Solution:
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
Answer:
[tex]6.28 * 10^{13}[/tex] + [tex]9.30 * 10^{11}[/tex] = [tex]6.373 * 10^{13}[/tex]
Explanation:
Given
[tex]6.28 * 10^{13}[/tex]
[tex]9.30 * 10^{11}[/tex]
Required
Add
The are quite a number of ways to solve this question.
I'll solve it using two methods
Method 1
[tex]6.28 * 10^{13}[/tex] + [tex]9.30 * 10^{11}[/tex]
Expand Both indices
[tex](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)[/tex]
Perform multiplication
= [tex]62800000000000 + 930000000000[/tex]
Add
[tex]= 63730000000000[/tex]
Convert to index form
[tex]= 6.373 * 10^{13}[/tex]
Method 2
[tex]6.28 * 10^{13}[/tex] + [tex]9.30 * 10^{11}[/tex]
Expand [tex]10^{13}: 10^{11+2} : 10^{11} * 10^{2}[/tex] --- According to law of indices
[tex]6.28 * 10^{11} * 10^{2}[/tex] + [tex]9.30 * 10^{11}[/tex]
Re-order
[tex]6.28 * 10^{2} * 10^{11}[/tex] + [tex]9.30 * 10^{11}[/tex]
Factorize [tex](10^{11}-is-a-common-factor)[/tex]
[tex]10^{11} (6.28 * 10^{2} + 9.30)[/tex]
Expand [tex]6.28 * 10^{2} -to-6.28 * 100-to-628[/tex]
[tex]10^{11} (628 + 9.30)[/tex]
Add 628 and 9.3
[tex]10^{11} (637.3)[/tex]
Reorder
[tex]637.3 * 10^{11}[/tex]
Represent in scientific notation
[tex]6.373 * 10^{11} * 10^{2}[/tex]
[tex]6.373 * 10^{13}[/tex]
