Question

Express the answer to 4.31x10^7 multiplied by 5.41x10^5 scientific notation.

Answer 1

The product of the two numbers is 2.33* 10^13

Step-by-step explanation:

Given

4.31x10⁷ and 5.41x10⁵

Required

Multiply

The multiplication of the two digits is represented as thus:

`Result = 4.31 * 10^7 * 5.41 * 10^5`

This can also be rewritten as

`Result = 4.31 * 5.41 * 10^7 * 10^5`

Multiply 4.31 and 5.41

`Result = 23.3171 * 10^7 * 10^5`

Apply laws of indices

`Result = 23.3171 * 10^(7+5)`

`Result = 23.3171 * 10^(12)`

The scientific notation is always in the form:
`a * 10^n`

Where
`1 \leq\ a \leq 10`

So:

23.3171 can be rewritten as 2.33171 * 10

So, we have:

`Result = 2.33171 * 10* 10^(12)`

Also, apply law of indices again

`Result = 2.33171 * 10^(1+12)`

`Result = 2.33171 * 10^(13)`

It's always advisable (but not compulsory to approximate to 1 or 2 decimal places)

So:

`Result = 2.33* 10^(13)`

Hence; the product of the two numbers is 2.33* 10^13