Answer:
a) [tex]1.19 \times 10^{-2} + 1.07\times 10^{-2}[/tex] is larger than [tex]1.19\times 10^{-2}[/tex]; b) [tex]1.19 \times 10^{-2} - 1.07\times 10^{-2}[/tex] is smaller than [tex]1.19\times 10^{-2}[/tex]; c) [tex](1.19\times 10^{-2})\cdot (1.07\times 10^{-2})[/tex] is smaller than [tex]1.19\times 10^{-2}[/tex]; d) [tex](1.19\times 10^{-2})/ (1.07\times 10^{-2})[/tex] is greater than [tex]1.19\times 10^{-2}[/tex].
Step-by-step explanation:
a) Is [tex]1.19 \times 10^{-2} + 1.07\times 10^{-2}[/tex] smaller or larger?
1) [tex]1.19 \times 10^{-2} + 1.07\times 10^{-2}[/tex] Given.
2) [tex](1.19+1.07)\times 10^{-2}[/tex] Distributive property.
3) [tex]2.26 \times 10^{-2}[/tex] Addition/Result.
[tex]1.19 \times 10^{-2} + 1.07\times 10^{-2}[/tex] is larger than [tex]1.19\times 10^{-2}[/tex].
b) Is [tex]1.19 \times 10^{-2} - 1.07\times 10^{-2}[/tex] smaller or larger?
1) [tex]1.19 \times 10^{-2} - 1.07\times 10^{-2}[/tex] Given.
2) [tex](1.19-1.07)\times 10^{-2}[/tex] Distributive property.
3) [tex][1.19+(-1.07)]\times 10^{-2}[/tex] Subtraction.
4) [tex]0.12\times 10^{-2}[/tex] Addition/Result.
[tex]1.19 \times 10^{-2} - 1.07\times 10^{-2}[/tex] is smaller than [tex]1.19\times 10^{-2}[/tex].
c) Is [tex](1.19\times 10^{-2})\cdot (1.07\times 10^{-2})[/tex] smaller or larger?
1) [tex](1.19\times 10^{-2})\cdot (1.07\times 10^{-2})[/tex] Given.
2) [tex](1.19\times 1.07)\cdot (10^{-2}\times 10^{-2})[/tex] Associative property/Commutative property.
3) [tex]1.27\times 10^{-4}[/tex] Multiplication/ ([tex]a^{b}\cdot a^{c} = a^{b+c}[/tex])/ [tex](-x)\cdot (-y) = x\cdot y[/tex] /Result.
[tex](1.19\times 10^{-2})\cdot (1.07\times 10^{-2})[/tex] is smaller than [tex]1.19\times 10^{-2}[/tex].
d) Is [tex](1.19\times 10^{-2})/ (1.07\times 10^{-2})[/tex] smaller or larger?
1) [tex](1.19\times 10^{-2})/ (1.07\times 10^{-2})[/tex] Given.
2) [tex](1.19\times 10^{-2})\cdot (1.07\times 10^{-2})^{-1}[/tex] Division.
3) [tex](1.19\times 10^{-2})\cdot (1.07\times 10^{2})[/tex] ([tex](a^{b})^{c} = a^{b\cdot c}[/tex]; [tex](-x)\cdot (-y) = x\cdot y[/tex])
4) [tex](1.19\times 1.07)\cdot (10^{-2}\cdot 10^{2})[/tex] Associative property/Commutative property.
5) [tex]1.27[/tex] Multiplication/([tex](a^{b})^{c} = a^{b\cdot c}[/tex]; [tex]a^{0} = 1[/tex])/Modulative property/Result.
[tex](1.19\times 10^{-2})/ (1.07\times 10^{-2})[/tex] is greater than [tex]1.19\times 10^{-2}[/tex].
