Round 82.684587348 to 4 decimal places.
The Correct Answer and Explanation is :
To round 82.684587348 to 4 decimal places, follow these steps:
- Identify the 4th decimal place: Look at the 4th digit after the decimal point. In this case, it’s 5 (82.6845…).
- Check the next digit (5th decimal place): This digit determines whether to round up or down. Here, the 5th digit is 8.
- Apply rounding rules:
- If the next digit is 5 or greater, round the 4th decimal place up.
- If it’s less than 5, leave the 4th decimal place unchanged.
Since the 5th digit is 8, round 5 up to 6.
The number rounded to 4 decimal places is 82.6846.
Explanation (300 Words)
Rounding numbers is a process used to approximate values, making them easier to use in calculations or communicate. It’s especially important in fields like science, engineering, and finance, where precision is needed but excessive decimal places can complicate work.
The number 82.684587348 has 9 digits after the decimal, which can be too detailed for most practical purposes. By rounding to 4 decimal places, we simplify the number without losing significant accuracy. Here’s why:
- Precision vs. Simplicity: The more decimal places you keep, the closer the number is to its true value. However, for general use, 4 decimal places provide a good balance of precision and simplicity.
- Step-by-Step Process:
- First, locate the digit at the place you’re rounding to (the 4th decimal place in this case).
- Next, observe the digit immediately following it to decide whether to round up or leave it unchanged. This is based on standard rounding rules.
- Why the 5th Decimal Matters: The 5th digit (8) tells us the value is closer to 82.6846 than 82.6845, so we round up.
- Applications: In real-world scenarios like reporting measurements or financial transactions, small differences beyond 4 decimal places often have negligible impact but can make data overly complex.
Rounding thus simplifies interpretation, saving time while maintaining accuracy to a practical degree.