Express (round off) each of the following to three significant figures:
0.002537, 12345000, 0.07966, 620.2
leading zeroes after the decimal do not count
trailing zeroes before the decimal do not count
For example,
0.002537 = 2.54E-3
12345000 = 1.23E7
To round off each of the given numbers to three significant figures, we follow these steps:
1. Identify the first three non-zero digits from the left (starting from the leftmost non-zero digit) or the first three digits counting from the decimal point.
2. Determine if the fourth digit is equal to or greater than 5. If it is, round up the third digit. If it is less than 5, leave the third digit as it is.
3. Replace all the remaining digits after the third significant figure with zeros.
Applying these steps to each number:
1. For 0.002537:
- The first three non-zero digits are 2, 5, and 3.
- The fourth digit is less than 5, so we leave the third digit as it is.
- The rounded number is 0.00254.
2. For 12345000:
- The first three non-zero digits are 1, 2, and 3.
- There is no fourth digit since there are no decimal points.
- The rounded number remains the same: 12345000.
3. For 0.07966:
- The first three non-zero digits are 7, 9, and 6.
- The fourth digit is greater than 5, so we round up the third digit.
- The rounded number is 0.080.
4. For 620.2:
- The first three non-zero digits are 6, 2, and 0.
- There is no fourth digit since there are no decimal points.
- The rounded number remains the same: 620.2.
Therefore, the numbers rounded to three significant figures are:
0.00254, 12345000, 0.080, 620.2.
To round off a number to three significant figures, you need to look at the first three digits and determine the correct rounding rule based on the fourth digit.
Let's go through each number one by one:
1. 0.002537
The first three digits are 0, 0, and 2. The fourth digit is 5, which is greater than or equal to 5. According to the rounding rule, when the fourth digit is 5 or above, you increase the last retained significant figure by 1. Thus, the rounded value is 0.00254.
2. 12,345,000
The first three digits are 1, 2, and 3. As for the fourth digit, it is 4, which is less than 5. In this case, the last retained significant figure remains the same. The rounded value is 12,300,000.
3. 0.07966
The first three digits are 0, 7, and 9. The fourth digit is 6, which is greater than or equal to 5. Therefore, according to the rounding rule, the last retained significant figure increases by 1. The rounded value is 0.0797.
4. 620.2
The first three digits are 6, 2, and 0. The fourth digit is 2, which is less than 5. Hence, the last retained significant figure stays the same. The rounded value is 620.