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Chapter 33: Problem 941

Use scientific notation to express each number. (a) 4,375 (b) 186,000 (c) \(0.00012\) (d) 4,005

Short Answer

Expert verified
(a) \(4.375 脳 10^3\) (b) \(1.86 脳 10^5\) (c) \(1.2 脳 10^{-4}\) (d) \(4.005 脳 10^3\)

Step by step solution

01

(a) Express 4,375 in scientific notation.

To express 4,375 in scientific notation, we need to move the decimal point in the number to the left until there is only one non-zero digit to the left of the decimal point. In this case, we need to move it 3 places to the left. Since we move the decimal point to the left, we'll multiply by a positive power of 10. The number will now look like this: \(4.375\). The power of 10 corresponds to the number of decimal places moved, so we have: \(4.375 脳 10^3\).
02

(b) Express 186,000 in scientific notation.

To express 186,000 in scientific notation, we need to move the decimal point in the number to the left until there is only one non-zero digit to the left of the decimal point. In this case, we need to move it 5 places to the left. Since we move the decimal point to the left, we'll multiply by a positive power of 10. The number will now look like this: \(1.86\). The power of 10 corresponds to the number of decimal places moved, so we have: \(1.86 脳 10^5\).
03

(c) Express 0.00012 in scientific notation.

To express 0.00012 in scientific notation, we need to move the decimal point in the number to the right until there is only one non-zero digit to the left of the decimal point. In this case, we need to move it 4 places to the right. Since we move the decimal point to the right, we'll multiply by a negative power of 10. The number will now look like this: \(1.2\). The power of 10 corresponds to the number of decimal places moved, so we have: \(1.2 脳 10^{-4}\).
04

(d) Express 4,005 in scientific notation.

To express 4,005 in scientific notation, we need to move the decimal point in the number to the left until there is only one non-zero digit to the left of the decimal point. In this case, we need to move it 3 places to the left. Since we move the decimal point to the left, we'll multiply by a positive power of 10. The number will now look like this: \(4.005\). The power of 10 corresponds to the number of decimal places moved, so we have: \(4.005 脳 10^3\).

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Most popular questions from this chapter

Find the roots of the equation \(x^{2}+12-85=0\).

Simplify: (a) \(2^{3} \cdot 2^{2}\) (b) \(a^{3} \cdot a^{5}\) (c) \(x^{6} \cdot x^{4}\)

Find \(\log _{10}\left(10^{2} \cdot 10^{-3} \cdot 10^{5}\right)\)

Simplify the following expressions: (a) \(-3^{-2}\) (b) \((-3)^{-2}\) (c) \((-3) /\left(4^{-1}\right)\)

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