Question

b) express each number in standard notation.

1. 8.6×10³ =
2. 5.37×10⁻⁴ =
3. 9.4×10⁻³ =
4. 7.259×10⁵ =
5. 8.806×10⁴ =
6. 5.14×10⁻³ =
7. 2.8×10⁻⁶ =
8. 3.63×10⁴ =

Explanation:

Step1: Recall standard - form rules

A number in standard form is written as \(a\times10^{n}\), where \(1\leqslant|a|\lt10\) and \(n\) is an integer.

Step2: Calculate for \(8.6\times10^{3}\)

\[8.6\times10^{3}=8.6\times1000 = 8600\]

Step3: Calculate for \(9.4\times10^{- 3}\)

\[9.4\times10^{-3}=\frac{9.4}{10^{3}}=\frac{9.4}{1000}=0.0094\]

Step4: Calculate for \(7.259\times10^{5}\)

\[7.259\times10^{5}=7.259\times100000 = 725900\]

Step5: Calculate for \(5.14\times10^{-3}\)

\[5.14\times10^{-3}=\frac{5.14}{10^{3}}=\frac{5.14}{1000}=0.00514\]

Step6: Calculate for \(8.806\times10^{4}\)

\[8.806\times10^{4}=8.806\times10000 = 88060\]

Step7: Calculate for \(2.8\times10^{-6}\)

\[2.8\times10^{-6}=\frac{2.8}{10^{6}}=\frac{2.8}{1000000}=0.0000028\]

Step8: Calculate for \(5.37\times10^{-4}\)

\[5.37\times10^{-4}=\frac{5.37}{10^{4}}=\frac{5.37}{10000}=0.000537\]

Step9: Calculate for \(3.63\times10^{4}\)

\[3.63\times10^{4}=3.63\times10000 = 36300\]

Answer:

1. \(8600\)
2. \(0.0094\)
3. \(725900\)
4. \(0.00514\)
5. \(88060\)
6. \(0.0000028\)
7. \(0.000537\)
8. \(36300\)