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Chapter 0: Problem 68

Write each number in decimal notation without the use of exponents. $$7 \times 10^{-5}$$

Short Answer

Expert verified
The decimal notation of \(7 \times 10^{-5}\) is 0.00007.

Step by step solution

01

Understanding the Scientific Notation

In the number \(7 \times 10^{-5}\), we notice that there is a positive integer (7) and \(10^{-5}\), which has a negative exponent. This means we are dealing with a decimal number that is less than 1.
02

Applying the Negative Exponent Rule

A negative exponent tells us to reciprocate the base to make the exponent positive. However when 10 is raised to any negative power, it simply means we move the decimal point of the number coupled with it to the left by as many places as the value of the negative exponent.
03

Conversion to Decimal Notation

In the given number, since the exponent is -5, we move the decimal point in the number 7 to the left by 5 places. Since there are more places to move than there are digits in the number 7, we fill in the extra places with zeros. Thus, the decimal notation of \(7 \times 10^{-5}\) is 0.00007.

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Most popular questions from this chapter

Factor the numerator and the denominator. Then simplify by dividing out the common factor in the numerator and the denominator. $$\frac{x^{2}+6 x+5}{x^{2}-25}$$

This will help you prepare for the material covered in the next section. a. Simplify: \(21 x+10 x\) b. Simplify: \(21 \sqrt{2}+10 \sqrt{2}\)

Find the intersection of the sets. $$\\{s, e, t\\} \cap\\{t, e, s\\}$$

Find the intersection of the sets. $$\\{a, b, c, d\\} \cap \varnothing$$

Find the intersection of the sets. $$\\{1,2,3,4\\} \cap\\{2,4,5\\}$$
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