A certain solution has a hydrogen ion concentration of 6.53 x 10^{-5} moles per liter. Write this number in standard notation. A hippopotamus can weigh up to 9900 pounds. Write thi... A certain solution has a hydrogen ion concentration of 6.53 x 10^{-5} moles per liter. Write this number in standard notation. A hippopotamus can weigh up to 9900 pounds. Write this number in scientific notation.
Understand the Problem
The question is asking us to convert a given hydrogen ion concentration from scientific notation to standard notation and also to express the weight of a hippopotamus given in pounds into scientific notation.
Answer
(a) $0.0000653$ moles per liter (b) $9.9 \times 10^{3}$ pounds
Answer for screen readers
(a) $0.0000653$ moles per liter
(b) $9.9 \times 10^{3}$ pounds
Steps to Solve
- Convert Hydrogen Ion Concentration to Standard Notation
Start with the scientific notation $6.53 \times 10^{-5}$.
To convert this to standard notation, move the decimal point 5 places to the left:
$$ 6.53 \rightarrow 0.0000653 $$
So, the hydrogen ion concentration in standard notation is $0.0000653$ moles per liter.
- Convert Weight of Hippopotamus to Scientific Notation
The weight of the hippopotamus is given as $9900$ pounds.
To express this in scientific notation, identify the significant figures and position the decimal:
$$ 9900 = 9.9 \times 10^{3} $$
Therefore, the weight in scientific notation is $9.9 \times 10^{3}$ pounds.
(a) $0.0000653$ moles per liter
(b) $9.9 \times 10^{3}$ pounds
More Information
- The conversion from scientific to standard notation involves moving the decimal point according to the exponent's value. A negative exponent indicates moving left, while a positive exponent indicates moving right.
- Scientific notation is useful for expressing large or small numbers succinctly, allowing easy comparison and calculation.
Tips
- For part (a): A common mistake is forgetting to move the decimal the correct number of places based on the exponent. Remember that a negative exponent indicates a left shift.
- For part (b): Some may not consider significant figures correctly or may misplace the decimal when converting to scientific notation. Double-check that the number you write is in the form $a \times 10^{n}$, where $1 \leq a < 10$.
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