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:
The correct answer is: D. 7.13 × 10⁴
Explanation:
Scientific notation is a way of writing very large or very small numbers in a compact form. It expresses numbers as a product of two factors:
- A number greater than or equal to 1 and less than 10 (called the coefficient)
- A power of 10
Step 1: Understand the Number
We are given the number 71,300. This is a large number, so we want to express it in scientific notation using powers of 10.
Step 2: Move the Decimal Point
To convert 71,300 to scientific notation, place a decimal point so that there is only one non-zero digit to the left of the decimal. For 71,300, that would be: 71,300=7.13×10?71,300 = 7.13 \times 10^?71,300=7.13×10?
We moved the decimal point 4 places to the left to go from 71,300 to 7.13: 71,300→7.1371,300 → 7.1371,300→7.13
Each movement of the decimal point to the left corresponds to an increase in the exponent of 10 by 1. Since we moved it 4 times, the exponent is 4.
So, 71,300=7.13×10471,300 = 7.13 \times 10^471,300=7.13×104
Step 3: Check the Coefficient
The number 7.13 is between 1 and 10, so it satisfies the rule for scientific notation. The power of 10 is 4, indicating how many times you would multiply 7.13 by 10 to get back to 71,300.
Step 4: Eliminate Incorrect Options
Let’s look at the choices:
- A. 7.13 × 10⁻⁴ → This would be a very small number (0.000713), not correct.
- B. 7.13 × 10⁻³ → This would be 0.00713, also incorrect.
- C. 7.13 × 10³ → This equals 7,130, which is too small.
- D. 7.13 × 10⁴ → This equals 71,300, correct!
Final Answer: D. 7.13 × 10⁴ ✅
