Exercise 2 Page 378

We want to subtract two numbers that are written in scientific notation. (1.5* 10^(- 2))-(3.5* 10^(-3)) Notice that the exponent of 10 is different for both numbers. Therefore, to subtract the numbers we will need to rewrite the first number as a multiple of 10^(-3). To do so, we will use the Product of Powers Property.

(1.5* 10^(- 2))-(3.5* 10^(-3))

WriteSum

Write as a sum

(1.5* 10^(1+(- 3)))-(3.5* 10^(- 3))

SumInExponentOne

a^(1+m)=a*a^m

(1.5* 10* 10^(- 3))-(3.5* 10^(- 3))

AssociativePropMult

Associative Property of Multiplication

((1.5* 10)* 10^(- 3))-(3.5* 10^(- 3))

Multiply

Multiply

(15* 10^(- 3))-(3.5* 10^(-3))

Now 10 has the same exponent in both numbers. To subtract the expressions, we can factor out 10^(- 3).

(15* 10^(- 3))-(3.5* 10^(-3))

FactorOut

Factor out 10^(- 3)

(15-3.5)* 10^(- 3)

SubTerm

Subtract term

11.5* 10^(- 3)

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 11.5 as the product of 1.15 and 10. Then we can simplify.

11.5* 10^(- 3)

Rewrite

Rewrite 11.5 as 1.15* 10

1.15* 10* 10^(- 3)

MultBasePow

a*a^m=a^(1+m)

1.15* 10^(1+(- 3))

AddNeg

a+(- b)=a-b

1.15* 10^(- 2)