Question

assume all numbers are measurements unless

1. state the number of significant figures, sig figs, in each of the following values:

(3 marks)

	# of sig figs
489.00
56,000
67,0\overline{0}0
34.6070
0.000010

Explanation:

Step1: Analyze 489.00

Trailing zeros after decimal are significant. Digits 4,8,9,0,0: 5 sig figs.

Step2: Analyze 56,000

Trailing zeros without decimal: ambiguous, but as written, 5 and 6 are significant: 2 sig figs (or 5 if zeros are significant, but standard: 2).

Step3: Analyze 67,0\overline{0}0

The bar over zero: that zero is significant. So 6,7,0 (barred), 0,0? Wait, 67,000 with a bar over the first zero: 6,7,0 (barred) are significant, then two zeros? Wait, 67,000 with a bar over the middle zero: 6,7,0 (barred), so 3 sig figs? Wait, no: 67,0\overline{0}0: the bar is over the second zero (from left: 6,7,0,0,0 with bar over third digit? Wait, 67,000: positions: 6 (1),7(2),0(3),0(4),0(5). Bar over 3rd zero: so 6,7,0 (barred) are significant: 3 sig figs? Wait, no, the bar is over the zero, meaning that zero is significant. So 6,7, and the zero with bar: 3 sig figs? Wait, maybe 67,000 with a bar over the middle zero: 6,7,0 (barred) are significant, so 3 sig figs.

Step4: Analyze 34.6070

All digits: 3,4,6,0,7,0. Trailing zero after decimal: significant. So 6 sig figs.

Step5: Analyze 0.000010

Leading zeros: not significant. 1 and 0 (trailing after 1): 2 sig figs.

Wait, let's redo each:

1. 489.00: digits 4,8,9,0,0. Trailing zeros after decimal: significant. So 5 sig figs.
2. 56,000: trailing zeros without decimal: if no decimal, ambiguous. But as a measurement, maybe 2 (5,6) or 5 (if zeros are significant). But standard: 2 sig figs (unless written as 5.6×10⁴, but here 56,000: 2 sig figs.
3. 67,0\overline{0}0: the bar over zero means that zero is significant. So digits: 6,7,0 (barred), and the other zeros? Wait, 67,000 with a bar over the middle zero: 6,7,0 (barred) are significant, so 3 sig figs.
4. 34.6070: digits 3,4,6,0,7,0. All are significant (trailing zero after decimal is significant). So 6 sig figs.
5. 0.000010: leading zeros: not significant. 1 and 0 (the last zero, after 1): 2 sig figs.

Answer:

Value	# of sig figs

| 0.0456 | 3 (wait, original 0.0456: leading zeros not significant, 4,5,6: 3? Wait, user wrote 4, but correct is 3. Wait, 0.0456: first non-zero is 4, then 5,6: 3 sig figs. Oh, user's mistake. Let's correct:

0.0456: 3 sig figs (4,5,6)

489.00: 5 (4,8,9,0,0)

56,000: 2 (5,6) or 5 (if zeros are significant, but standard: 2)

67,0\overline{0}0: 3 (6,7,0 with bar)

34.6070: 6 (3,4,6,0,7,0)

0.000010: 2 (1,0)

So filling the table:

0.0456: 3 (user had 4, wrong)

489.00: 5

56,000: 2 (or 5, but likely 2)

67,0\overline{0}0: 3

34.6070: 6

0.000010: 2

But let's do each step properly:

0.0456:

Leading zeros (0.0) are not significant. Non-zero digits: 4,5,6. So 3 sig figs.

489.00:

Digits: 4,8,9,0,0. Trailing zeros after decimal are significant. So 5 sig figs.

56,000:

Trailing zeros without decimal: ambiguous. If it's 56000 (no decimal), the zeros may be placeholders. So significant figures: 5 and 6. So 2 sig figs.

67,0\overline{0}0:

The bar over the zero indicates that zero is significant. So digits: 6,7,0 (barred). The other zeros: are they significant? The bar is over one zero, so 6,7,0 (barred) are significant. So 3 sig figs.

34.6070:

All digits: 3,4,6,0,7,0. Trailing zero after decimal is significant. So 6 sig figs.

0.000010:

Leading zeros (0.0000) are not significant. Non-zero digit: 1, then trailing zero after 1 (which is significant because it's after a non-zero digit and there's a decimal? Wait, 0.000010: the decimal is present, so the trailing zero after 1 is significant. So digits: 1,0. So 2 sig figs.

So the table should be:

Value	# of sig figs
489.00	5
56,000	2
67,0\overline{0}0	3
34.6070	6
0.000010	2

But the user's first entry (0.0456) was marked 4, which is incorrect. Correct is 3.