Rounding And Significant Figures Worksheet - Free Printable

Problem: Rounding Numbers to Significant Figures

The task involves rounding numbers to 1, 2, and 3 significant figures, as well as categorizing numbers based on their rounded values. Let's solve each part step by step.

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#### Part 1: Round these numbers to 1 significant figure

1. 328 → 300 (Already provided)
2. 57 → 60
- The first significant figure is 5. The next digit is 7, which is ≥ 5, so we round up.
3. 817 → 800
- The first significant figure is 8. The next digit is 1, which is < 5, so we round down.
4. 15.6 → 20
- The first significant figure is 1. The next digit is 5, which rounds up.
5. 0.735 → 0.7
- The first significant figure is 7. The next digit is 3, which is < 5, so we round down.
6. 9326 → 9000
- The first significant figure is 9. The next digit is 3, which is < 5, so we round down.

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#### Part 2: Round these numbers to 2 significant figures

1. 352 → 350 (Already provided)
2. 926 → 930
- The first two significant figures are 92. The next digit is 6, which is ≥ 5, so we round up.
3. 1868 → 1900
- The first two significant figures are 18. The next digit is 6, which is ≥ 5, so we round up.
4. 15.9 → 16
- The first two significant figures are 15. The next digit is 9, which is ≥ 5, so we round up.
5. 0.273 → 0.27
- The first two significant figures are 27. The next digit is 3, which is < 5, so we round down.
6. 2.284 → 2.3
- The first two significant figures are 22. The next digit is 8, which is ≥ 5, so we round up.

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#### Part 3: Round these numbers to 3 significant figures

1. 273.7 → 274 (Already provided)
2. 8237 → 8240
- The first three significant figures are 823. The next digit is 7, which is ≥ 5, so we round up.
3. 635.2 → 635
- The first three significant figures are 635. The next digit is 2, which is < 5, so we round down.
4. 0.3837 → 0.384
- The first three significant figures are 383. The next digit is 7, which is ≥ 5, so we round up.
5. 5.372 → 5.37
- The first three significant figures are 537. The next digit is 2, which is < 5, so we round down.
6. 1.736 → 1.74
- The first three significant figures are 173. The next digit is 6, which is ≥ 5, so we round up.

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#### Part 4: Write the numbers below in the correct place

We need to categorize the following numbers:
- 221
- 246
- 257
- 224.6
- 216.3
- 254.8
- 225.3
- 255

Into the following categories:
1. Rounds to 200 to 1sf
2. Rounds to 250 to 2sf
3. Rounds to 225 to 3sf

##### Step-by-Step Analysis:

1. Rounds to 200 to 1sf:
- A number rounds to 200 to 1sf if its first significant figure is 2.
- 221, 246, 257, 224.6, 216.3, 254.8, 225.3, 255 all have 2 as their first significant figure.
- All numbers fit this category.

2. Rounds to 250 to 2sf:
- A number rounds to 250 to 2sf if its first two significant figures are 25.
- 257, 254.8, 255 round to 250 to 2sf.
- 221, 246, 224.6, 216.3, 225.3 do not fit this category.

3. Rounds to 225 to 3sf:
- A number rounds to 225 to 3sf if its first three significant figures are 225.
- 225.3 rounds to 225 to 3sf.
- 221, 246, 257, 224.6, 216.3, 254.8, 255 do not fit this category.

##### Final Categorization:

| Rounds to 200 to 1sf | Rounds to 250 to 2sf | Rounds to 225 to 3sf |
|-----------------------|-----------------------|-----------------------|
| 221, 246, 257, 224.6, 216.3, 254.8, 225.3, 255 | 257, 254.8, 255 | 225.3 |

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Final Answer:

\[
\boxed{
\begin{array}{l}
\text{Part 1:} \\
1) \, 300, \, 2) \, 60, \, 3) \, 800, \, 4) \, 20, \, 5) \, 0.7, \, 6) \, 9000 \\
\text{Part 2:} \\
1) \, 350, \, 2) \, 930, \, 3) \, 1900, \, 4) \, 16, \, 5) \, 0.27, \, 6) \, 2.3 \\
\text{Part 3:} \\
1) \, 274, \, 2) \, 8240, \, 3) \, 635, \, 4) \, 0.384, \, 5) \, 5.37, \, 6) \, 1.74 \\
\text{Part 4:} \\
\text{Rounds to 200 to 1sf: } 221, 246, 257, 224.6, 216.3, 254.8, 225.3, 255 \\
\text{Rounds to 250 to 2sf: } 257, 254.8, 255 \\
\text{Rounds to 225 to 3sf: } 225.3
\end{array}
}
\]