Praxis Core Academic Skills for Educators: Mathematics (5733)Number and QuantityMedium
A scientist is observing the growth of a crystal. The crystal's length is currently 3.2 x 10^-4 meters. If it grows by 2.5 x 10^-5 meters each day, what will its length be after 2 days?
- A5.7 x 10^-4 meters
- B3.45 x 10^-4 meters
- C3.7 x 10^-4 meters
- D5.7 x 10^-5 meters
Show answer & explanationAnswer & explanation
Correct answer: C. 3.7 x 10^-4 meters
First, calculate the total growth over 2 days: 2.5 x 10^-5 meters/day * 2 days = 5.0 x 10^-5 meters. Next, convert the initial length to the same exponent as the growth: 3.2 x 10^-4 = 32 x 10^-5 meters. Now add the total growth: 32 x 10^-5 + 5 x 10^-5 = 37 x 10^-5 meters. Convert back to standard scientific notation: 3.7 x 10^-4 meters.
Why the other options are wrong
- A. This might result from an error in the initial exponent conversion or miscalculation.
- B. This might result from adding only one day's growth or an error in exponent alignment.
- D. This might result from adding the exponents or an error in converting 3.2 x 10^-4 to 32 x 10^-5.
Adding Numbers in Scientific Notation
To add or subtract numbers in scientific notation, their exponents must be the same. Adjust one number's coefficient and exponent if necessary, then add/subtract the coefficients.
- Exponents must match before addition/subtraction.
- Adjusting the exponent requires moving the decimal point in the coefficient.
- The final answer should be in standard scientific notation (coefficient between 1 and 10).
Memory trick: Align the power, then add the number!