To round each number to two significant figures, follow these steps:
1. Identify the first two significant figures.
2. Round the number appropriately based on the value of the third digit.
Let's address each number one by one:
(a) 0.436
- The first two significant figures are 4 and 3.
- The third digit is 6, which is greater than 5. So, round the second digit up by 1.
Thus, 0.436 rounded to two significant figures is 0.44.
(b) 9.000
- The first significant figure is 9.
- Since the number has trailing zeros, they are not counted beyond the significant figures.
Thus, 9.000 rounded to two significant figures is 9.0.
(c) 27.2
- The first two significant figures are 2 and 7.
- The third digit is 2, which is less than 5, so the second digit remains unchanged.
Thus, 27.2 rounded to two significant figures is 27.
(d) 135
- The first two significant figures are 1 and 3.
- The third digit is 5, indicating rounding up the second digit.
Thus, 135 rounded to two significant figures is 140 (since 1.4 × 10^2 = 140).
(e) \(1.497 \times 10^{-3}\)
- The first two significant figures are 1 and 4.
- The third digit is 9, which is greater than 5, so the second digit is rounded up by 1.
Thus, \(1.497 \times 10^{-3}\) rounded to two significant figures is 0.0015.
(f) 0.445
- The first two significant figures are 4 and 4.
- The third digit is 5, indicating rounding up the second digit.
Thus, 0.445 rounded to two significant figures is 0.45.
So the final results are:
- (a) \(0.44\)
- (b) \(9.0\)
- (c) \(27\)
- (d) \(140\)
- (e) \(0.0015\)
- (f) [tex]\(0.45\)[/tex]
