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Chapter 10: Problem 43

For Exercises \(33-48,\) convert to scientific notation. $$0.0000491$$

Short Answer

Expert verified
4.91 \times 10^{-5}

Step by step solution

01

Understand Scientific Notation

Scientific notation expresses numbers as a product of a coefficient (between 1 and 10) and a power of 10. For example, the number 123 can be written as \(1.23 \times 10^2\).
02

Identify the Decimal Movement

Place the decimal point such that there's only one non-zero digit to its left. For 0.0000491, move the decimal point to the right, stopping after the 4, giving us 4.91.
03

Count the Decimal Places Moved

Count how many places the decimal point has been moved to the right. In this case, it鈥檚 5 places.
04

Express as a Power of 10

Since we moved the decimal 5 places to the right, we multiply by \(10^{-5}\). Therefore, 0.0000491 can be written as \(4.91 \times 10^{-5}\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Decimal Movement
When working with scientific notation, one of the first steps is handling the decimal movement. This involves positioning the decimal point so that only one non-zero digit remains to its left. For instance, with the number 0.0000491, we need to move the decimal point five places to the right, which results in 4.91. Each move counts as a shift, and this count helps in forming the power of 10 part of scientific notation. Remember, every step to the right decreases the power of 10 by one.
Coefficient
The coefficient in scientific notation is the part of the number that is multiplied by a power of 10. It must be a number between 1 and 10, but not including 10 itself. Using our example of 0.0000491, after shifting the decimal, we get 4.91 as the coefficient. The coefficient allows us to express very large or small numbers in a more compact and manageable form. This helps in performing arithmetic operations more efficiently.
Power of 10
In scientific notation, the power of 10 indicates how many times the decimal point needs to be moved to revert back to the original number. For our number 0.0000491, we moved the decimal point five places to the right. Therefore, we multiply our coefficient (4.91) by 10 raised to the power of -5. This is because moving the decimal to the right equates to negative exponents. Thus, the scientific notation for 0.0000491 is expressed as \(4.91 \times 10^{-5}\).
Prealgebra
Understanding scientific notation falls under the domain of prealgebra. Prealgebra is the foundation of algebra and helps in mastering basic math skills. By learning how to convert numbers into scientific notation, students prepare themselves for more complex algebraic concepts. Besides, scientific notation is widely used in science and engineering to handle very large or very small numbers with ease. Mastering these basics through simple and systematic steps will lay a solid groundwork for future mathematical learning.

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Most popular questions from this chapter

Simplify. Write the answers with positive exponents only. $$\left(p^{4}\right)^{-5}$$

Simplify. Write the answer with positive exponents only. $$2 x^{-2} y^{-3}$$

Simplify. $$v^{9} v^{30} v^{55}$$

$$\text { Fill in the blanks }\left(x^{3}\right)^{5}=x \square \cdot \square=x^{15}$$

Which is greater? \(\left(4^{4}\right)^{5}\) or \(\left(4^{5}\right)^{4}\)
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