Part 1Write the following in standard notation.55 times ×10Superscript negative 9−9 Part 155 times ×10Superscript negative 9−9equals=[input]enter your response here (Simplify your answer. Type an integer or a decimal.)

Question

Part 1Write the following in standard notation.55 times ×10Superscript negative 9−9 Part 155 times ×10Superscript negative 9−9equals=[input]enter your response here ​(Simplify your answer. Type an integer or a​ decimal.)

BlackTom AI · Accepted Answer

Scientific notation moves the decimal point by powers of ten. Here 55 × 10^(-9) means 55 multiplied by 1/10^9 (i.e., divide 55 by 1,000,000,000).

1) Relevant concepts
- 10^(-9) = 0.000000001.
- Multiplying by 10^(-n) shifts the decimal point n places to the left.
- Converting a number to standard decimal form can be done by rewriting 55 as 5.5 × 10^1 and combining powers of ten.

2) Step-by-step reasoning
- Rewrite 55 as 5.5 × 10^1 so that 55 × 10^(-9) = (5.5 × 10^1) × 10^(-9).
- Combine exponents: 10^1 × 10^(-9) = 10^(1-9) = 10^(-8).
- So the product is 5.5 × 10^(-8).

3) Intermediate calculations (decimal shifting)
- Start with 5.5. Multiplying by 10^(-8) moves the decimal 8 places left:
  1 move: 0.55
  2 moves: 0.055
  3 moves: 0.0055
  4 moves: 0.00055
  5 moves: 0.000055
  6 moves: 0.0000055
  7 moves: 0.00000055
  8 moves: 0.000000055
- Thus 5.5 × 10^(-8) = 0.000000055.

4) Why this answer is correct
- The algebraic combination of powers shows the exponent becomes -8, and shifting the decimal of 5.5 eight places left yields 0.000000055, which is exactly 55 divided by 10^9.

5) Why other possible answers would be incorrect
- 0.0000000055 would be 5.5 × 10^(-9) (one extra left shift), ten times smaller than the correct value.
- 0.00000055 would be 5.5 × 10^(-7) (one fewer left shift), ten times larger than the correct value.
- 0.000000000055 would be 5.5 × 10^(-11), far too small.
These common mistakes come from shifting the decimal the wrong number of places.

6) Conclusion
The correct standard decimal form is 0.000000055, which matches the provided answer.

Part 1Write the following in standard notation.55 times ×10Superscript negative 9−9 Part 155 times ×10Superscript negative 9−9equals=[input]enter your response here (Simplify your answer. Type an integer or a decimal.)多项填空题

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Part 1Write the following in standard notation.55 times ×10Superscript negative 9−9 Part 155 times ×10Superscript negative 9−9equals=[input]enter your response here ​(Simplify your answer. Type an integer or a​ decimal.)多项填空题