Question

using scientific measurements

1. a chemical reaction was carried out three times. the mass of the product was 8.93 g for the first trial, 8.94 g for the second trial, and 8.92 g for the third trial. under the conditions of the experiment, the reaction is known to yield 8.60 g of product. the three mass values measured are

a. accurate.
b. precise.
c. both accurate and precise.
d. neither accurate nor precise.

1. for numbers less than 0.1, such as 0.06, the zeros to the right of the decimal point but before the first nonzero digit

a. are significant.
b. show the decimal place of the first digit.
c. show that the zero on the left side of the decimal is not significant.
d. are always uncertain.

1. the number of significant figures in the measurement 0.000305 kg is

a. two.
b. three.
c. six.
d. seven.

1. written in scientific notation, the measurement 0.000065 cm is

a. 6.5 x 10⁻⁴ cm
b. 6.5 x 10⁻⁵ cm
c. 6.5 x 10⁻⁶ cm
d. 6.5 x 10⁵ cm

1. when the difference between a measured value and the known value is expressed as percentage error, it is usually written as

a. a positive number.
b. a negative number.
c. both positive and negative.
d. either a negative number or a positive number.

1. a measurement is accurate if it

a. is reproducible.
b. is close to the true value.
c. has many decimal places.
d. has many significant figures.

Explanation:

• Question 24: Precision refers to the closeness of repeated measurements to each other. The values 8.93 g, 8.94 g, and 8.92 g are close to each other, so they are precise. Accuracy is closeness to the true - value (8.60 g in this case), and these values are not close to 8.60 g, so they are not accurate.
• Question 25: Zeros to the right of the decimal point but before the first non - zero digit are placeholders that show the decimal place of the first digit.
• Question 26: In 0.000305, the leading zeros are not significant. The significant figures are 3, 0, and 5, so there are three significant figures.
• Question 27: To write 0.000065 in scientific notation, we move the decimal point 5 places to the right to get a number between 1 and 10 (6.5) and multiply by 10⁻⁵.
• Question 28: Percentage error is calculated as $\frac{\text{measured value}-\text{known value}}{\text{known value}}\times100\%$. The difference can be positive or negative depending on whether the measured value is greater or less than the known value.
• Question 29: Accuracy is defined as how close a measurement is to the true value.

Answer:

1. b. precise
2. b. show the decimal place of the first digit
3. b. three
4. b. $6.5\times10^{- 5}$ cm
5. d. either a negative number or a positive number
6. b. is close to the true value