Question

If A = 0.1+ 0.2 + 0.3 + ..... + 9.9 and B = 0.02 + 0.04 + 0.06 + .....+1.98 what is the value of A /B ?

Answer 1

Answer:

The value of A/B is 5

Step-by-step explanation:

Given:

$A=0.1+0.2+0.3+ .....+9.9$

$A=0.1[1+2+3+ .....+99]$

Also,

$B=0.02+0.04+0.06+ .....+1.98$

$B=0.02[1+2+3+ .....+99]$

Now,

$\frac{A}{B}$

$=\frac{0.1[1+2+3+ .....+99]}{0.02[1+2+3+ .....+99]}$

$=\frac{0.1}{0.02}$

$=\frac{10}{2}$

$=5$

$\implies\boxed{\bf\frac{A}{B}=5}$

Answer 2

The value of A/B is 5

Step-by-step explanation:

A=0.1+0.2+0.3+.....+9.9

B=0.02+0.04+0.06+....+1.98

We can see that 0.2 is a factor of every term of B

Therefore, B can be written as

$B=0.2(0.1+0.2+0.3+....+9.9)$

To find the value of A/B we will divide A by B

Now, A divided by B

Then, we get

$\frac{A}{B}=\frac{0.1+0.2+0.3+....+9.9}{0.2(0.1+0.2+0.3+....+9.9)}$

Same terms of numerator and denominator are cancel out to each other

Therefore, we get

$\frac{A}{B}=\frac{1}{0.2}=\frac{1}{\frac{2}{10}}$

When we remove decimal then we write 10  in denominator of given decimal number because decimal is after one digit from right side.

When denominator is in fraction then, it will be reciprocals.

Therefore, $\frac{A}{B}=\frac{10}{2}=5$

Hence, A/B=5

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