Solve {l}{400*20000}{37*2000}{(4*10^{-3})(2*10^{5})}{(3*10^-1)(6*10^-8)}{(6.7*10^3)(4.0*10^5)}

$$\left. \begin{array} { l } { 400 \times 20000 } \\ { 37 \times 2000 } \\ { ( 4 \times 10 ^ { - 3 } ) ( 2 \times 10 ^ { 5 } ) } \\ { ( 3 \times 10 ^ { - 1 } ) ( 6 \times 10 ^ { - 8 } ) } \\ { ( 6.7 \times 10 ^ { 3 } ) ( 4.0 \times 10 ^ { 5 } ) } \end{array} \right.$$

Sort

$$0.000000018,800,74000,8000000,2680000000$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -3 and 5 to get 2.

$$sort(400\times 20000,37\times 2000,4\times 10^{2}\times 2,3\times 10^{-1}\times 6\times 10^{-8},6.7\times 10^{3}\times 4\times 10^{5})$$

To multiply powers of the same base, add their exponents. Add -1 and -8 to get -9.

$$sort(400\times 20000,37\times 2000,4\times 10^{2}\times 2,3\times 10^{-9}\times 6,6.7\times 10^{3}\times 4\times 10^{5})$$

To multiply powers of the same base, add their exponents. Add 3 and 5 to get 8.

$$sort(400\times 20000,37\times 2000,4\times 10^{2}\times 2,3\times 10^{-9}\times 6,6.7\times 10^{8}\times 4)$$

Multiply 400 and 20000 to get 8000000.

$$sort(8000000,37\times 2000,4\times 10^{2}\times 2,3\times 10^{-9}\times 6,6.7\times 10^{8}\times 4)$$

Multiply 37 and 2000 to get 74000.

$$sort(8000000,74000,4\times 10^{2}\times 2,3\times 10^{-9}\times 6,6.7\times 10^{8}\times 4)$$

Calculate 10 to the power of 2 and get 100.

$$sort(8000000,74000,4\times 100\times 2,3\times 10^{-9}\times 6,6.7\times 10^{8}\times 4)$$

Multiply 4 and 100 to get 400.

$$sort(8000000,74000,400\times 2,3\times 10^{-9}\times 6,6.7\times 10^{8}\times 4)$$

Multiply 400 and 2 to get 800.

$$sort(8000000,74000,800,3\times 10^{-9}\times 6,6.7\times 10^{8}\times 4)$$

Calculate 10 to the power of -9 and get \frac{1}{1000000000}.

$$sort(8000000,74000,800,3\times \frac{1}{1000000000}\times 6,6.7\times 10^{8}\times 4)$$

Multiply 3 and \frac{1}{1000000000} to get \frac{3}{1000000000}.

$$sort(8000000,74000,800,\frac{3}{1000000000}\times 6,6.7\times 10^{8}\times 4)$$

Multiply \frac{3}{1000000000} and 6 to get \frac{9}{500000000}.

$$sort(8000000,74000,800,\frac{9}{500000000},6.7\times 10^{8}\times 4)$$

Calculate 10 to the power of 8 and get 100000000.

$$sort(8000000,74000,800,\frac{9}{500000000},6.7\times 100000000\times 4)$$

Multiply 6.7 and 100000000 to get 670000000.

$$sort(8000000,74000,800,\frac{9}{500000000},670000000\times 4)$$

Multiply 670000000 and 4 to get 2680000000.

$$sort(8000000,74000,800,\frac{9}{500000000},2680000000)$$

Convert decimal numbers in the list 8000000,74000,800,\frac{9}{500000000},2680000000 to fractions.

$$8000000,74000,800,\frac{9}{500000000},2680000000$$

To sort the list, start from a single element 8000000.

$$8000000$$

Insert 74000 to the appropriate location in the new list.

$$74000,8000000$$

Insert 800 to the appropriate location in the new list.

$$800,74000,8000000$$

Insert \frac{9}{500000000} to the appropriate location in the new list.

$$\frac{9}{500000000},800,74000,8000000$$

Insert 2680000000 to the appropriate location in the new list.

$$\frac{9}{500000000},800,74000,8000000,2680000000$$

Evaluate

$$8000000,\ 74000,\ 800,\ 0.000000018,\ 2680000000$$