Answer :
To solve the problem of sorting the numbers based on the number of significant figures they have, let's analyze each number:
1. 201:
- Significant Figures: All non-zero digits are significant. Here, we have 3 significant figures.
- Category: Three Significant Figures
2. 100.0:
- Significant Figures: Trailing zeros after the decimal point are significant. Here, we have 4 significant figures.
- Category: Four Significant Figures
3. 1,200:
- Significant Figures: Trailing zeros in a whole number without a decimal point are not significant. We consider the two non-zero digits, so we have 2 significant figures.
- Category: Two Significant Figures
4. 1.200:
- Significant Figures: Trailing zeros after the decimal point are significant. Here, we have 4 significant figures.
- Category: Four Significant Figures
5. 4.0:
- Significant Figures: Trailing zeros after the decimal point are significant. Here, we have 2 significant figures.
- Category: Two Significant Figures
6. 40:
- Significant Figures: Trailing zeros in a whole number without a decimal point are not significant. We consider the one non-zero digit, so we have 1 significant figure.
- Category: One Significant Figure
7. 355:
- Significant Figures: All non-zero digits are significant. Here, we have 3 significant figures.
- Category: Three Significant Figures
8. 1.808:
- Significant Figures: All non-zero digits and zeros between significant digits are significant. Here, we have 4 significant figures.
- Category: Four Significant Figures
9. 0.4:
- Significant Figures: Leading zeros are not significant. We consider the non-zero digit, so we have 1 significant figure.
- Category: One Significant Figure
10. 2,710:
- Significant Figures: Trailing zeros in a whole number without a decimal point are not significant. We consider the three non-zero digits, so we have 3 significant figures.
- Category: Three Significant Figures
Now we sort the numbers into their respective categories:
- One Significant Figure:
- 40
- 0.4
- Two Significant Figures:
- 1,200
- 4.0
- Three Significant Figures:
- 201
- 355
- 2,710
- Four Significant Figures:
- 100.0
- 1.200
- 1.808
Here's the sorted table:
[tex]\[ \begin{array}{|c|c|c|c|} \hline \begin{array}{c} \text{One Significant} \\ \text{Figure} \end{array} & \begin{array}{c} \text{Two Significant} \\ \text{Figures} \end{array} & \begin{array}{c} \text{Three Significant} \\ \text{Figures} \end{array} & \begin{array}{c} \text{Four Significant} \\ \text{Figures} \end{array} \\ \hline 40 & 1,200 & 201 & 100.0 \\ 0.4 & 4.0 & 355 & 1.200 \\ & & 2,710 & 1.808 \\ \hline \end{array} \][/tex]
1. 201:
- Significant Figures: All non-zero digits are significant. Here, we have 3 significant figures.
- Category: Three Significant Figures
2. 100.0:
- Significant Figures: Trailing zeros after the decimal point are significant. Here, we have 4 significant figures.
- Category: Four Significant Figures
3. 1,200:
- Significant Figures: Trailing zeros in a whole number without a decimal point are not significant. We consider the two non-zero digits, so we have 2 significant figures.
- Category: Two Significant Figures
4. 1.200:
- Significant Figures: Trailing zeros after the decimal point are significant. Here, we have 4 significant figures.
- Category: Four Significant Figures
5. 4.0:
- Significant Figures: Trailing zeros after the decimal point are significant. Here, we have 2 significant figures.
- Category: Two Significant Figures
6. 40:
- Significant Figures: Trailing zeros in a whole number without a decimal point are not significant. We consider the one non-zero digit, so we have 1 significant figure.
- Category: One Significant Figure
7. 355:
- Significant Figures: All non-zero digits are significant. Here, we have 3 significant figures.
- Category: Three Significant Figures
8. 1.808:
- Significant Figures: All non-zero digits and zeros between significant digits are significant. Here, we have 4 significant figures.
- Category: Four Significant Figures
9. 0.4:
- Significant Figures: Leading zeros are not significant. We consider the non-zero digit, so we have 1 significant figure.
- Category: One Significant Figure
10. 2,710:
- Significant Figures: Trailing zeros in a whole number without a decimal point are not significant. We consider the three non-zero digits, so we have 3 significant figures.
- Category: Three Significant Figures
Now we sort the numbers into their respective categories:
- One Significant Figure:
- 40
- 0.4
- Two Significant Figures:
- 1,200
- 4.0
- Three Significant Figures:
- 201
- 355
- 2,710
- Four Significant Figures:
- 100.0
- 1.200
- 1.808
Here's the sorted table:
[tex]\[ \begin{array}{|c|c|c|c|} \hline \begin{array}{c} \text{One Significant} \\ \text{Figure} \end{array} & \begin{array}{c} \text{Two Significant} \\ \text{Figures} \end{array} & \begin{array}{c} \text{Three Significant} \\ \text{Figures} \end{array} & \begin{array}{c} \text{Four Significant} \\ \text{Figures} \end{array} \\ \hline 40 & 1,200 & 201 & 100.0 \\ 0.4 & 4.0 & 355 & 1.200 \\ & & 2,710 & 1.808 \\ \hline \end{array} \][/tex]
