Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN: 9780134463216
Author: Robert F. Blitzer
Publisher: PEARSON
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Statements and Logic
Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.
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The image contains three mathematical expressions involving scientific notation. Each expression ends with an equals sign and a blank box, indicating that the solution should be written there. 1. **Expression 1:** \( 1.00 \times 10^{-8} + 1.51 \times 10^{4} = \) [Blank Box] This expression involves the addition of two numbers in scientific notation. The first term is \( 1.00 \times 10^{-8} \) (a very small number), and the second term is \( 1.51 \times 10^{4} \) (a larger number). 2. **Expression 2:** \[ \frac{1.51 \times 10^{4} + 9.54 \times 10^{5}}{6.89 \times 10^{4}} = \] This is a fraction where the numerator also involves adding two terms in scientific notation: \( 1.51 \times 10^{4} \) and \( 9.54 \times 10^{5} \). The denominator is \( 6.89 \times 10^{4} \). 3. **Expression 3:** \[ \frac{3.00 \times 10^{-6}}{(1.00 \times 10^{-8})(1.51 \times 10^{4})} = \] This is a division problem where the numerator is \( 3.00 \times 10^{-6} \), and the denominator involves the product of two terms in scientific notation: \( 1.00 \times 10^{-8} \) and \( 1.51 \times 10^{4} \). These expressions test the student's ability to handle and manipulate scientific notations, including addition, multiplication, and division of numbers in this format.
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Transcribed Image Text:The image contains three mathematical expressions involving scientific notation. Each expression ends with an equals sign and a blank box, indicating that the solution should be written there. 1. **Expression 1:** \( 1.00 \times 10^{-8} + 1.51 \times 10^{4} = \) [Blank Box] This expression involves the addition of two numbers in scientific notation. The first term is \( 1.00 \times 10^{-8} \) (a very small number), and the second term is \( 1.51 \times 10^{4} \) (a larger number). 2. **Expression 2:** \[ \frac{1.51 \times 10^{4} + 9.54 \times 10^{5}}{6.89 \times 10^{4}} = \] This is a fraction where the numerator also involves adding two terms in scientific notation: \( 1.51 \times 10^{4} \) and \( 9.54 \times 10^{5} \). The denominator is \( 6.89 \times 10^{4} \). 3. **Expression 3:** \[ \frac{3.00 \times 10^{-6}}{(1.00 \times 10^{-8})(1.51 \times 10^{4})} = \] This is a division problem where the numerator is \( 3.00 \times 10^{-6} \), and the denominator involves the product of two terms in scientific notation: \( 1.00 \times 10^{-8} \) and \( 1.51 \times 10^{4} \). These expressions test the student's ability to handle and manipulate scientific notations, including addition, multiplication, and division of numbers in this format.
Certainly! Below is a transcription of the text as it would appear on an educational website, along with detailed explanations of any mathematical operations or notations. --- ### Scientific Notation Practice Problems Scientific notation is a way to express very large or very small numbers conveniently. Below are a few practice problems that involve multiplication, division, and combining these operations in scientific notation. 1. **Multiplication Problem:** \[ (2.83 \times 10^6) \cdot (9.54 \times 10^5) = \_\_\_\_\_\_ \] - In this problem, you need to multiply two numbers that are expressed in scientific notation. Remember to multiply the coefficients (2.83 and 9.54) and then add the exponents of 10. 2. **Division Problem:** \[ \frac{1.51 \times 10^4}{6.89 \times 10^4} = \_\_\_\_\_\_ \] - Here, you need to divide two numbers in scientific notation. Divide the coefficients (1.51 by 6.89) and subtract the exponents of 10. 3. **Combined Multiplication and Division:** \[ \frac{(3.00 \times 10^{-6}) \cdot (3.00 \times 10^{-5})}{(1.00 \times 10^{-8}) \cdot (1.51 \times 10^4)} = \_\_\_\_\_\_ \] - This problem involves both multiplication and division of numbers in scientific notation. First, multiply the numerators together and the denominators together, then divide the results. Multiply and divide the coefficients and handle the exponents accordingly (adding exponents when multiplying and subtracting when dividing). When solving these problems: - **Multiplication rule for exponents:** \( (a \times 10^b) \cdot (c \times 10^d) = (a \cdot c) \times 10^{b+d} \) - **Division rule for exponents:** \( \frac{a \times 10^b}{c \times 10^d} = \left(\frac{a}{c}\right) \times 10^{b-d} \) Carefully follow these steps to find the correct answers. Practice will help you
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Transcribed Image Text:Certainly! Below is a transcription of the text as it would appear on an educational website, along with detailed explanations of any mathematical operations or notations. --- ### Scientific Notation Practice Problems Scientific notation is a way to express very large or very small numbers conveniently. Below are a few practice problems that involve multiplication, division, and combining these operations in scientific notation. 1. **Multiplication Problem:** \[ (2.83 \times 10^6) \cdot (9.54 \times 10^5) = \_\_\_\_\_\_ \] - In this problem, you need to multiply two numbers that are expressed in scientific notation. Remember to multiply the coefficients (2.83 and 9.54) and then add the exponents of 10. 2. **Division Problem:** \[ \frac{1.51 \times 10^4}{6.89 \times 10^4} = \_\_\_\_\_\_ \] - Here, you need to divide two numbers in scientific notation. Divide the coefficients (1.51 by 6.89) and subtract the exponents of 10. 3. **Combined Multiplication and Division:** \[ \frac{(3.00 \times 10^{-6}) \cdot (3.00 \times 10^{-5})}{(1.00 \times 10^{-8}) \cdot (1.51 \times 10^4)} = \_\_\_\_\_\_ \] - This problem involves both multiplication and division of numbers in scientific notation. First, multiply the numerators together and the denominators together, then divide the results. Multiply and divide the coefficients and handle the exponents accordingly (adding exponents when multiplying and subtracting when dividing). When solving these problems: - **Multiplication rule for exponents:** \( (a \times 10^b) \cdot (c \times 10^d) = (a \cdot c) \times 10^{b+d} \) - **Division rule for exponents:** \( \frac{a \times 10^b}{c \times 10^d} = \left(\frac{a}{c}\right) \times 10^{b-d} \) Carefully follow these steps to find the correct answers. Practice will help you
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