Textbook Question
Write each of the following in scientific notation with two significant figures:
d. 0.000 25 cm
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Ch.2 Chemistry and Measurements
Timberlake14th EditionChemistry: An Introduction to General, Organic, and Biological ChemistryISBN: 9781292472249
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Table of contents
- Ch.1 Chemistry in Our Lives19
- Ch.2 Chemistry and Measurements80
- Ch.3 Matter and Energy53
- Ch.4 Atoms and Elements58
- Ch.5 Nuclear Chemistry42
- Ch.6 Ionic and Molecular Compounds57
- Ch.7 Chemical Quantities and Reactions38
- Ch.8 Gases30
- Ch.9 Solutions50
- Ch.10 Acids and Bases and Equilibrium64
- Ch.11 Introduction to Organic Chemistry: Hydrocarbons77
- Ch.12 Alcohols, Thiols, Ethers, Aldehydes, and Ketones82
- Ch.13 Carbohydrates54
- Ch.14 Carboxylic Acids, Esters, Amines, and Amides91
- Ch.15 Lipids61
- Ch.16 Amino Acids, Proteins, and Enzymes84
- Ch.17 Nucleic Acids and Protein Synthesis86
- Ch.18 Metabolic Pathways and ATP Production73
Timberlake14th EditionChemistry: An Introduction to General, Organic, and Biological ChemistryISBN: 9781292472249Not the one you use?Change textbook
Chapter 2, Problem 16
Indicate if the zeros are significant in each of the following measurements:
a. 20.05 °C
b. 5.00 m
c. 0.000 02 g
d. 120 000 yr
e. 8.05 × 102 L
Verified step by step guidance1
Step 1: Understand the rules for determining significant figures. Zeros are significant if they are (a) between nonzero digits, (b) at the end of a number with a decimal point, or (c) in scientific notation as part of the coefficient. Leading zeros (zeros before the first nonzero digit) are not significant, and trailing zeros in a number without a decimal point are ambiguous unless specified.
Step 2: Analyze part (a) 20.05 °C. The zeros are between nonzero digits, so they are significant. This measurement has four significant figures.
Step 3: Analyze part (b) 5.00 m. The zeros are at the end of the number and there is a decimal point, so they are significant. This measurement has three significant figures.
Step 4: Analyze part (c) 0.000 02 g. The leading zeros (zeros before the first nonzero digit) are not significant. Only the '2' is significant, so this measurement has one significant figure.
Step 5: Analyze parts (d) and (e). For (d) 120 000 yr, the trailing zeros are ambiguous because there is no decimal point, so it is unclear how many are significant. For (e) 8.05 x 10² L, the zero is between nonzero digits, so it is significant. This measurement has three significant figures.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Significant Figures
Significant figures are the digits in a number that contribute to its precision. This includes all non-zero digits, any zeros between significant digits, and trailing zeros in the decimal portion. Understanding significant figures is crucial for determining which zeros in a measurement are significant, as they indicate the precision of the measurement.
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Significant Figures (Simplified) Example 2
Leading Zeros
Leading zeros are the zeros that precede all non-zero digits in a number. They are not considered significant because they do not affect the value of the number. For example, in the measurement 0.000 02 g, the leading zeros are not significant, while the '2' is significant.
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Trailing Zeros
Trailing zeros are the zeros that follow non-zero digits in a number. Their significance depends on the presence of a decimal point. In a measurement like 20.05 °C, all zeros are significant, while in a whole number without a decimal, such as 120,000 yr, the trailing zeros may not be significant unless specified otherwise.
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Related Practice
Textbook Question
Identify the numbers in each of the following statements as measured or exact:
a. Sandra has a patient with a mass of 67.5 kg.
Textbook Question
Use the metric ruler to measure the length in each of the following, and write the measurement, the estimated digit, and the number of significant figures:
a. <IMAGE>
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Textbook Question
In which of the following pairs do both numbers contain the same number of significant figures?
a. 11.0 m and 11.00 m
b. 0.0250 m and 0.205 m
c. 0.000 12 s and 12 000 s
d. 250.0 L and 2.5 × 10-2 L
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Textbook Question
In which of the following pairs do both numbers contain the same number of significant figures?
a. 0.005 75 g and 5.75 × 10-3 g
b. 405 K and 405.0 K
c. 150 000 s and 1.50 × 104 s
d. 3.8 × 10-2 L and 3.0 × 105 L
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Textbook Question
Write each of the following in scientific notation with two significant figures:
c. 100 000 m
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