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question 3 (1 point) how many significant figures are in the number 301…

Question

question 3 (1 point) how many significant figures are in the number 3010.00 a) 2 b) 3 c) 4 d) 5 e) 6

Explanation:

Step1: Recall significant figure rules

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

Step2: Analyze the number 3010.00

  • The digit 3 is non - zero, so it is significant.
  • The zero between 3 and 1 (3\(0\)10.00) is between two non - zero digits, so it is significant.
  • The digit 1 is non - zero, so it is significant.
  • The zero after 1 (301\(0\).00) is a trailing zero in a decimal number, so it is significant.
  • The two trailing zeros after the decimal point (3010.\(00\)) are also significant.

Now, let's count the significant figures: 3, 0, 1, 0, 0, 0? Wait, no. Wait, 3010.00:

  • 3 (significant)
  • 0 (between 3 and 1, significant)
  • 1 (significant)
  • 0 (after 1, in the decimal part? Wait, 3010.00 can be thought of as 3.01000×10³. Wait, no, let's do digit by digit:

The number is 3, 0, 1, 0,., 0, 0.
Non - zero digits: 3,1. Zeros:

  • Zero between 3 and 1: significant.
  • Zero after 1 (the fourth digit): since there is a decimal point, the trailing zeros (including the zero before the decimal and the ones after) are significant. Wait, the number 3010.00:

Digits: 3 (1st), 0 (2nd, between 3 and 1, significant), 1 (3rd, significant), 0 (4th, trailing zero in a number with decimal, significant), 0 (5th, trailing zero after decimal, significant), 0 (6th, trailing zero after decimal, significant)? Wait, no, I made a mistake. Let's use the rules properly:

  1. All non - zero digits are significant: 3 and 1 are non - zero, so that's 2 digits.
  2. Zeros between non - zero digits are significant: the zero between 3 and 1 (the second digit) is significant, so now we have 3 digits (3,0,1).
  3. Trailing zeros in a decimal number are significant: the number has a decimal point, so the zeros after the non - zero digits (the zero after 1, and the two zeros after the decimal) are significant. So the number 3010.00 has digits: 3, 0, 1, 0, 0, 0? No, wait, 3010.00 is 3 (thousands place), 0 (hundreds place), 1 (tens place), 0 (ones place),. (decimal), 0 (tenths place), 0 (hundredths place).

Now, applying the rules:

  • Non - zero: 3,1 (2 digits)
  • Zero between non - zero: 0 (between 3 and 1) → 3 digits (3,0,1)
  • Trailing zeros in decimal: the zero in the ones place (because there is a decimal, this zero is significant), and the two zeros after the decimal. So the zeros are: 0 (hundreds), 0 (ones), 0 (tenths), 0 (hundredths)? No, no. Wait, the correct way:

The number 3010.00:

  • The 3 is significant.
  • The 0 between 3 and 1 is significant (because it's between two non - zeros).
  • The 1 is significant.
  • The 0 after 1 (the fourth digit) is significant because the number has a decimal point (trailing zero in a decimal number is significant).
  • The two zeros after the decimal (the fifth and sixth digits) are also significant (trailing zeros after decimal are significant).

So let's count: 3 (1), 0 (2), 1 (3), 0 (4), 0 (5), 0 (6)? Wait, no, that's wrong. Wait, 3010.00:

Let's write it in scientific notation to see: 3.01000×10³? No, 3010.00 = 3.01000×10³? Wait, no, 3010.00 = 3.01000×10³? Wait, 3010.00 divided by 10³ is 3.01000. So the significant figures are the digits in 3.01000, which are 3,0,1,0,0,0? No, no, 3.01000 has six significant figures? Wait, no:

Wait, the rules for significant figures:

  • Rule 1: Non - zero digits are significant. So 3 and 1 are significant.
  • Rule 2: Zeros between non - zero digits are significant. So the zero between 3 and 1 is significant.
  • Rule 3: Trailing zeros in a number with a decimal point are significant. So t…

Answer:

e) 6