Question

1. 0.00023 2.3×10^(-4) 17. 0.97 9.7×10^(-1) 18. 0.00000894 8.94×10^(-7) 19. the height of mount everest: 29,029 feet 20. the weight of a grain of sugar: 0.00000625 6.25×10^(-7) directions: place a <, > or = in the circle to complete each statement. 21. 10^(-4) 10^(-5) 22. 10^(-2) 10^(-3) 23. 7.9×10^8 1.2×10^9 24. 2.5×10^(-4) 4.3×10^(-6) 25. 620,000 6.5×10^4 26. 7.25×10^6 72,500,000 27. 8.16×10^(-3) 0.00816 28. 0.0000028 5.3×10^(-6)

Explanation:

Step1: Convert numbers to standard form

For scientific - notation numbers \(a\times10^{n}\), if \(n>0\), move the decimal point \(n\) places to the right; if \(n < 0\), move the decimal point \(|n|\) places to the left.

• \(27.8.16\times10^{-3}=0.00816\) (already in standard form as written in the non - scientific part).
• \(25.620000 = 6.2\times10^{5}\), \(6.5\times10^{4}=65000\), since \(65000<620000\), the symbol is \(<\).
• \(23.7.9\times10^{8}=790000000\), \(1.2\times10^{9}=1200000000\), since \(790000000<1200000000\), the symbol is \(<\).
• \(21.10^{4}=10000\), \(10^{5}=100000\), since \(10000<100000\), the symbol is \(<\).
• \(16.0.00023 = 2.3\times10^{-4}\), \(2.3\times10^{-4}=2.3\times10^{-4}\), the symbol is \(=\).
• \(17.0.97 = 9.7\times10^{-1}\), \(9.7\times10^{-1}=9.7\times10^{-1}\), the symbol is \(=\).
• \(20.0.00000625 = 6.25\times10^{-6}\), \(6.25\times10^{-6}=6.25\times10^{-6}\), the symbol is \(=\).
• \(22.10^{-2}=0.01\), \(10^{-3}=0.001\), since \(0.01>0.001\), the symbol is \(>\).
• \(24.2.5\times10^{-4}=0.00025\), \(4.3\times10^{-6}=0.0000043\), since \(0.00025>0.0000043\), the symbol is \(>\).
• \(26.7.25\times10^{6}=7250000\), \(7250000 = 7250000\), the symbol is \(=\).
• \(28.0.0000028 = 2.8\times10^{-6}\), \(5.3\times10^{-6}=5.3\times10^{-6}\), since \(2.8\times10^{-6}<5.3\times10^{-6}\), the symbol is \(<\).

Answer:

1. \(=\)
2. \(=\)
3. (No question provided for 18 in the clear part, assuming it's a formatting issue)
4. (No clear operation for 19 in the provided text)
5. \(=\)
6. \(<\)
7. \(>\)
8. \(<\)
9. \(>\)
10. \(<\)
11. \(=\)
12. (No operation shown for 27 in the clear part)
13. \(<\)