Question

solve.
a. $8.06 \times 10^3 = $

b. $400 \times 10^5 = $

c. $700 \times 10^4 = $

Explanation:

Part a

Step1: Recall scientific notation rule

To multiply a number by \(10^n\), we move the decimal point \(n\) places to the right. For \(8.06\times10^{3}\), \(n = 3\).

Step2: Move decimal point

Moving the decimal point in \(8.06\) three places to the right: \(8.06\times10^{3}=8060\).

Part b

Step1: Rewrite 400 in scientific notation

\(400 = 4\times10^{2}\), so \(400\times10^{5}=4\times10^{2}\times10^{5}\).

Step2: Use exponent rule \(a^m\times a^n=a^{m + n}\)

\(4\times10^{2}\times10^{5}=4\times10^{2 + 5}=4\times10^{7}\).

Step3: Convert to standard form

\(4\times10^{7}=40000000\).

Part c

Step1: Rewrite 700 in scientific notation

\(700 = 7\times10^{2}\), so \(700\times10^{4}=7\times10^{2}\times10^{4}\).

Step2: Use exponent rule \(a^m\times a^n=a^{m + n}\)

\(7\times10^{2}\times10^{4}=7\times10^{2+4}=7\times10^{6}\).

Step3: Convert to standard form

\(7\times10^{6}=7000000\).

Answer:

a. \(8060\)
b. \(40000000\) (or \(4\times10^{7}\))
c. \(7000000\) (or \(7\times10^{6}\))