Scientific Notation Trivia Questions

Explanation
The given number, 0.0006730, can be written in scientific notation as 6.730 x 10^-4. In scientific notation, the number is expressed as a decimal between 1 and 10 multiplied by a power of 10. In this case, the decimal is 6.730 and the power of 10 is -4, indicating that the decimal point is moved 4 places to the left.

Explanation
The given number, 50 000.0, can be written in scientific notation as 5.000 00 x 10^4. In scientific notation, the number is represented as a decimal number between 1 and 10 (in this case, 5.000 00), multiplied by a power of 10 (in this case, 10^4). This notation is commonly used to represent very large or very small numbers in a concise and standardized form.

Explanation
The given number, 4.000 05 x 10^7, is written in scientific notation. To convert it to ordinary notation, we multiply the decimal part (4.000 05) by the power of 10 (10^7). This gives us 40 000 5000.

Explanation
The given number, 7.050 x 10^-3, is written in scientific notation. To convert it into ordinary notation, we can simply move the decimal point three places to the left, as the exponent -3 indicates a negative power of 10. Therefore, the ordinary notation for 7.050 x 10^-3 is 0.007050.

Explanation
The given expression is the sum of two numbers in scientific notation. To add numbers in scientific notation, we need to make sure that the exponents are the same. In this case, we can rewrite 8.205 x 10^4 as 82.05 x 10^3 and 7.266 x 10^2 as 0.7266 x 10^3. Now, we can add the two numbers together, which gives us 82.05 x 10^3 + 0.7266 x 10^3 = 82.7766 x 10^3. Finally, we can convert this back to scientific notation, which gives us 8.278 x 10^4. Therefore, the correct answer is 8.278 x 10^4.

Explanation
The given expression involves subtracting two numbers written in scientific notation. To subtract these numbers, we need to make sure that the exponents are the same. In this case, both numbers have an exponent of -2. We can then subtract the coefficients: 3.5011 - 9.2448 = -5.7437. Since the exponent remains the same, the answer is -5.7437 x 10^-2. However, scientific notation is typically written with a positive coefficient, so we can rewrite this as -0.057437 x 10^-2. Finally, we can round this to two significant figures, resulting in the answer 2.5766 x 10^-2.

Explanation
The given expression is a multiplication of two numbers in scientific notation. To multiply numbers in scientific notation, we multiply the coefficients and add the exponents. In this case, we have (8.61 x 10^5) multiplied by (7.9304 x 10^-8). Multiplying the coefficients gives us 68.175084, and adding the exponents gives us 10^-3. Therefore, the product is 6.8175084 x 10^-3, which can be approximated as 6.83 x 10^-3 in scientific notation.

Explanation
The given expression is a division of two numbers in scientific notation. To divide numbers in scientific notation, we subtract the exponents and divide the coefficients. In this case, the coefficient 2.35 divided by 1.00 gives us 2.35, and the exponents 6 minus 4 gives us 2. Therefore, the answer is 2.35 x 10^2.