1.13 x 10^1 + 9.1 x 10^-1 =?

Can anyone help me to solve this and put it into steps for me?

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### 1.13 x 10^1 + 9.1 x 10^-1 =?

We know that

10^1 = 10

10^3 = 10*10*10

10^2=10*10

10^3*10^2 = (10*10*10)(10*10)= 10^5

**10^3*10^2=10^5. Therefore, 10^3*10^2=10^(3+2)=10^5.**

10^5/10^2 = 10^3 = 10^(5-2)=10^5*10^-2. Therefore,

10^-2 =1/10^-2.

Similarly** 10^-1 = 1/10. We shall use this.**

Solution /simplification:

1.13*10^1+9,1*10^-1.

First term:

1.13*10^1 =1.13*10. Replaced 10^1 = 10.

1.13*10 is like "113*10 =1130 and putting decimal after two degits from the left as the multiplicand and multiplier together have 2+0 =2 digits after the decimal mark." So,

1.13*10 = **11.30** (1)

Second term:

9.1*10^-1 = 9.1/10. Replaced 10^-1 by 1/10

9.1/10 : Dividing by 10 is like shifting decimal point to left by one place. So,

9.1/10 =.91 or **0.91 ** (2)

Adding the value so obtained of the two terms, we get:

11.30+0.91=**12.21**. Therefore,

### 1.13 x 10^1 + 9.1 x 10^-1 = **12.21**

We have to find out the value of:

(1.13 x 10^1) + (9.1 x 10^-1)

Now 10^1 = 10, and 10^-1 = 1/10

Please remember: A^-X = 1/(A^X)

Therefore:

(1.13 x 10^1) + (9.1 x 10^-1) = (1.13 x 10) + (9.1 x 1/10)

= 11.3 + 9.1

= 12.21

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