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Ch.1 - Introduction: Matter, Energy, and Measurement
All textbooksBrown 15th EditionCh.1 - Introduction: Matter, Energy, and MeasurementProblem 51
Chapter 1, Problem 51

Carry out the following operations and express the answers in exponential notation with the appropriate number of significant figures.
a. 2.791×104 + 8.76×103
b. 4.67×102 − 5.4437×104
c. (2.481×10−2 + 7.33×10−4) × (1.924×10−2 + 6.70)
d. (1.3×10−4 − 3.746×10−2)/(1.3×102 − 3.746×104)

Verified step by step guidance
1
a. Align the exponents for the addition: Convert 8.76×10^3 to 0.876×10^4.
a. Add the coefficients: 2.791 + 0.876 = 3.667.
a. Express the result in exponential notation: 3.667×10^4.
a. Determine the number of significant figures: The result should have 3 significant figures, so round to 3.67×10^4.
b. Align the exponents for the subtraction: Convert 4.67×10^2 to 0.0467×10^4.
b. Subtract the coefficients: 0.0467 - 5.4437 = -5.397.
b. Express the result in exponential notation: -5.397×10^4.
b. Determine the number of significant figures: The result should have 3 significant figures, so round to -5.40×10^4.
c. Perform the addition inside the parentheses: 2.481×10^−2 + 7.33×10^−4 = 2.5543×10^−2.
c. Perform the addition inside the parentheses: 1.924×10^−2 + 6.70 = 6.71924.
c. Multiply the results: 2.5543×10^−2 × 6.71924.
c. Express the result in exponential notation with the appropriate significant figures.
d. Perform the subtraction in the numerator: 1.3×10^−4 - 3.746×10^−2.
d. Perform the subtraction in the denominator: 1.3×10^2 - 3.746×10^4.
d. Divide the results from the numerator and denominator.
d. Express the result in exponential notation with the appropriate 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. When performing calculations, the result should be reported with the same number of significant figures as the measurement with the least number of significant figures to ensure accuracy.
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Exponential Notation

Exponential notation is a way of expressing numbers that are too large or too small to be conveniently written in decimal form. It is represented as a product of a number (the coefficient) and a power of ten. For example, 2.5 × 10^3 represents 2500. This notation simplifies calculations, especially when dealing with very large or very small quantities.
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Order of Operations

The order of operations is a set of rules that dictates the sequence in which calculations should be performed to ensure consistent results. The common acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) helps remember this order. Following these rules is crucial when performing multiple operations in a single expression, especially in scientific calculations.
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Textbook Question

Carry out the following operations and express the answers in exponential notation with the appropriate number of significant figures.

a. 2.791×104 + 8.76×103

b. 4.67×102 − 5.4437×104

c. (2.481×10−2 + 7.33×10−4) × (1.924×10−2 + 6.70)

d. (1.3×10−4 − 3.746×10−2)/(1.3×102 − 3.746×104)

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