1) Write 78,982,468 in scientific notation rounded off to 3 significant figures. A)
B)
C)
D)
E) None of the above 2) Perform the following calculation and round your answer to the correct number of significant figures:
A) 111.0 B) 111.05 C) 111.1 D) 111.10 E) 111.051 F) None of the above 3) Water is 88.8% oxygen by mass. What mass of water contains 77.7 g of oxygen? Make sure to show your math work, if you want to receive credit. A) 69.0 g B) 87.5 g C)
g D)
g E) None of the above 4) The speed of light is
m/s. Convert this to feet per nanosecond (ft/ns). Make sure to show your math work, if you want to receive credit. Useful unit equation: 1.000 meter = 3.281 ft A)
ft/ns B) 0.0914 ft/ns C) 0.984 ft/ns D)
ft/ns E) None of the above
The Correct Answer and Explanation is:
Let’s go through each of the four questions in the image and solve them with proper math and explanation.
1) Scientific Notation of 78,982,468 rounded to 3 significant figures
Step-by-step:
- Identify the first three significant figures: 7, 8, and 9.
- Convert to scientific notation: 78,982,468≈7.90×10778,982,468 \approx 7.90 \times 10^7
Answer: B) 7.90 × 10⁷
2) 91.421 + 19.63 rounded to correct sig figs
Step-by-step:
- Add the numbers:
91.421+19.63=111.05191.421 + 19.63 = 111.051 - Decimal places rule: Round to the least number of decimal places.
91.421 has 3 decimals, 19.63 has 2 → round to 2 decimals
Final result: 111.05
Answer: B) 111.05
3) Mass of water for 77.7 g of oxygen (88.8% O₂)
Step-by-step:
- Let the mass of water = xx
- Since water is 88.8% oxygen by mass: 0.888x=77.7⇒x=77.70.888≈87.5 g0.888x = 77.7 \Rightarrow x = \frac{77.7}{0.888} \approx 87.5 \, \text{g}
Answer: B) 87.5 g
4) Convert 3.00 × 10⁸ m/s to ft/ns
Step-by-step:
- 1 meter = 3.281 ft
- 1 nanosecond = 10−910^{-9} seconds
Convert m/s to ft/ns: 3.00×108 m/s×3.281 ft1 m×1 s109 ns=3.00×108×3.281109≈0.984 ft/ns3.00 \times 10^8 \, \text{m/s} \times \frac{3.281 \, \text{ft}}{1 \, \text{m}} \times \frac{1 \, \text{s}}{10^9 \, \text{ns}} = \frac{3.00 \times 10^8 \times 3.281}{10^9} \approx 0.984 \, \text{ft/ns}
Answer: C) 0.984 ft/ns
✅ Final Answers:
- B
- B
- B
- C
Explanation:
These problems test key scientific and mathematical skills. Question 1 focuses on scientific notation, which is used to express large numbers concisely. The number 78,982,468 rounded to 3 significant figures becomes 7.90 × 10⁷, where trailing zero holds significance.
Question 2 emphasizes the rules of significant figures in addition. When adding or subtracting, the result is limited by the least number of decimal places in the operands. 91.421 (3 decimals) + 19.63 (2 decimals) = 111.051, rounded to 2 decimal places gives 111.05.
In Question 3, a percentage problem is used to reverse-engineer the total mass based on a part (oxygen). Knowing that water is 88.8% oxygen allows us to set up an equation and solve for the whole. The simple algebra yields 87.5 g of water for 77.7 g of oxygen.
Question 4 integrates unit conversions with scientific notation. Speed of light is 3.00 × 10⁸ m/s. Converting meters to feet (using 3.281 ft/m) and seconds to nanoseconds (1 ns = 10⁻⁹ s) leads to a multiplication and division: 3.00×108×3.281/109=0.984 ft/ns3.00 \times 10^8 \times 3.281 / 10^9 = 0.984 \, \text{ft/ns}
These problems together highlight practical applications of scientific notation, significant figures, proportions, and unit conversions—all vital skills in science and engineering.
