Question

`(8xx10^-7)(2xx10^5)`?

scientific notation

Answer 1

The answer of this calculation is `1.6 xx 10^-1`

Explanation:

When multiplying numbers in scientific notation, first you multiply the whole numbers.

In this case, they are `8 and 2`, which equals `16.`

Then for the exponents: when multiplying, you add the exponents. So that would be `-7 +5 = -2`.

We have `16 xx 10^-2`.

But in scientific notation, there must be only ONE digit before the decimal point.

`16 xx 10^-2 = 1.6 xx10^-1`

In decimal notation the answer is `0.16`

Answer 2

`=16 xx 10^-2 = 1.6 xx 10^-1`

Explanation:

Multiplying in scientific notation can be compared to multiplying in algebra:

`3x^4 xx 5x^3` can also be written as:

`color(red)(3xx5) xx color(blue)(x^4 xx x^3)`

`= color(red)(15) xx color(blue)(x^(4+3)" "larr` bases are both `x`, so add the indices

`= color(red)(15) xx color(blue)(x^7)`

In scientific notation you might have:

`3xx 10^8 xx 4 xx 10^11`

`= color(red)(3xx4) xx color(blue)(10^8 xx 10^11)`

`= color(red)(12) xx color(blue)(10^19)`

However in scientific notation, there must be one digit before the decimal point:

`color(red)(12) xxcolor(blue)(10^19) = color(red)(1.2) xx color(blue)(10^20)`

In this example we have:

`8 xx 10^-7 xx 2xx10^5`

`= color(red)(8 xx2) xx color(blue)(10^-7 xx10^5)`

`=color(red)(16) xx color(blue)(10^(-7+5))`

`=color(red)(16) xx color(blue)(10^-2)`

However in scientific notation, there must be one digit before the decimal point:

`=color(red)(16) xx color(blue)(10^-2) = color(red)(1.6) xx color(blue)(10^-1)`

It is usual to give an answer in the same format as the question.

In decimal format this answer would be `0.16`