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Chapter 2: Problem 19

Express 743000000 in scientific notation to the following number of significant figures: a. one significant figure b. two significant figures c. four significant figures

Short Answer

Expert verified
a. \(7 × 10^8)\n b. \(7.4 × 10^8)\n c. \(7.430 × 10^8\)

Step by step solution

01

Convert to scientific notation

We can express any number in scientific notation as the product of two factors - one being a number between 1 and 10 (or −1 and −10), and the other being a positive or negative power of 10. Convert 743000000 to scientific notation by moving the decimal point to the right of the first digit and counting how many places you moved it. Here, we moved the point 8 places to the right, so 743000000 in scientific notation is \(7.43 × 10^8\).
02

Adjust for one significant figure

To express the number with one significant digit, we only keep the first digit and round off the rest. Hence, the answer in this case is \(7 × 10^8\).
03

Adjust for two significant figures

To express the number with two significant figures, we keep the first two digits and round off the rest. Thus, the answer in this case is \(7.4 × 10^8\).
04

Adjust for four significant figures

To express the number with four significant figures, we keep the first four digits and round off the rest. However, there is only one nonzero digit after the first three in the original number. So, we simply keep that nonzero digit with the others, making the answer \(7.430 × 10^8\). Remember to include the trailing zeros as they are significant.

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