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Chapter 1: Problem 116

After rounding of the number 9595 to 3 significant digits the value becomes .............. (a) 9600 (b) 9000 (c) 9590 (d) 9500

Short Answer

Expert verified
After rounding the number 9595 to 3 significant digits, the value becomes \(9600\).

Step by step solution

01

Identify the first three significant digits

Recall that the first three significant digits are the first three non-zero digits in the number. In this case, the first three significant digits are 9, 5, and 9, going from left to right.
02

Look at the digit after the third significant digit

The number 9595 has only four digits, and we have already identified the first three significant digits. Therefore, the digit after the third significant digit is the fourth digit, which is 5.
03

Determine whether to round up or down

Since the digit after the third significant digit is 5, we round up. This means that we increase the third significant digit by 1 (9 + 1 = 10) and replace the digits after the third significant digit with zeros. Remember that when the third digit is 9 and it's rounded up, it becomes 10. In this case, we'll carry over the 1 and add it to the second digit, making the second digit 6, and adjusting the third digit to 0.
04

Round the number

Rounding the original number 9595 to 3 significant digits, we get: 9 (first significant digit) 6 (second significant digit, after rounding) 0 (third significant digit, since we rounded 9 to 10) 0 (replace the following digits with zeros) Thus, the rounded number is 9600.
05

Select the correct option

Finally, we compare our rounded number to the given options: (a) 9600 (b) 9000 (c) 9590 (d) 9500 As our result was 9600, we select option (a) as the correct answer.

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