Exercise 14 Page 366

We want to subtract two numbers that are written in scientific notation. (6.4* 10^5)-(5.4* 10^4) Notice that the exponent of 10 is different for both numbers. Therefore, to subtract the numbers we will need to first rewrite the first number as a multiple of 10^4. To do so we will use the Product of Powers Property.

(6.4* 10^5)-(5.4* 10^4)

WriteSum

Write as a sum

(6.4* 10^(1 + 4))-(5.4* 10^4)

SumInExponentOne

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

(6.4* 10* 10^4)-(5.4* 10^4)

Multiply

Multiply

(64* 10^4)-(5.4* 10^4)

Now, 10 has the same exponent in both numbers. To subtract the expressions, we can factor out 10^4.

(64* 10^4)-(5.4* 10^4)

FactorOut

Factor out 10^4

(64-5.4)* 10^4

SubTerm

Subtract term

58.6* 10^4

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 58.6 as the product of 5.86 and 10. Then, we can simplify.

58.6* 10^4

Rewrite

Rewrite 58.6 as 5.86* 10

5.86* 10* 10^4

MultBasePow

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

5.86* 10^(1+4)

AddTerms

Add terms

5.86* 10^5