Question 1: Round 0.0056789 to 3 significant figures.

Answer: 0.00568

Question 2: Round 12345.6789 to 4 significant figures.

Answer: 12350

Question 3: Express 0.000987654 in scientific notation rounded to 3 significant figures.

Answer: 9.88×10⁻⁴

Question 4: Round 987654321 to 3 significant figures.

Answer: 9.88×10⁸

Question 1: A car's speed is measured as 123.456789 km/h. Round this to 4 significant figures and explain why this is appropriate for reporting the speed.

Answer: 123.5 km/h

Question 2: A scientist records a measurement as 0.000456789. After rounding to 3 significant figures, what is the new measurement? Justify your rounding decision.

Answer: 0.000457

Question 3: A quantity is reported as 5.6789×10⁴. What is the number rounded to 3 significant figures? Write your answer in standard form.

Answer: 5.68×10⁴

Question 4: Explain why rounding 2.34567 to 3 significant figures as 2.35 might be considered a mistake in some scientific contexts.

Answer: Because 2.35 rounds the number incorrectly, potentially losing precision; the correct rounding is 2.35 only if the third digit is 5 or more. Otherwise, it should be 2.34 if rounding down is preferred, but generally, 2.35 is correct here.

Question 1: A construction project estimates the amount of gravel needed as 12345.6789 kg. Round this to 3 significant figures for an order of magnitude estimate.

Answer: 1.23×10⁴ kg

Question 2: A pharmaceutical company records a drug concentration as 0.000987654 mg/mL. If they report this to 3 significant figures for standard lab reports, what is the rounded value?

Answer: 0.000988 mg/mL

Question 1: A measurement reads 9876543.21 in scientific notation. Round this to 3 significant figures and convert back to standard form.

Answer: 9.88×10⁶

Question 2: A recent physics experiment reports a value as 0.000123456789. After rounding to 3 significant figures, what potential errors could occur if this value is used in subsequent calculations?

Answer: Loss of precision could lead to significant errors in calculations, especially if the rounded value is used in further multiplications or divisions, magnifying initial inaccuracies.

Question 1: Identify the mistake in rounding 0.00456789 to 3 significant figures as 0.00456. Correct the rounding and justify your reasoning.

Answer: The correct rounding is 0.004568 because the fourth digit is 7, which means the third digit should be rounded up from 6 to 7.

Question 2: A student rounds 123.456 to 3 significant figures as 123. This is correct or not? Explain.

Answer: It is correct because 123 has three significant figures. The zeros after 3 are not significant.

Question 3: A figure is given as 9.8765×10⁻³. If rounded incorrectly to 9.87×10⁻³, what is the potential impact in a scientific context?

Answer: Rounding incorrectly can cause small but critical errors in sensitive calculations, affecting the accuracy of experimental results or models.