Decimal: Understanding the Basics

Decimal is a fundamental concept in mathematics that is used to represent numbers in base-10. It is an essential tool in various fields, including finance, engineering, and science. In this article, we will explore the basics of decimals, including what they are, how to convert them, and how to perform basic operations with them.

What is Decimal?

Decimal is a number system that uses ten digits, i.e., 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. It is different from other number systems such as binary, which uses only two digits (0 and 1), and hexadecimal, which uses sixteen digits (0 to 9 and A to F).

Decimal numbers consist of a whole number part and a decimal part separated by a decimal point. For example, the number -14 has a whole number part of 3 and a decimal part of 0.1- The decimal part represents a fraction of the whole number, where the denominator is a power of ten. In the case of 0.14, the denominator is 10^2, which is equal to 100.

Converting Decimals

Converting decimals is a straightforward process. To convert a decimal to a fraction, we need to follow these steps:

Step 1: Write down the decimal as the numerator of a fraction.

Step 2: Determine the denominator by placing 1 in the denominator and as many zeros as there are digits to the right of the decimal point in the numerator. For example, if the decimal is 0.25, the denominator would be 100.

Step 3: Simplify the fraction if possible.

For example, to convert 0.75 to a fraction, we would write:

0.75 = 75/100

Simplifying the fraction by dividing both the numerator and denominator by 25, we get:

0.75 = 3/4

Performing Operations with Decimals

Performing operations with decimals is similar to performing operations with whole numbers. The only difference is that we need to pay attention to the decimal point. Here are the steps for adding, subtracting, multiplying, and dividing decimals:

Addition

Step 1: Line up the decimal points of the numbers.

Step 2: Add the numbers as if they were whole numbers.

Step 3: Place the decimal point in the answer directly below the decimal points in the numbers being added.

For example, to add -14 and -23, we would write:

-14

+-23

-----

-37

Subtraction

Step 1: Line up the decimal points of the numbers.

Step 2: Subtract the numbers as if they were whole numbers.

Step 3: Place the decimal point in the answer directly below the decimal points in the numbers being subtracted.

For example, to subtract -14 from -67, we would write:

-67

--14

-----

-53

Multiplication

Step 1: Ignore the decimal points and multiply the numbers as if they were whole numbers.

Step 2: Count the total number of decimal places in both numbers being multiplied.

Step 3: Place the decimal point in the answer so that the total number of decimal places is equal to the sum of the decimal places in the original numbers.

For example, to multiply -14 and -23, we would write:

-14 x -23 = 3862

Counting the total number of decimal places (2), we place the decimal point two places from the right in the answer:

-14 x -23 = -8612

Division

Step 1: Move the decimal point in the divisor (the number being divided) to the right until it becomes a whole number.

Step 2: Move the decimal point in the dividend (the number being divided) the same number of places to the right.

Step 3: Divide the numbers as if they were whole numbers.

Step 4: Place the decimal point in the answer directly above the decimal point in the dividend.

For example, to divide -14 by -23, we would write:

314

-----

123

Moving the decimal point in the divisor one place to the right, we get:

314

-----

1230

Moving the decimal point in the dividend one place to the right, we get:

3-4

-----

1230

Dividing the numbers as if they were whole numbers, we get:

3-4

-----

1230

Placing the decimal point in the answer directly above the decimal point in the dividend, we get:

-14 ÷ -23 = -5528

Conclusion

In conclusion, decimals are an essential tool in mathematics and various fields. Understanding the basics of decimals, including what they are, how to convert them, and how to perform basic operations with them, is crucial for success in these fields. With the steps outlined in this article, you should be able to work with decimals with ease.