Write the following in Hindu – Arabic numerals.

(a) 43

(b) 69

(c) 135

(d) 222

(e) 282

(f) 513

To convert Arabic numerals into Hindu-Arabic numerals, we essentially recognize that Hindu-Arabic numerals are the same as the Arabic numerals we commonly use today. The term "Hindu-Arabic" refers to the numeral system that originated in India and was transmitted to the Islamic world, eventually reaching Europe. Here’s how the numbers you provided translate:

Conversion of Arabic Numerals

• (a) 43 - In Hindu-Arabic numerals, this remains 43.
• (b) 69 - This also stays the same as 69.
• (c) 135 - This is represented as 135.
• (d) 222 - This translates to 222.
• (e) 282 - This is 282 in Hindu-Arabic numerals.
• (f) 513 - This remains 513.

Understanding the System

The Hindu-Arabic numeral system is a base-10 system, which means it uses ten symbols (0-9) to represent numbers. Each digit's position in a number determines its value. For example, in the number 135, the '1' represents one hundred, the '3' represents thirty, and the '5' represents five. This positional value is a key feature of the system, allowing for efficient representation of large numbers.

Historical Context

This numeral system was developed by Indian mathematicians around the 6th century and later transmitted to the Islamic world, where it was further developed and popularized. By the 10th century, it began to spread into Europe, replacing the Roman numeral system due to its efficiency in calculations.

In summary, the numbers you listed are already in Hindu-Arabic form, as they are the same as the Arabic numerals we use today. This numeral system is foundational in mathematics and everyday counting, making it essential for various applications in both academic and practical contexts.