Write the following quotient in scientific notation.
(1.9 × 10⁸) ÷ (2 × 10³)
□×10⁴
(1.9 × 10⁸) ÷ (2 × 10³) can be simplified as follows:
(1.9 ÷ 2) × (10⁸ ÷ 10³)
0.95 × 10⁵
Therefore, the given quotient in scientific notation is 0.95 × 10⁵.
To write the given quotient in scientific notation, we need to multiply the two numbers together and adjust the decimal place to obtain a number between 1 and 10. Here's how:
1. First, multiply the two numbers:
(1.9 × 10⁸) ÷ (2 × 10³) = (1.9 ÷ 2) × (10⁸ ÷ 10³)
2. Simplify the quotient inside the parentheses:
(1.9 ÷ 2) = 0.95
3. Simplify the powers of 10:
10⁸ ÷ 10³ = 10⁵
4. Multiply the simplified numbers together:
0.95 × 10⁵
5. Adjust the decimal place to make the number between 1 and 10. In this case, the decimal point needs to be moved 5 places to the right:
0.95 × 10⁵ = 9.5 × 10⁴
Therefore, the quotient (1.9 × 10⁸) ÷ (2 × 10³) is equal to 9.5 × 10⁴ in scientific notation.
To divide the given numbers in scientific notation, you follow these steps:
Step 1: Divide the coefficients (numbers in front).
1.9 ÷ 2 = 0.95
Step 2: Divide the exponents.
10⁸ ÷ 10³ = 10⁵
Step 3: Combine the results from steps 1 and 2 and place them in scientific notation.
The quotient in scientific notation is 0.95 × 10⁵.
Note that we kept the same base (10) and added the exponents since dividing by a number in scientific notation is the same as dividing by the coefficients and subtracting the exponents.