Question

how many significant figures are in this number ? 678.02400

Explanation:

Step1: Recall Significant Figure Rules

Significant figures (sig figs) rules: Non - zero digits are significant. Zeros between non - zero digits are significant. Trailing zeros in a decimal number are significant.

Step2: Analyze Each Digit in 678.02400

• The digits 6, 7, 8 are non - zero, so they are significant.
• The zero between 8 and 2 (the 0 in 678.02400) is between non - zero digits, so it is significant.
• The digits 2 and 4 are non - zero, so they are significant.
• The two trailing zeros (the last two 0s in 678.02400) are in a decimal number, so they are significant.

Now, let's count: 6, 7, 8, 0, 2, 4, 0, 0. That's 8 digits. Wait, wait, let's do it again. 6 (1), 7 (2), 8 (3), 0 (4), 2 (5), 4 (6), 0 (7), 0 (8). Wait, no, wait the number is 678.02400. Let's list each significant figure:

6 (significant), 7 (significant), 8 (significant), 0 (between 8 and 2, significant), 2 (significant), 4 (significant), 0 (trailing, significant), 0 (trailing, significant). Wait, that's 8? Wait no, let's count again. 6,7,8,0,2,4,0,0. Wait, 6 (1), 7 (2), 8 (3), 0 (4), 2 (5), 4 (6), 0 (7), 0 (8). Wait, but let's check the rules again. Trailing zeros in a decimal are significant. So in 678.02400, the digits are:

• 6: sig
• 7: sig
• 8: sig
• 0: sig (between 8 and 2)
• 2: sig
• 4: sig
• 0: sig (trailing, after 4)
• 0: sig (trailing, last one)

Wait, that's 8? Wait no, wait 678.02400. Let's write the number as digits: 6,7,8,.,0,2,4,0,0. So the significant figures are 6,7,8,0,2,4,0,0. Wait, that's 8? Wait, no, wait I think I made a mistake. Wait 678.02400: let's count each significant digit:

1. 6
2. 7
3. 8
4. 0 (between 8 and 2)
5. 2
6. 4
7. 0 (after 4)
8. 0 (last one)

Wait, that's 8? Wait, no, wait the number is 678.02400. Let's check the rules for significant figures:

• All non - zero digits: 6,7,8,2,4 (that's 5 digits)
• Zeros between non - zero digits: the 0 between 8 and 2 (1 digit)
• Trailing zeros in the decimal part: the two zeros at the end (2 digits)

So total: 5 + 1+ 2 = 8? Wait, no, 6,7,8 (3), 0 (1), 2,4 (2), 0,0 (2). 3+1 + 2+2=8. Yes, so the number of significant figures is 8. Wait, no, wait 678.02400: let's list them:

6 (1), 7 (2), 8 (3), 0 (4), 2 (5), 4 (6), 0 (7), 0 (8). So 8 significant figures.

Answer:

8