Exercise 1 Page 356

We want to add two numbers that are written in scientific notation. (8.2* 10^2)+(3.41* 10^(- 1)) Notice that the exponent of 10 is different for both numbers. Therefore, to add the numbers we will need to first rewrite the first number as a multiple of 10^(- 1). To do so, we will use the Product of Powers Property.

(8.2* 10^2)+(3.41* 10^(- 1))

WriteSum

Write as a sum

(8.2* 10^(- 1+3))+(3.41* 10^(- 1))

SumInExponent

a^(m+n)=a^m*a^n

(8.2* 10^(- 1)* 10^3)+(3.41* 10^(- 1))

CommutativePropMult

Commutative Property of Multiplication

(8.2* 10^3* 10^(- 1))+(3.41* 10^(- 1))

CalcPow

Calculate power

(8.2* 1000* 10^(- 1))+(3.41* 10^(- 1))

Multiply

Multiply

(8200* 10^(- 1))+(3.41* 10^(- 1))

Now, 10 has the same exponent in both numbers. To add the expressions, we can factor out 10^(- 1).

(8200* 10^(- 1))+(3.41* 10^(- 1))

FactorOut

Factor out 10^(- 1)

(8200+3.41)* 10^(- 1)

AddTerms

Add terms

8203.41* 10^(- 1)

Recall that the first factor of a number written in scientific notation must be greater than or equal to 1 and less than 10. Therefore, we need to rewrite 8203.41 as the product of 8.20341 and 1000. Then, we can simplify.

8203.41* 10^(- 1)

Rewrite

Rewrite 8203.41 as 8.20341* 1000

8.20341* 1000* 10^(- 1)

WritePow

Write as a power

8.20341* 10^3* 10^(- 1)

MultPow

a^m*a^n=a^(m+n)

8.20341* 10^(3 + (- 1))

AddNeg

a+(- b)=a-b

8.20341* 10^2