Talking about significant figures, my Physics textbook lists 5 rules for determining significant figures. 1) All nonzero digits are significant. 2) Zeros to the right of nonzero digits in a number containing a decimal point are significant. 4) Zeros to the right of the decimal point, but the left of the first nonzero digit (such as .000324) are significant. 5) Zeros between nonzero digits (such as 26,007) are significant. I'm stuck on #3, which says: Zeros at the end of a number without a decimal point are ambiguous. It then lists a few examples: In 6800 there are two significant digits. In 10,000 there is one significant digit. In 650 there are three significant digits. Why is the zero in 650 significant, but not in 6800 and 10,000? Sorry if this question is confusing. Thanks for any and all help! :-)

No problem, I can help clarify that for you!

According to the third rule, zeros at the end of a number without a decimal point are considered ambiguous. This means that they may or may not be significant, depending on the context.

Let's take a closer look at the examples given in your textbook:

1) In 6800, there are two significant digits. The zeros at the end are not significant because there is no decimal point. These zeros act as placeholders to indicate the magnitude of the number but do not add any extra precision to the measurement.

2) In 10,000, there is one significant digit. Similarly, the zero at the end is not considered significant because there is no decimal point present.

3) In 650, there are three significant digits. Here, the zero is significant because it is located between two nonzero digits. This is the fifth rule, where zeros between nonzero digits are significant.

In summary, the position of the zero relative to the significant digits and the decimal point determines whether it is considered significant or not. If the zero is at the end of a number without a decimal point, it is generally considered ambiguous and should be clarified by additional information.

I hope this helps! Let me know if you have any further questions.

No problem! Let me help you understand why the zero in 650 is significant while the zeros in 6800 and 10,000 are not.

The principle behind this rule is to avoid ambiguity in the number of significant figures. Zeros at the end of a number without a decimal point can be uncertain because they could be trailing zeros due to the accuracy of the measurement or they could be simply placeholders in the magnitude of the number.

In the case of 650, the zero at the end represents the accuracy of the measurement, indicating that it has been measured to the nearest unit. Therefore, this zero is significant because it contributes to the precision of the value.

On the other hand, in the numbers 6800 and 10,000, the zeros at the end are placeholders, indicating the magnitude of the numbers rather than the precision of the values. These zeros do not provide any additional information about the measurement's accuracy, and therefore, they are not considered significant.

It's important to note that if these numbers were stated with a decimal point, such as 6800. or 10,000., then the zeros would be significant depending on the specific rules concerning decimals stated in your textbook.

Remember, when determining significant figures, it's crucial to follow the given rules to ensure accurate representation of the measurement's precision.