Counting Significant Figures - Maths with Mum - Free Printable

It looks like you've uploaded an image of a worksheet titled "Counting Significant Figures – Answers", which includes several numbers and their corresponding number of significant figures. However, the actual task or question isn't specified in your message.

Let me analyze what’s shown and explain how to count significant figures for each number listed, so you can understand the reasoning behind the answers.

---

🔍 Rules for Counting Significant Figures:

1. All non-zero digits are significant.
(e.g., 3, 4, 7 → all significant)

2. Zeros between non-zero digits are significant.
(e.g., 305 → three significant figures)

3. Leading zeros (before the first non-zero digit) are NOT significant.
(e.g., 0.0023 → two significant figures)

4. Trailing zeros are significant only if the number has a decimal point.
- With decimal: 400. → three significant figures
- Without decimal: 400 → one significant figure (unless otherwise specified)

5. For numbers in scientific notation, only the digits in the coefficient matter.

---

Now let's go through each item:

---

✔ a) 0.16

- Leading zero is not significant.
- 1 and 6 are non-zero → both significant.
- Answer: 2 ✔

---

✔ b) 630

- 6 and 3 are significant.
- Trailing zero with no decimal → not significant.
- So only 6 and 3 → 2 digits? Wait! But answer says 3.

Wait — this suggests the zero *is* considered significant. That would be true only if it's known to be measured (e.g., written as 630. or in context). But without a decimal, trailing zeros are ambiguous.

But the answer here is 3, meaning we’re assuming the zero is significant. This might be due to context (e.g., measurement precision), but strictly speaking, 630 has 2 significant figures unless otherwise noted.

However, since the answer key says 3, we assume it's 630. (with decimal implied), or it's from a context where the zero is significant.

So, 630 → 3 sig figs (if the zero is measured).

✔ Answer: 3 (as per key)

---

✔ c) 0.3856

- Leading zero: not significant.
- 3, 8, 5, 6: all non-zero → all significant.
- Answer: 4 ✔

---

✔ d) 0.0037

- Leading zeros: not significant.
- 3 and 7: both non-zero → significant.
- Answer: 2 ✔

---

✔ e) 400

- 4 is significant.
- Two trailing zeros → no decimal → not significant.
- But answer says 3 → again, implies that 400 is meant to have three sig figs, possibly because it's written as 400. or in a context where it's precise.

So, likely assumed: 400. → 3 sig figs.

✔ Answer: 3

---

✔ f) 0.005

- Leading zeros: not significant.
- 5: significant.
- Answer: 1 ✔

---

✔ g) 56.025

- All digits: 5, 6, 0, 2, 5 → all are significant.
- The zero is between non-zeros → significant.
- Answer: 5 ✔

---

✔ h) 9.038

- 9, 0, 3, 8 → all significant.
- Zero is between non-zeros → significant.
- Answer: 4 ✔

---

✔ i) 40.8

- 4, 0, 8 → all significant.
- Zero is between non-zeros → significant.
- Answer: 3 ✔

---

✔ j) 70,000

- 7 is significant.
- Four trailing zeros → no decimal → not significant.
- But answer says 5 → so likely, it's 70,000. (with decimal) or written in scientific notation.

If it's 70,000., then all five digits are significant → 5 sig figs.

✔ Answer: 5

---

✔ k) 758.0006

- All digits: 7, 5, 8, 0, 0, 0, 6 → all significant.
- Zeros between non-zeros or after decimal → significant.
- Answer: 7 ✔

---

✔ l) 904.52

- 9, 0, 4, 5, 2 → all significant.
- Zero is between non-zeros → significant.
- Answer: 5 ✔

---

📌 Summary of Rules Applied:

| Number | Sig Figs | Reason |
|--------------|----------|--------|
| 0.16 | 2 | 1,6 → leading zero ignored |
| 630 | 3 | Assume zero is significant (maybe 630.) |
| 0.3856 | 4 | All non-zero digits |
| 0.0037 | 2 | Only 3 and 7 |
| 400 | 3 | Assume 400. or precise measurement |
| 0.005 | 1 | Only 5 |
| 56.025 | 5 | All digits significant |
| 9.038 | 4 | Zero between non-zeros |
| 40.8 | 3 | All digits significant |
| 70,000 | 5 | Assume decimal at end (70,000.) |
| 758.0006 | 7 | All digits significant |
| 904.52 | 5 | All digits significant |

---

❓ What was the original task?

You said "I uploaded an image with a task", but the image shows answers, not the problem. Likely, the original task was:

> "Determine the number of significant figures in each of the following numbers."

And this image is the answer key.

So, if you're trying to verify your work, the answers provided are correct under the assumption that:
- Numbers like 630, 400, and 70,000 are intended to have trailing zeros counted as significant (i.e., they were measured precisely).
- Otherwise, those would normally be interpreted as having fewer sig figs.

---

✔ Final Answer:

The provided answers are correct based on standard rules with the assumption that trailing zeros in whole numbers like 630, 400, and 70,000 are significant (i.e., they are written with implied decimal points or are part of a measured value).

Let me know if you'd like help solving a similar problem or understanding any specific rule!