Question

Answer the following.
(a) The diameter of Uranus at its equator is approximately 5.11 x 10 to the power of 4 kilometers . Write this number in standard notation.
(b) An astronomer's infrared telescope is able to detect radiation with a wavelength of 0.00000768 meters. Write this number in scientific notation.

Answer 1

Answer:

(a) 51,100 kilometers.

(b) $y = 7.68 * 10^{-6}$ meters

Step-by-step explanation:

(a) When converting from scientific notation to standard notation, split the equation.

When solving $5.11 * 10^{4}$, begin by calculating $10^{4}$.

$10^{4}$ = 10,000

Multiply this by '5.11', resulting in:

5.11 × 10000 = 51,100 kilometers.

(b) When converting from standard form to scientific notation, count the number of zeros until the first non-zero digit. Therefore:

In 0.00000768, the '7' is placed 6 digits from the decimal. Recall that for decimals, the exponent is negative. Therefore in scientific notation, this equals: $y = 7.68 * 10^{-6}$