Question

a. $4\cdot10^{3} + 7\cdot10^{2} + 8\cdot10 + 2 + 9\cdot10^{-1} + 6\cdot10^{-2} = \square$
b. $3\cdot10^{4} + 7\cdot10^{-2} + 9\cdot10^{-3} = \square$
c. $7\cdot10^{4} + 8\cdot10^{-3} = \square$
d. $10^{-2} + 10^{-3} + 10^{-5} = \square$

Explanation:

Step1: Solve part a

Calculate each term: \(4 \cdot 10^3 = 4000\), \(7 \cdot 10^2 = 700\), \(8 \cdot 10 = 80\), \(2 = 2\), \(9 \cdot 10^{-1} = 0.9\), \(6 \cdot 10^{-2} = 0.06\).
Sum them: \(4000 + 700 + 80 + 2 + 0.9 + 0.06 = 4782.96\).

Step2: Solve part b

Calculate each term: \(3 \cdot 10^4 = 30000\), \(7 \cdot 10^{-2} = 0.07\), \(9 \cdot 10^{-3} = 0.009\).
Sum them: \(30000 + 0.07 + 0.009 = 30000.079\).

Step3: Solve part c

Calculate each term: \(7 \cdot 10^4 = 70000\), \(8 \cdot 10^{-3} = 0.008\).
Sum them: \(70000 + 0.008 = 70000.008\).

Step4: Solve part d

Calculate each term: \(10^{-2} = 0.01\), \(10^{-3} = 0.001\), \(10^{-5} = 0.00001\).
Sum them: \(0.01 + 0.001 + 0.00001 = 0.01101\).

Answer:

a. \(4782.96\)
b. \(30000.079\)
c. \(70000.008\)
d. \(0.01101\)