A certain solution has a hydrogen ion concentration of 0.00000165 moles per liter. Write this number in scientific notation. An African bush elephant can weigh up to 2.8 × 10^4 pou... A certain solution has a hydrogen ion concentration of 0.00000165 moles per liter. Write this number in scientific notation. An African bush elephant can weigh up to 2.8 × 10^4 pounds. Write this number in standard notation.

Understand the Problem

The question is asking to convert two measurements into specific notations: (a) the hydrogen ion concentration to scientific notation and (b) the weight of the African bush elephant to standard notation.

Answer

(a) $1.65 \times 10^{-6}$ moles per liter (b) $28000$ pounds

Steps to Solve

Converting Hydrogen Ion Concentration to Scientific Notation

To convert the number (0.00000165) to scientific notation, we need to move the decimal point to the right until we have a number between 1 and 10.

The decimal moves 6 places to the right:

$$ 0.00000165 = 1.65 \times 10^{-6} $$

Writing the Weight of the African Bush Elephant in Standard Notation

To convert (2.8 \times 10^4) to standard notation, we need to multiply (2.8) by (10,000) (since (10^4 = 10,000)):

$$ 2.8 \times 10^4 = 2.8 \times 10000 = 28000 $$

(a) (1.65 \times 10^{-6}) moles per liter

(b) (28000) pounds

More Information

In scientific notation, a number is expressed as a product of a number between 1 and 10 and a power of 10. This is useful for representing very large or very small numbers conveniently. Standard notation is simply the regular way we write numbers.

Tips

For Scientific Notation: A common mistake is misplacing the decimal point or not counting the shifts accurately. Be careful to count the number of places you move the decimal.
For Standard Notation: A mistake can occur if someone forgets to actually multiply with (10,000) and only writes (2.8) instead of converting it properly.

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