Question

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

Answer 1

Answer:

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

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