Rounding Significant Figures - Free Printable

Let's solve the problem step by step.

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Task:

We are given a set of numbers, and we need to:
1. Round each number to 2 significant figures.
2. Then, round the rounded numbers again to 2 significant figures (i.e., apply rounding twice).
3. Finally, compare the two results and determine which one is closer to the original number.

We are also asked to find the rounds to 10 or 100, but that seems to be a separate part — likely referring to rounding to the nearest 10 or 100.

But looking at the image, it appears there are two parts:

- Part A: Round three-digit numbers to 2 significant figures → then round those to 2 significant figures again.
- Part B: Same process for larger numbers.
- Then: "Which of the numbers below is the correct place – each number range is one box, both boxes, or neither box?"

And finally: "Rounds to 10 or 100" with options:
→ 12, 14.8, 7.75, 15.9, 15.3, 13.4, 14, 14.5, 16

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Let’s go through each section carefully.

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## ✔ Part A: Round three-digit numbers to 2 sig figs (A)

| Original | → Rounded to 2 sig figs |
|--------|-------------------------|
| 3127 | → 3100 (since 3127 → 3.1 × 10³) |
| 103 | → 100 (1.0 × 10²) |
| 4583 | → 4600 (4.6 × 10³) |
| 7123.28| → 7100 (7.1 × 10³) |
| 131307 | → 130000 (1.3 × 10⁵) |
| 1303.03| → 1300 (1.3 × 10³) |

Now, round these rounded values again to 2 sig figs:

| Rounded once | → Rounded again to 2 sig figs |
|--------------|-------------------------------|
| 3100 | → 3100 (already 2 sig figs) |
| 100 | → 100 (same) |
| 4600 | → 4600 |
| 7100 | → 7100 |
| 130000 | → 130000 (1.3 × 10⁵ → already 2 sig figs) |
| 1300 | → 1300 |

So, no change in any case — because all were already correctly expressed in 2 sig figs.

✔ So final answers for A:
- 3127 → 3100 → 3100
- 103 → 100 → 100
- 4583 → 4600 → 4600
- 7123.28 → 7100 → 7100
- 131307 → 130000 → 130000
- 1303.03 → 1300 → 1300

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## ✔ Part B: Round four-digit numbers to 2 sig figs (B)

| Original | → Rounded to 2 sig figs |
|--------|-------------------------|
| 3127 | → 3100 (same as before) |
| 4143 | → 4100 (4.1 × 10³) |
| 712.6 | → 710 (7.1 × 10²) |
| 154.285| → 150 (1.5 × 10²) |
| 1891.75| → 1900 (1.9 × 10³) |

Now, round those again to 2 sig figs:

| Rounded once | → Rounded again to 2 sig figs |
|--------------|-------------------------------|
| 3100 | → 3100 |
| 4100 | → 4100 |
| 710 | → 710 |
| 150 | → 150 |
| 1900 | → 1900 |

Again, no changes — all already have 2 sig figs.

So:
- 3127 → 3100 → 3100
- 4143 → 4100 → 4100
- 712.6 → 710 → 710
- 154.285 → 150 → 150
- 1891.75 → 1900 → 1900

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## ✔ Part C: Which of the numbers below is the correct place?

> "Which of the numbers below is the correct place – each number range is one box, both boxes, or neither box?"

This is ambiguous, but likely refers to a number line or range where we classify numbers based on whether they round to certain values.

But since no visual is provided, let's assume this refers to the final question:

> Rounds to 10 or 100

List:
12, 14.8, 7.75, 15.9, 15.3, 13.4, 14, 14.5, 16

We are to determine which of these round to 10 or 100 when rounded to the nearest 10 or 100?

But "rounds to 10 or 100" could mean:
- Rounded to nearest 10: e.g., 12 → 10, 15 → 20, etc.
- Rounded to nearest 100: e.g., all these are < 100 → round to 0 or 100?

But most are between 7 and 16 → so rounding to nearest 100 would give 0 or 100.

But let's interpret it as:

> Which of these numbers round to 10 when rounded to the nearest 10?

Or perhaps: Which numbers round to 10 or 100?

Let’s check each:

| Number | Round to nearest 10 | Round to nearest 100 |
|--------|----------------------|-----------------------|
| 12 | 10 | 0 |
| 14.8 | 10 | 0 |
| 7.75 | 10 | 0 |
| 15.9 | 20 | 0 |
| 15.3 | 10 | 0 |
| 13.4 | 10 | 0 |
| 14 | 10 | 0 |
| 14.5 | 10 or 20? → 20 (since 0.5 rounds up) | 0 |
| 16 | 20 | 0 |

Now, which round to 10?

- 12 → 10 ✔
- 14.8 → 10 ✔
- 7.75 → 10 ✔
- 15.3 → 10 ✔
- 13.4 → 10 ✔
- 14 → 10 ✔
- 14.5 → 20 ✘
- 15.9 → 20 ✘
- 16 → 20 ✘

So only 12, 14.8, 7.75, 15.3, 13.4, 14 round to 10.

Now, which round to 100?

All are less than 100 → so:
- Nearest 100: 0 or 100?
- Numbers < 50 → round to 0
- Numbers ≥ 50 → round to 100

But all these numbers are < 50 → so all round to 0 when rounding to nearest 100.

So none of them round to 100.

Thus, only numbers that round to 10 are relevant.

So answer:
Numbers that round to 10:
→ 12, 14.8, 7.75, 15.3, 13.4, 14

But wait: 14.5 rounds to 20, not 10.

So list of numbers that round to 10:
- 12
- 14.8
- 7.75
- 15.3
- 13.4
- 14

14.5 → 20 → ✘

So six numbers round to 10.

Now, if the question says “Rounds to 10 or 100”, and asks which ones do:

Then only the ones that round to 10 qualify (since none round to 100).

So final answer:

✔ Answer:

The numbers that round to 10 (and thus satisfy “rounds to 10 or 100”) are:
- 12, 14.8, 7.75, 15.3, 13.4, 14

(Note: 14.5 rounds to 20, so excluded; 15.9 and 16 also round to 20.)

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## 🔚 Final Answer Summary:

Part A (3-digit numbers):

- 3127 → 3100 → 3100
- 103 → 100 → 100
- 4583 → 4600 → 4600
- 7123.28 → 7100 → 7100
- 131307 → 130000 → 130000
- 1303.03 → 1300 → 1300

Part B (4-digit numbers):

- 3127 → 3100 → 3100
- 4143 → 4100 → 4100
- 712.6 → 710 → 710
- 154.285 → 150 → 150
- 1891.75 → 1900 → 1900

Part C: Which numbers round to 10 or 100?

Only those that round to 10 (since none round to 100):

✔ Numbers that round to 10:
12, 14.8, 7.75, 15.3, 13.4, 14

✘ 14.5 → 20
✘ 15.9 → 20
✘ 16 → 20

So final boxed answer:

> Numbers that round to 10 or 100: 12, 14.8, 7.75, 15.3, 13.4, 14

Let me know if you'd like a visual explanation or if the "boxes" refer to something else!