Round up the following upto three significant figures:(i) 34.216 (ii) 10.4107 (iii) 0.04597(iv) 2808

1. Break Down the Problem

We need to round each number to three significant figures. Significant figures are the digits in a number that carry meaningful information about its precision.

2. Relevant Concepts

To round a number to a specific number of significant figures:

• Identify the significant figures in the number.
• Look at the digit immediately following the last significant figure to determine whether to round up or down.

3. Analysis and Detail

Let’s analyze each number one by one:

1. 34.216:

   • Significant figures: 34.2 (3 significant figures)
   • The digit after '2' is '1', which is less than 5, so we don’t round up.
   • Result: 34.2

2. 10.4107:

   • Significant figures: 10.4 (3 significant figures)
   • The digit after '4' is '1', which is less than 5, so we don’t round up.
   • Result: 10.4

3. 0.04597:

   • Significant figures: 0.0460 (3 significant figures)
   • The digit after '5' is '7', which is greater than 5, so we round up.
   • Result: 0.0460

4. 2808:

   • Significant figures: 2810 (3 significant figures)
   • The digit after '0' is '8', which is greater than 5, so we round up.
   • Result: 2810

4. Verify and Summarize

All calculations have been carefully checked.

• 34.216 rounds to 34.2
• 10.4107 rounds to 10.4
• 0.04597 rounds to 0.0460
• 2808 rounds to 2810

Final Answer

1. 34.2
2. 10.4
3. 0.0460
4. 2810