Question

1. which of the following digits is always significant?

any nonzero digit.
zeros without a decimal point.
zeros after a decimal point in a whole number.
zeros before the first nonzero digit.

1. how many significant figures does 0.00420 g have?

3
4
2
1

1. what is scientific notation?

a way to list numbers in order from smallest to largest.
a method of writing numbers between 1 and 10 multiplied by a power of 10.
a way to compare measurements.
a way to round numbers to the nearest whole number.

Explanation:

Question 4

To determine which digit is always significant, we analyze each option:

• "Any nonzero digit": By the rules of significant figures, all nonzero digits are always significant.
• "Zeros without a decimal point": These (trailing zeros in a whole number without a decimal) are ambiguous and not always significant (e.g., 100 could have 1 or 3 significant figures depending on context).
• "Zeros after a decimal point in a whole number": If the number is a whole number with a decimal (e.g., 100.), the trailing zeros are significant, but this is a specific case, not always applicable.
• "Zeros before the first nonzero digit": These are leading zeros and are never significant (e.g., 0.001 has 1 significant figure, the leading zeros don't count).

So the correct option is "Any nonzero digit".

To find the number of significant figures in \( 0.00420 \) g, we apply the rules:

• Leading zeros (the three zeros before 4) are not significant.
• The nonzero digits (4 and 2) are significant.
• The trailing zero after the decimal (after 2) is significant because it is after a nonzero digit and there is a decimal point.

So we count 4, 2, and 0 (the trailing one), which is 3 significant figures.

To identify the correct definition of scientific notation:

• "A way to list numbers in order from smallest to largest": This is ordering numbers, not scientific notation.
• "A method of writing numbers between 1 and 10 multiplied by a power of 10": This matches the definition of scientific notation (e.g., \( 3.2 \times 10^4 \)).
• "A way to compare measurements": Comparing measurements is not scientific notation.
• "A way to round numbers to the nearest whole number": Rounding is a different operation.

So the correct option is "A method of writing numbers between 1 and 10 multiplied by a power of 10".

Answer:

Any nonzero digit.

Question 5