Question

scientific notation is a way of writing very or very numbers using the powers of 10. a number written in scientific notation has the form a×10ⁿ where 1≤a<10. converting scientific notation to standard form is easy! the exponent tells you the directions and the number of places to move the decimal. directions: write each number in standard form. scientific notation standard form 1. 4.3×10² 2. 2.19×10¹ 3. 5×10⁴ 4. 7.2×10⁻¹ 5. 3×10⁻⁶ 6. 8.52×10⁻³ directions: place a <, > or = in the circle to complete each statement. 13. 8×10⁵ 〇 1×10⁴ 14. 5.52×10² 〇 9.4×10³ 15. 7.54×10⁻² 〇 4.73×10⁻¹ 16. 9.89×10⁻⁷ 〇 3.14×10⁻⁵ 17. 240,000 〇 1.7×10⁴ 18. 8×10⁴ 〇 800000 19. 5.2×10⁻⁸ 〇 0.000000052 20. 0.0009 〇 7.5×10⁻³ © gina wilson (all things algebra®) llc

Explanation:

Step1: Recall scientific - notation to standard - form rule

For \(a\times10^{n}\), if \(n>0\), move decimal \(n\) places right; if \(n < 0\), move decimal \(|n|\) places left.

Step2: Convert \(4.3\times10^{2}\) to standard form

Since \(n = 2>0\), move decimal 2 places right: \(4.3\times10^{2}=430\).

Step3: Convert \(2.19\times10^{7}\) to standard form

Since \(n = 7>0\), move decimal 7 places right: \(2.19\times10^{7}=21900000\).

Step4: Convert \(5\times10^{4}\) to standard form

Since \(n = 4>0\), move decimal 4 places right: \(5\times10^{4}=50000\).

Step5: Convert \(7.2\times10^{-1}\) to standard form

Since \(n=-1 < 0\), move decimal 1 place left: \(7.2\times10^{-1}=0.72\).

Step6: Convert \(3\times10^{-6}\) to standard form

Since \(n=-6 < 0\), move decimal 6 places left: \(3\times10^{-6}=0.000003\).

Step7: Convert \(8.52\times10^{-3}\) to standard form

Since \(n=-3 < 0\), move decimal 3 places left: \(8.52\times10^{-3}=0.00852\).

Step8: Compare \(8\times10^{5}\) and \(1\times10^{4}\)

\(8\times10^{5}=800000\) and \(1\times10^{4}=10000\), so \(8\times10^{5}>1\times10^{4}\).

Step9: Compare \(5.52\times10^{2}\) and \(9.4\times10^{3}\)

\(5.52\times10^{2}=552\) and \(9.4\times10^{3}=9400\), so \(5.52\times10^{2}<9.4\times10^{3}\).

Step10: Compare \(7.54\times10^{-2}\) and \(4.73\times10^{-1}\)

\(7.54\times10^{-2}=0.0754\) and \(4.73\times10^{-1}=0.473\), so \(7.54\times10^{-2}<4.73\times10^{-1}\).

Step11: Compare \(9.89\times10^{-9}\) and \(3.14\times10^{-5}\)

\(9.89\times10^{-9}=0.00000000989\) and \(3.14\times10^{-5}=0.0000314\), so \(9.89\times10^{-9}<3.14\times10^{-5}\).

Step12: Convert \(240000\) to scientific - notation (\(2.4\times10^{5}\)) and compare with \(1.7\times10^{4}\)

\(2.4\times10^{5}=240000\) and \(1.7\times10^{4}=17000\), so \(240000>1.7\times10^{4}\).

Step13: Convert \(8\times10^{4}\) to standard form (\(80000\)) and compare with \(800000\)

\(8\times10^{4}=80000\), so \(8\times10^{4}<800000\).

Step14: Convert \(5.2\times10^{-8}\) to standard form (\(0.000000052\)) and compare with \(0.0000000052\)

\(5.2\times10^{-8}=0.000000052\), so \(5.2\times10^{-8}>0.0000000052\).

Step15: Convert \(0.0009\) to scientific - notation (\(9\times10^{-4}\)) and compare with \(7.5\times10^{-3}\)

\(9\times10^{-4}=0.0009\) and \(7.5\times10^{-3}=0.0075\), so \(0.0009<7.5\times10^{-3}\).

Answer:

1. \(430\)
2. \(21900000\)
3. \(50000\)
4. \(0.72\)
5. \(0.000003\)
6. \(0.00852\)
7. \(>\)
8. \(<\)
9. \(<\)
10. \(<\)
11. \(>\)
12. \(<\)
13. \(>\)
14. \(<\)