Part 1Determine the number of significant digits in each of the given approximate numbers. 200200; 200.0200.0; 20 0 overbar200 Part 1The number of significant digits in 200200 is [input]22 .

Question

Part 1Determine the number of significant digits in each of the given approximate numbers. 200200​; 200.0200.0​; 20 0 overbar200 Part 1The number of significant digits in 200200 is [input]22 .

BlackTom AI · Accepted Answer

All digits shown in an explicitly approximate number are treated as significant; thus 200200 has six significant digits.

1) Relevant knowledge points and concepts
- Significant-figure rules: nonzero digits are always significant. Zeros between nonzero digits are significant. Leading zeros are not significant. Trailing zeros in an integer without a decimal point can be ambiguous unless the number is explicitly given as an approximation; when a number is specifically stated to be an approximation (or written with an overbar/decimal), all displayed digits are treated as significant.

2) Step-by-step reasoning
- Write the number with digits separated: 2 0 0 2 0 0.
- Identify nonzero digits: the two 2’s (first and fourth positions) are significant.
- Identify zeros: the two zeros between the first 2 and the second 2 are between nonzero digits → significant. The two zeros after the final 2 are trailing zeros; because the problem explicitly labels the values as approximate numbers, those trailing zeros are also significant.

3) Intermediate counting steps
- Count each digit considered significant:
  - First digit: 2 → significant (1)
  - Second digit: 0 (between nonzero digits or part of the approximation) → significant (2)
  - Third digit: 0 (between nonzero digits) → significant (3)
  - Fourth digit: 2 → significant (4)
  - Fifth digit: 0 (trailing, but given as part of the approximation) → significant (5)
  - Sixth digit: 0 (trailing, but given as part of the approximation) → significant (6)

4) Why the correct answer is correct
- Because the number is presented as an approximate value, every digit shown (including zeros between nonzero digits and trailing zeros) counts as a significant digit. That yields a total of six significant digits.

5) Why other counts would be incorrect
- Claiming 3 significant digits would count only the nonzero digits and ignore zeros between them — incorrect because interior zeros are significant.
- Claiming 4 or 5 would arbitrarily treat some zeros as non-significant; without additional notation (like a decimal point omitted or a bar indicating repeating zeros), the problem’s “approximate” label means all displayed digits are significant.

6) Conclusion
- The number 200200 has 6 significant digits, which matches the provided answer: 6.

Part 1Determine the number of significant digits in each of the given approximate numbers. 200200; 200.0200.0; 20 0 overbar200 Part 1The number of significant digits in 200200 is [input]22 .Multiple fill-in-the-blank

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Part 1Determine the number of significant digits in each of the given approximate numbers. 200200​; 200.0200.0​; 20 0 overbar200 Part 1The number of significant digits in 200200 is [input]22 .Multiple fill-in-the-blank