Write 71 300 in scientific notation. A. 7.13 x 10-4 C. 7.13 x 103 B. 7.13 x 10-3 D. 7.13 x 104
The Correct Answer and Explanation is:
Correct Answer: D. 7.13 × 10⁴
Explanation: Writing 71,300 in Scientific Notation
Scientific notation is a way of expressing very large or very small numbers in a more concise and manageable form. It is written as:a×10na \times 10^na×10n
Where:
- aaa is a number greater than or equal to 1 and less than 10.
- nnn is an integer that tells us how many times to multiply or divide by 10.
Step-by-Step Process for 71,300
- Place the Decimal:
To write 71,300 in scientific notation, we first convert it into a number between 1 and 10.
Move the decimal point in 71,300 to the left until only one non-zero digit remains to the left of the decimal. 71,300=7.13×10?71,300 = 7.13 \times 10^?71,300=7.13×10? - Count the Decimal Places:
Count how many places you moved the decimal to get from 71,300 to 7.13.- The original number is 71,300.0
- The decimal moves 4 places to the left:
- From after the second zero → between 7 and 1
- Write the Exponent:
Since we moved the decimal 4 places to the left, the exponent is +4. (Positive exponent means the original number was large.) - Final Answer in Scientific Notation: 71,300=7.13×10471,300 = 7.13 \times 10^471,300=7.13×104
Common Mistakes to Avoid
- Negative exponents are only used for numbers less than 1 (e.g., 0.00713).
- Don’t forget to adjust the exponent according to how many places the decimal point moves.
- Always ensure the number aaa is between 1 and 10.
Answer Recap
✅ Correct Answer: D. 7.13 × 10⁴
