Praxis Core Academic Skills for Educators: Mathematics (5733)Number and QuantityHard
A technician is weighing chemical samples. Sample A weighs 0.00000000000035 grams. Sample B weighs 8.2 x 10^-14 grams. What is the difference in weight between Sample A and Sample B?
- A5.7 x 10^-14 grams
- B5.7 x 10^-13 grams
- C4.7 x 10^-14 grams
- D4.7 x 10^-13 grams
Show answer & explanationAnswer & explanation
Correct answer: C. 4.7 x 10^-14 grams
To find the difference, both numbers are already in scientific notation with the same exponent (10^-14). Subtract the smaller coefficient from the larger coefficient: 8.2 x 10^-14 grams - 3.5 x 10^-14 grams = (8.2 - 3.5) x 10^-14 grams = 4.7 x 10^-14 grams.
Why the other options are wrong
- A. This might result from an arithmetic error during subtraction.
- B. This might result from an error in exponent manipulation or miscalculation.
- D. This might result from an error in exponent manipulation or miscalculation.
Subtracting Numbers in Scientific Notation (Same Exponents)
When subtracting numbers in scientific notation that share the same exponent, simply subtract their coefficients and keep the common exponent. Ensure the result is in standard scientific notation.
- Exponents must be identical for direct subtraction.
- Subtract the coefficients (the numerical parts).
- The exponent of 10 remains unchanged.
- Resulting coefficient should be between 1 and 10 (normalize if needed).
Memory trick: Exponents match, then subtract the batch!