(a) The signal from a certain satellite takes approximately 0.04 seconds to reach Earth. Write this number in scientific notation. (b) The total surface area of Asia is approximate... (a) The signal from a certain satellite takes approximately 0.04 seconds to reach Earth. Write this number in scientific notation. (b) The total surface area of Asia is approximately 1.72 x 10^7 square miles. Write this number in standard notation.

Question image

Understand the Problem

The question is asking to express a time duration in scientific notation and a surface area in standard notation. It involves converting 0.04 seconds to scientific notation and the surface area of Asia, which is given in scientific notation, into standard notation.

Answer

(a) $4.0 \times 10^{-2}$ seconds (b) $17,200,000$ square miles
Answer for screen readers

(a) $4.0 \times 10^{-2}$ seconds

(b) $17,200,000$ square miles

Steps to Solve

  1. Convert time duration to scientific notation

To convert $0.04$ seconds to scientific notation, we express it in the form $a \times 10^n$, where $1 \leq a < 10$.

Here, we can write:

$$ 0.04 = 4.0 \times 10^{-2} $$

  1. Convert surface area from scientific notation to standard notation

The surface area of Asia is given as $1.72 \times 10^7$ square miles. To convert this to standard notation, we multiply $1.72$ by $10^7$.

This is done by moving the decimal point seven places to the right:

$$ 1.72 \times 10^7 = 17200000 $$

(a) $4.0 \times 10^{-2}$ seconds

(b) $17,200,000$ square miles

More Information

In scientific notation, a number is expressed as a coefficient multiplied by a power of ten. The conversion from scientific notation to standard notation involves expanding the power of ten.

Tips

  1. Confusing Positive and Negative Exponents: When converting to scientific notation, some may mistakenly use a positive exponent instead of a negative for small numbers.
  2. Misplacing the Decimal: In converting scientific notation to standard notation, ensure you count the correct number of decimal places when moving the decimal point.

AI-generated content may contain errors. Please verify critical information

Thank you for voting!