Question

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?

Answer 1

a)
`1.19 * 10^(-2) + 1.07* 10^(-2)` is larger than
`1.19* 10^(-2)`; b)
`1.19 * 10^(-2) - 1.07* 10^(-2)` is smaller than
`1.19* 10^(-2)`; c)
`(1.19* 10^(-2))\cdot (1.07* 10^(-2))` is smaller than
`1.19* 10^(-2)`; d)
`(1.19* 10^(-2))/ (1.07* 10^(-2))` is greater than
`1.19* 10^(-2)`.

Explanation:

a) Is
`1.19 * 10^(-2) + 1.07* 10^(-2)` smaller or larger?

1)
`1.19 * 10^(-2) + 1.07* 10^(-2)` Given.

2)
`(1.19+1.07)* 10^(-2)` Distributive property.

3)
`2.26 * 10^(-2)` Addition/Result.

`1.19 * 10^(-2) + 1.07* 10^(-2)` is larger than
`1.19* 10^(-2)`.

b) Is
`1.19 * 10^(-2) - 1.07* 10^(-2)` smaller or larger?

1)
`1.19 * 10^(-2) - 1.07* 10^(-2)` Given.

2)
`(1.19-1.07)* 10^(-2)` Distributive property.

3)
`[1.19+(-1.07)]* 10^(-2)` Subtraction.

4)
`0.12* 10^(-2)` Addition/Result.

`1.19 * 10^(-2) - 1.07* 10^(-2)` is smaller than
`1.19* 10^(-2)`.

c) Is
`(1.19* 10^(-2))\cdot (1.07* 10^(-2))` smaller or larger?

1)
`(1.19* 10^(-2))\cdot (1.07* 10^(-2))` Given.

2)
`(1.19* 1.07)\cdot (10^(-2)* 10^(-2))` Associative property/Commutative property.

3)
`1.27* 10^(-4)` Multiplication/ (
`a^(b)\cdot a^(c) = a^(b+c)`)/
`(-x)\cdot (-y) = x\cdot y` /Result.

`(1.19* 10^(-2))\cdot (1.07* 10^(-2))` is smaller than
`1.19* 10^(-2)`.

d) Is
`(1.19* 10^(-2))/ (1.07* 10^(-2))` smaller or larger?

1)
`(1.19* 10^(-2))/ (1.07* 10^(-2))` Given.

2)
`(1.19* 10^(-2))\cdot (1.07* 10^(-2))^(-1)` Division.

3)
`(1.19* 10^(-2))\cdot (1.07* 10^(2))` (
`(a^(b))^(c) = a^(b\cdot c)`;
`(-x)\cdot (-y) = x\cdot y`)

4)
`(1.19* 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* 10^(-2))/ (1.07* 10^(-2))` is greater than
`1.19* 10^(-2)`.