Question

Compute 6.28x10^13+9.30x10^11

Answer 1

`6.28 * 10^(13)` +
`9.30 * 10^(11)` =
`6.373 * 10^(13)`

Step-by-step explanation:

Given

`6.28 * 10^(13)`

`9.30 * 10^(11)`

Required

Add

The are quite a number of ways to solve this question.

I'll solve it using two methods

Method 1

`6.28 * 10^(13)` +
`9.30 * 10^(11)`

Expand Both indices

`(6.28 * 10 * 10 * 10 * 10 * 10 * 10 * 10 * 10 * 10 * 10 * 10 * 10 * 10) + (9.30 * 10 * 10 * 10 * 10 * 10 * 10 * 10 * 10 * 10 * 10 * 10)`

Perform multiplication

=
`62800000000000 + 930000000000`

Add

`= 63730000000000`

Convert to index form

`= 6.373 * 10^(13)`

Method 2

`6.28 * 10^(13)` +
`9.30 * 10^(11)`

Expand
`10^(13): 10^(11+2) : 10^(11) * 10^(2)` --- According to law of indices

`6.28 * 10^(11) * 10^(2)` +
`9.30 * 10^(11)`

Re-order

`6.28 * 10^(2) * 10^(11)` +
`9.30 * 10^(11)`

Factorize
`(10^(11)-is-a-common-factor)`

`10^(11) (6.28 * 10^(2) + 9.30)`

Expand
`6.28 * 10^(2) -to-6.28 * 100-to-628`

`10^(11) (628 + 9.30)`

Add 628 and 9.3

`10^(11) (637.3)`

Reorder

`637.3 * 10^(11)`

Represent in scientific notation

`6.373 * 10^(11) * 10^(2)`

`6.373 * 10^(13)`

Answer 2

The calculation is:

6.28 * 10^13 + 9.30 * 10^11

6.28 * 10^2 * 10^11 + 9.30 * 10^11

(628 + 9.30) * 10^11

637.3 * 10^11