Question

Which zeros are significant in the following values?

a. 25.050 g
b. 12,500 mi
c. 0.00250 kg
d. 1.0250 L
e. 5,000,500 s
f. 1.302 x 10^15 atoms

Answer 1

a. 25.050 g: 4 significant figures (trailing zeros in a decimal), b. 12,500 mi: 3 significant figures (trailing zeros in a whole number without a decimal), c. 0.00250 kg: 3 significant figures (trailing zeros in a decimal), d. 1.0250 L: 5 significant figures (trailing zeros in a decimal), e. 5,000,500 s: 7 significant figures (zeros in a large number without a decimal), f. 1.302 x 10^15 atoms: 4 significant figures (all zeros in scientific notation are significant).

This correct answer is above all.

Step-by-step explanation:

In the context of significant figures, zeros can be categorized as follows:

Leading Zeros:

Leading zeros are zeros that precede all non-zero digits in a decimal number.

Leading zeros are not considered significant.

Examples:

In 0.00250 kg (c), the leading zeros before 2 are not significant.

Trailing Zeros in a Decimal:

Trailing zeros that appear to the right of a non-zero digit in a decimal number are considered significant.

Examples:

In 25.050 g (a), the trailing zero after 5 is significant.

In 1.0250 L (d), the trailing zero after 5 is significant.

In 0.00250 kg (c), the trailing zero after 2 is significant.

Trailing Zeros in a Whole Number without a Decimal:

Trailing zeros in a whole number without a decimal point are not considered significant unless a decimal point is explicitly stated.

Examples:

In 12,500 mi (b), the trailing zeros are not considered significant unless a decimal point is explicitly stated.

Zeros in Scientific Notation:

All zeros in the coefficient of a number written in scientific notation are considered significant.

Example:

In 1.302 x 10^15 atoms (f), all the digits in the coefficient (1.302) are considered significant.

Zeros in Large Numbers:

Zeros in large numbers without a decimal point are considered significant.

Example:

In 5,000,500 s (e), all the zeros are considered significant.

In summary:

a. 25.050 g - 4 significant figures (trailing zeros in a decimal)

b. 12,500 mi - 3 significant figures (trailing zeros in a whole number without a decimal)

c. 0.00250 kg - 3 significant figures (leading zeros are not counted, but trailing zeros in a decimal are counted)

d. 1.0250 L - 5 significant figures (trailing zeros in a decimal)

e. 5,000,500 s - 7 significant figures (zeros in a large number without a decimal)

f. 1.302 x 10^15 atoms - 4 significant figures (all zeros in scientific notation are significant)

This correct answer is above all.

Answer 2

The zeros that are significant in each value are explained with examples.

Step-by-step explanation:

In each value, the zeros that are significant are the ones that occur between nonzero digits, or at the end of a number with a decimal point.

a. 25.050 g - All the zeros are significant, as they occur between nonzero digits.

b. 12,500 mi - All the zeros are significant, as they occur between nonzero digits.

c. 0.00250 kg - The zeros before the decimal point are not significant. The zeros after the decimal point are significant, as they occur between nonzero digits.

d. 1.0250 L - All the zeros are significant, as they occur between nonzero digits.

e. 5,000,500 s - The zeros at the beginning and end of the number are not significant. The zero in the middle is significant, as it occurs between nonzero digits.

f. 1.302 x 10^15 atoms - All the zeros are significant, as they occur between nonzero digits.