Question

Multiplying with Scientific Notation

Use the calculator to find the product of 4.17 and 2.3 × 106. Which statements are true about finding the product? Check all that apply.

4.17 is equivalent to 4.17 × 100.

4.17 is equivalent to 4.17 × 101.

The product has a positive exponent.

The coefficient is 6.

The E in the product is the indicator that the solution is in scientific notation.

The exponent of the product is the product of the original exponents.

Answer 1

First find the product:
4.17 × (2.3 × 10^6) = (4.17 × 2.3) × 10^6 = 9.591 × 10^6.

Now check the statements:

- 4.17 is equivalent to 4.17 × 100. — False (that would be 417).
- 4.17 is equivalent to 4.17 × 101. — False (that would be 41.7 if meant 10^1, or 417 if meant 101). The correct form is 4.17 × 10^0.
- The product has a positive exponent. — True (9.591 × 10^6, exponent is +6).
- The coefficient is 6. — False (the coefficient is 9.591).
- The E in the product is the indicator that the solution is in scientific notation. — True (e.g., 9.591E6 means 9.591 × 10^6).
- The exponent of the product is the product of the original exponents. — False (exponents add when multiplying powers of 10).