Express each number in exponential notation. (a) \(8950 .;\)(b) \(10,700 . ;(\text { c) } 0.0240 ; \text { (d) } 0.0047 ; \text { (e) } 938.3 ; \text { (f) } 275,482\).

Short Answer

Expert verified
(a) \(8.95 * 10^{3}\) (b) \(1.07 * 10^{4}\) (c) \(2.40 * 10^{-2}\) (d) \(4.7 * 10^{-3}\) (e) \(9.383 * 10^{2}\) (f) \(2.75482 * 10^{5}\)

Step by step solution

01

Expressing numbers in exponential notation

The rule to express numbers in exponential notation is to have one non-zero digit to the left of the decimal. Move the decimal point as needed to create this number and then record the number of places and direction you moved the decimal as a power of 10. If the decimal was moved to the left, the power of 10 will be positive and if it was moved to the right, the power of 10 will be negative.
02

Apply the rule to the given numbers

(a) For the number 8950, move the decimal three places to the left. The number is then written as \(8.95 * 10^{3}\).\n (b) For the number 10,700, move the decimal four places to the left. The number is then written as \(1.07 * 10^{4}\).\n (c) For the number 0.0240, move the decimal two places to the right. The number is then written as \(2.40 * 10^{-2}\).\n (d) For the number 0.0047, move the decimal three places to the right. The number is then written as \(4.7 * 10^{-3}\).\n (e) For the number 938.3, move the decimal two places to the left. The number is then written as \(9.383 * 10^{2}\).\n (f) For the number 275,482, move the decimal five places to the left. The number is then written as \(2.75482 * 10^{5}\).

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