Question

a. $4\cdot10^{3} + 7\cdot10^{2} + 8\cdot10 + 2 + 9\cdot10^{-1} + 6\cdot10^{-2} = \dfrac{119574}{25}$
b. $3\cdot10^{4} + 7\cdot10^{-2} + 9\cdot10^{-3} = \dfrac{30000079}{10000}$
c. $7\cdot10^{4} + 8\cdot10^{-3} = \dfrac{8750001}{125}$
d. $10^{-2} + 10^{-3} + 10^{-5} = \square$

Explanation:

Step1: Convert each term to fraction

$10^{-2}=\frac{1}{100}$, $10^{-3}=\frac{1}{1000}$, $10^{-5}=\frac{1}{100000}$
So the expression becomes $\frac{1}{100}+\frac{1}{1000}+\frac{1}{100000}$

Step2: Find a common denominator

The least common denominator of 100, 1000, 100000 is 100000.
Convert each fraction:
$\frac{1}{100}=\frac{1000}{100000}$, $\frac{1}{1000}=\frac{100}{100000}$, $\frac{1}{100000}=\frac{1}{100000}$

Step3: Add the fractions

$\frac{1000 + 100 + 1}{100000}=\frac{1101}{100000}$

Answer:

$\frac{1101}{100000}$