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Which would give a significantly smaller value than 1.19 x 10^-2 and which would give a significantly larger value?

1.19 x 10^-2 + 1.07 x 10^-2 smaller or larger?

1.19 x 10^-2 - 1.07 x 10^-2 smaller or larger?

1.19 x 10^-2 x 1.07 x 10^-2 smaller or larger?

1.19 x 10^-2 / 1.07 x 10^-2 (this problem is division) smaller or larger?

Respuesta :

xero099

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].