals are used in daily life in money, measurements, and even in computers. In computers, we change binary to decimal or hexadecimal to decimal. Knowing decimal place value and decimal places helps us write and round numbers correctly.
 

There are two types of decimals terminating decimals (that end, like 0.5) and non-terminating decimals (that go on forever, like 0.333…).
 

You can also use a decimal calculator to change decimal to percent or percent to decimal easily.
 

Decimals have a long history. The idea of zero came from the Indian mathematician Aryabhata, which helped form modern decimals. Later, Simon Stevin and John Napier made decimals popular in math.
 

Decimals are a set of numbers that express both whole numbers and fractional parts. They play a vital role in everyday calculations to scientific operations. Several properties that make decimals a convenient way to represent numbers are listed below:
 

• Placing decimal in multiplication: When we add or subtract decimals, we should align the decimal points correctly. For example, 13.56 + 9.5 = 23.06. When multiplying decimals, we multiply them as whole numbers and then place the decimal point based on the total decimal places. For example, 3.5 × 1.4 = 4.9.
  
   
• Dividing decimals: To divide decimals, we shift the decimal point to make the divisor a whole number. For example, 4.0 ÷ 0.2 = 20. We can also use a decimal calculator for quick answers. Between two decimals like 0.1 and 0.2, there are more decimals, such as 0.15 and 0.17.
  
   
• Decimal fraction conversion: Decimals can be changed into fractions and vice versa. To convert a decimal to a fraction, write it over its place value; for example, 0.25 = \(\frac{1}{4}\). To convert a fraction to a decimal, divide the numerator by the denominator; for example, \(\frac{3}{8}\) as a decimal is 0.375 and \(\frac{1}{8}\) as a decimal is 0.125.
  
   
• Decimal percent conversion: Decimals can also be written as percentages. To convert decimal to percent, multiply by 100 (0.75 = 75%), and to convert percent to decimal, divide by 100 (45% = 0.45). In computers, numbers are also written in binary, hex, and decimal forms. We can change binary to decimal or hexadecimal to decimal easily using conversion methods.
  
   
• Understanding terminating decimals: Some decimals stop after a few digits, they are called terminating decimals. For example, 1/4 = 0.25 is a terminating decimal.

Decimals are divided into three main types based on the numbers that appear after the decimal point: terminating decimals, non-terminating decimals, and recurring decimals. Understanding these categories helps us easily convert between decimals and fractions.
 

• Terminating decimals
  Terminating decimals are those that stop after a few digits. They have a fixed number of decimal places, and division by them gives no remainder. For example, 0.25 is a terminating decimal because it ends after two digits. You can convert this decimal to a fraction as 0.25 = \(\frac{25}{100}\) = \(\frac{1}{4}\). Similarly, \(\frac{1}{8}\) as a decimal is 0.125 and \(\frac{3}{8}\) as a decimal is 0.375 both are terminating decimals.
   

• Non-Terminating decimals
  Non-terminating decimals go on endlessly after the decimal point. They have an infinite number of digits. Some of them follow a pattern, while others don’t. For example, 0.5555... continues forever, so it is a non-terminating decimal. When these decimals repeat, they are known as recurring decimals.
  
   
• Recurring decimals
  Recurring decimals are non-terminating decimals with repeating digits or groups of digits. For instance, 1.6777... repeats the digit 7 infinitely. These decimals can also be written as fractions. For example, \(\frac{1}{3}\)= 0.3333... and \(\frac{1}{7}\) = 0.142857142857....

Here, understanding the different types of decimals helps students solve math problems more easily. The two most common types are pure decimals and mixed decimals.

• Pure decimal
  Pure decimals are numbers that have digits only after the decimal point, without any whole number part. Their value is always less than 1. These decimals are often used to represent fractions. For example, 0.5, 0.25, 0.0089.
  
   
• Mixed decimals
  Mixed decimals are numbers that include both a whole number part and a fractional part, separated by a decimal point. The digits to the left of the point are whole numbers, while those on the right represent fractions. For example, 3.67, 11.42, 540.9

Decimals are an essential part of both learning and daily life.
They help students develop accuracy, precision, and problem-solving skills in academics and real-world applications.
 

• Decimals help us get accurate results in both everyday calculations and academic concepts.
   
• They are essential in daily life when dealing with money, weight, and length, where whole numbers alone cannot give exact values. For example, a weighing machine may show 52.6 kg instead of 52 kg, decimals help us read the same measurement.
  
   
• In higher-level math topics such as algebra, percentages, and ratios, understanding decimals is essential for solving problems correctly.
  
   
• Students who understand decimals well can perform better at science, engineering, technology, computer programming, and coding.
  
   
• Decimals play a key role in achieving accuracy and precision in both academic learning and real-world applications.

To solve mathematical problems effectively, we need to understand some tips and tricks. Here are some valuable tips and tricks for kids to learn more about decimals. 
 

• Always remember the place values of decimal digits. The values of digits, after the decimal point, are such as tenths, hundredths, thousandths, and so on. 
  
   
• Align the decimal points when adding or subtracting numbers.
  
   
• When we multiply, overlook the decimal point and multiply it as a whole number. After that, apply the point to the result.
  
   
• If some numbers have fewer place values, add leading zeroes to make calculations straightforward.
   

• When dividing decimals, if the divisor is not a whole number, multiply both the divisor and dividend by the same power of 10 to make the divisor a whole number, then perform the division as usual, placing the decimal point correctly in the quotient.
   

• Use visual aids such as charts and decimal grids, and introduce simple conversions, such as fraction-to-decimal and decimal-to-fraction, to strengthen understanding.
   

• Parents can encourage children to relate decimals to everyday situations, such as measuring ingredients, reading price tags, and converting percentages to decimals and vice versa while shopping.

In our everyday life, decimals play an essential role in ensuring accuracy and precision. Whether it’s checking our weight, calculating distance, or handling money, decimals are everywhere around us. Here are some real-life applications of decimals:
 

• In our daily life, prices in shops and banks are written in decimal form, such as ₹8.55. Even interest rates for loans and savings are often shown in decimals, like 1.7%.
  
   
• When measuring body weight, we often see decimal values for accuracy, for example, 65.4 kg. Similarly, the lengths of various objects are recorded in decimal form, such as 2.75 meters.
  
   
• Distances are usually measured with decimal precision. For example, the distance between two places can be 5.8 km instead of a whole number.
  
   
• In science, decimals are used in calculations to ensure accurate, precise results.
  
   
• Decimal values also play a key role in measuring time, for example, an athlete completing a race in 7.65 seconds.