Fill in the blanks. In scientific notation, 360,000 = \boxed{} \times 10^{\boxed{}}.
The Correct Answer and Explanation is:
Of course! Here are the correct numbers to fill in the blanks, along with a detailed explanation.
Answer:
360,000 = 3.6 × 10⁵
Explanation:
The problem requires converting the standard number 360,000 into scientific notation. Scientific notation is a method used to express very large or very small numbers concisely. It follows the format a × 10ᵇ, where:
- ‘a’ is the coefficient, a number that must be greater than or equal to 1 but less than 10 (1 ≤ |a| < 10).
- ‘b’ is the exponent, an integer representing the power of 10.
Here is the step-by-step process to convert 360,000:
1. Find the Coefficient (a):
First, we need to find a number between 1 and 10 by moving the decimal point in 360,000. In a whole number, the decimal point is understood to be at the end (360,000.). To create a coefficient between 1 and 10, we must move the decimal point so that only one non-zero digit is to its left. For 360,000, we move the decimal point to sit between the ‘3’ and the ‘6’.
This gives us the coefficient 3.6. This number correctly fills the first blank.
2. Find the Exponent (b):
Next, we determine the exponent by counting the number of places the decimal point was moved.
Original position: 360,000.
New position: 3.60000
We moved the decimal point 5 places to the left.
- The direction of the move determines the sign of the exponent. Since we moved the decimal to the left for a large number (a number greater than 1), the exponent is positive.
- The number of places moved determines the value of the exponent.
Therefore, the exponent is +5. This number fills the second blank (the superscript box).
3. Final Result and Verification:
By combining the coefficient and the exponent, we get the final expression in scientific notation: 3.6 × 10⁵.
We can verify this is correct by performing the calculation:
10⁵ = 10 × 10 × 10 × 10 × 10 = 100,000.
3.6 × 100,000 = 360,000.
This matches the original number, confirming our answer is correct.
