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Chapter 2: Problem 152

Express \(23,000,000\) in scientific notation having: (a) Two significant figures (b) Three significant figures (c) Five significant figures (d) Six significant figures (e) Eight significant figures

Short Answer

Expert verified
(a) \(2.3 \times 10^7\) (b) \(2.30 \times 10^7\) (c) \(23.000 \times 10^6\) (d) \(23.0000 \times 10^6\) (e) \(23.000000 \times 10^6\)

Step by step solution

01

(a) Two significant figures

: To write \(23,000,000\) with two significant figures, we round it to the nearest ten million, which is \(23,000,000\). In scientific notation, this becomes: \(2.3 \times 10^7\)
02

(b) Three significant figures

: To write \(23,000,000\) with three significant figures, we round it to the nearest million, which also remains \(23,000,000\). In scientific notation, this becomes: \(2.30 \times 10^7\)
03

(c) Five significant figures

: To write \(23,000,000\) with five significant figures, we round it to the nearest ten thousand. In this case, there are no ten thousands, so the number remains unchanged. In scientific notation, this becomes: \(23.000 \times 10^6\)
04

(d) Six significant figures

: To write \(23,000,000\) with six significant figures, we round it to the nearest thousand. Again, there are no thousands, so the number remains unchanged. In scientific notation, this becomes: \(23.0000 \times 10^6\)
05

(e) Eight significant figures

: To write \(23,000,000\) with eight significant figures, we need more decimal places than the original number has. In this case, we'll simply add more trailing zeros after the decimal point, without rounding. In scientific notation, this becomes: \(23.000000 \times 10^6\)

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