How do you multiply $(2 x 10^{4}) (3 x 10^{5})$ $(2x10^4)(3x10^5)$ ?

Question

How do you multiply $(2 x 10^{4}) (3 x 10^{5})$ $(2x10^4)(3x10^5)$ ?

1 Answer

Impact of this question

12998 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-03-25T02:08:17

I'm not sure, but I think you mean $(2 \times 10^{4}) (3 \times 10^{5})$ $(2xx10^4)(3xx10^5)$ (Use two x, 'xx' inside to get x instead of $x$ $x$

You can change the order of multiplication, so you'll multiply the parts that do not involve $10$ $10$ to a power separately from the parts that do involve $10$ $10$ to a power:

$(2 \times 10^{4}) (3 \times 10^{5}) = 2 \times 10^{4} \times 3 \times 10^{5}$ $(2xx10^4)(3xx10^5)=2xx10^4xx3xx10^5$

$= 2 \times 3 \times 10^{4} \times 10^{5}$ $=2xx3xx10^4xx10^5$

$= (2 \times 3) \times (10^{4} \times 10^{5})$ $=(2xx3)xx(10^4xx10^5)$

$= 6 \times (10^{4 + 5})$ $=6xx(10^(4+5))$

$= 6 \times 10^{9}$ $=6xx10^9$

Here's another example that skips some steps:

$(3 \times 10^{5}) (4 \times 10^{8})$ $(3xx10^5)(4xx10^8)$

$= (3 \times 4) \times (10^{5} \times 10^{8})$ $=(3xx4)xx(10^5xx10^8)$

$= 12 \times (10^{5 + 8})$ $=12xx(10^(5+8))$

$= 12 \times 10^{13}$ $=12xx10^13$

But that is not in scientific notation, so we re-write it:

$12 = 1.2 \times 10^{1}$ $12=1.2xx10^1$ So
$12 \times 10^{13} = 1.2 \times 10^{1} \times 10^{13}$ $12xx10^13=1.2xx10^1xx10^13$
$1.2 \times (10^{1 + 13})$ $1.2xx(10^(1+13))$

The final answer is:
$1.2 \times 10^{14}$ $1.2xx10^14$

Science

Math

Humanities

... and beyond

How do you multiply $(2 x 10^{4}) (3 x 10^{5})$ $(2x10^4)(3x10^5)$ ?

1 Answer

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you multiply (2x104)(3x105)(2x10^4)(3x10^5)?

1 Answer

Related questions

Impact of this question

How do you multiply $(2 x 10^{4}) (3 x 10^{5})$ $(2x10^4)(3x10^5)$ ?