Question

answer the following to complete tasks. 1. the distance from the earth to mars is 225,000,000 km. round it to 2 significant figures and express in scientific notation (include the unit). 2. explain why 0.0002000 has more significant figures than 0.0002.

Explanation:

Step1: Round 225000000 to 2 significant figures

The first two significant - figures are 22. Since the next digit (5) is 5 or greater, we round up. So 225000000 rounds to 230000000.

Step2: Convert to scientific notation

Scientific notation is of the form $a\times10^{n}$, where $1\leq a < 10$ and $n$ is an integer. For 230000000, $a = 2.3$ and $n = 8$. So the distance is $2.3\times10^{8}$ km.

Step3: Explain significant - figures for 0.0002000 and 0.0002

For 0.0002, the leading zeros are not significant. So it has 1 significant figure. For 0.0002000, the leading zeros are not significant, but the trailing zeros after the non - zero digit 2 are significant. So 0.0002000 has 4 significant figures. Trailing zeros in a decimal number are significant as they indicate the precision of the measurement.

Answer:

1. $2.3\times10^{8}$ km
2. In 0.0002, only the 2 is significant (leading zeros are not significant), so it has 1 significant figure. In 0.0002000, the 2 is significant and the three trailing zeros after 2 are also significant, so it has 4 significant figures.