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Chapter 3: Problem 1

Write \(28.403951\) to (a) 6 s.f., (b) 5 s.f., (c) 4 s.f., (d) 3 s.f., (e) 2s.f., (f) 1 s.f.

Short Answer

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Question: Write the number 28.403951 to (a) 6 significant figures, (b) 5 significant figures, (c) 4 significant figures, (d) 3 significant figures, (e) 2 significant figures, and (f) 1 significant figure. Answer: (a) 28.403952, (b) 28.404, (c) 28.40, (d) 28.4, (e) 28.5, and (f) 30.

Step by step solution

01

(a) 6 Significant Figures

The number \(28.403951\) already has 8 significant figures, so we will keep the first 6 digits and consider the 7th digit, which is 5. Since it is equal to or greater than 5, we will round up. Thus, the number to 6 significant figures will be \(28.403\,95\,\underline{2}\).
02

(b) 5 Significant Figures

Keep the first 5 digits and consider the 6th digit, which is 9. Since it is equal to or greater than 5, we will round up. The number to 5 significant figures will be \(28.40\,3\,\underline{10}\,\). But we cannot have "10" as a digit, so carry over 1 to the previous digit (3). Therefore, the number to 5 significant figures will be \(28.404\).
03

(c) 4 Significant Figures

Keep the first 4 digits and consider the 5th digit, which is 3. Since it is less than 5, we don't need to round up. The number to 4 significant figures will be \(28.40\).
04

(d) 3 Significant Figures

Keep the first 3 digits and consider the 4th digit, which is 4. Since it is less than 5, we don't need to round up. The number to 3 significant figures will be \(28.4\).
05

(e) 2 Significant Figures

Keep the first 2 digits and consider the 3rd digit, which is 8. Since it is equal to or greater than 5, we will round up. The number to 2 significant figures will be \(28\,\underline{5}\).
06

(f) 1 Significant Figure

Keep the first digit and consider the 2nd digit, which is 8. Since it is equal to or greater than 5, we will round up. The number to 1 significant figure will be \(\underline{3}0\).

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