Question 1: Round 0.00456789 to 3 significant figures.

Answer: 0.00457

Question 2: Round 12345.6789 to 4 significant figures.

Answer: 12350

Question 3: Express 987654321 in scientific notation rounded to 3 significant figures.

Answer: 9.88×10^8

Question 4: Round 0.000987654 to 3 significant figures.

Answer: 0.000988

Question 1: A scientist records a measurement as 0.0003456789 grams. Round this to 4 significant figures and explain why.

Answer: 0.0003457; because the first four significant figures are 3, 4, 5, and 7, and the fifth digit (8) causes rounding up.

Question 2: A car's speed is measured as 123.456789 km/h. Round to 3 significant figures and justify your choice.

Answer: 123 km/h; because the first three significant figures are 1, 2, and 3, and the remaining digits are dropped with rounding.

Question 3: In a calculation, you multiply 3.4567×10^4 by 0.000123456. Round your answer to 3 significant figures.

Answer: 4.26

Question 1: A researcher measures the density of a substance as 2.456789 g/cm^3. Rounded to 3 significant figures, what is the density? Why is it important to specify the number of significant figures in reporting measurements?

Answer: 2.46 g/cm^3; because the first three significant figures are 2, 4, and 6, with rounding after the third digit. Specifying significant figures communicates the precision of the measurement.

Question 2: A company's annual revenue is reported as $1,234,567,890. Rounded to 3 significant figures, what is the figure? Discuss how this impacts the interpretation of the data.

Answer: $1.23×10^9$; because the first three significant figures are 1, 2, and 3, and this form emphasizes the scale while maintaining significant information.

Question 1: Construct a triangle on the grid where the side lengths are 3.456, 7.891, and 2.345, each rounded to 3 significant figures. Describe your process.

Answer: Sides rounded to 3 sf: 3.46, 7.89, 2.35; draw the triangle with these lengths, ensuring the rounded lengths are accurately represented.

Question 2: A physics experiment records a voltage as 0.000987654321 volts. Round to 4 significant figures, then calculate the voltage squared, rounded to 3 significant figures.

Answer: 0.000988; voltage squared = (0.000988)^2 ≈ 9.76×10^-7, rounded to 3 sf as 9.76×10^-7

Question 1: Express 0.000456789 in scientific notation rounded to 3 significant figures.

Answer: 4.57×10^-4

Question 2: Calculate 12500 divided by 3. Rounded to 3 significant figures, what is the result?

Answer: 4170

Question 3: A measurement is recorded as 0.0056789. Identify and correct a common mistake made when rounding to 3 significant figures.

Answer: Incorrect: 0.00568; Correct: 0.005679; because the third significant digit is 8, which does not cause rounding up.