Question

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

Answer 1

Answer:

a) $1.19 \times 10^{-2} + 1.07\times 10^{-2}$ is larger than $1.19\times 10^{-2}$; b) $1.19 \times 10^{-2} - 1.07\times 10^{-2}$ is smaller than $1.19\times 10^{-2}$; c) $(1.19\times 10^{-2})\cdot (1.07\times 10^{-2})$ is smaller than $1.19\times 10^{-2}$; d) $(1.19\times 10^{-2})/ (1.07\times 10^{-2})$ is greater than $1.19\times 10^{-2}$.

Step-by-step explanation:

a) Is $1.19 \times 10^{-2} + 1.07\times 10^{-2}$ smaller or larger?

1) $1.19 \times 10^{-2} + 1.07\times 10^{-2}$ Given.

2) $(1.19+1.07)\times 10^{-2}$ Distributive property.

3) $2.26 \times 10^{-2}$ Addition/Result.

$1.19 \times 10^{-2} + 1.07\times 10^{-2}$ is larger than $1.19\times 10^{-2}$.

b) Is $1.19 \times 10^{-2} - 1.07\times 10^{-2}$ smaller or larger?

1) $1.19 \times 10^{-2} - 1.07\times 10^{-2}$ Given.

2) $(1.19-1.07)\times 10^{-2}$ Distributive property.

3) $[1.19+(-1.07)]\times 10^{-2}$ Subtraction.

4) $0.12\times 10^{-2}$ Addition/Result.

$1.19 \times 10^{-2} - 1.07\times 10^{-2}$ is smaller than $1.19\times 10^{-2}$.

c) Is $(1.19\times 10^{-2})\cdot (1.07\times 10^{-2})$ smaller or larger?

1) $(1.19\times 10^{-2})\cdot (1.07\times 10^{-2})$ Given.

2) $(1.19\times 1.07)\cdot (10^{-2}\times 10^{-2})$ Associative property/Commutative property.

3) $1.27\times 10^{-4}$ Multiplication/ ($a^{b}\cdot a^{c} = a^{b+c}$)/ $(-x)\cdot (-y) = x\cdot y$ /Result.

$(1.19\times 10^{-2})\cdot (1.07\times 10^{-2})$ is smaller than $1.19\times 10^{-2}$.

d) Is $(1.19\times 10^{-2})/ (1.07\times 10^{-2})$ smaller or larger?

1) $(1.19\times 10^{-2})/ (1.07\times 10^{-2})$ Given.

2) $(1.19\times 10^{-2})\cdot (1.07\times 10^{-2})^{-1}$ Division.

3) $(1.19\times 10^{-2})\cdot (1.07\times 10^{2})$ ($(a^{b})^{c} = a^{b\cdot c}$; $(-x)\cdot (-y) = x\cdot y$)

4) $(1.19\times 1.07)\cdot (10^{-2}\cdot 10^{2})$ Associative property/Commutative property.

5) $1.27$ Multiplication/($(a^{b})^{c} = a^{b\cdot c}$; $a^{0} = 1$)/Modulative property/Result.

$(1.19\times 10^{-2})/ (1.07\times 10^{-2})$ is greater than $1.19\times 10^{-2}$.