Answer:
Please check the explanation.
Step-by-step explanation:
Given the expression
[tex]\left(5.91\times \:10^{-3}\right)-\left(8.7\times \:10^{10}\right)[/tex]
[tex]\mathrm{Remove\:parentheses}:\quad \left(a\right)=a[/tex]
[tex]=5.91\times \:10^{-3}-8.7\times \:10^{10}[/tex]
as
[tex]5.91\times \:10^{-3}[/tex]
[tex]\mathrm{Apply\:exponent\:rule}:\quad \:a^{-b}=\frac{1}{a^b}[/tex]
[tex]=5.91\times \frac{1}{10^3}[/tex]
[tex]=\frac{5.91}{1000}[/tex]
[tex]=0.00591[/tex]
similarly
[tex]8.7\times \:10^{10}[/tex]
Convert element to a decimal form
[tex]10^{10}=10000000000[/tex]
so
[tex]=10000000000\times \:8.7[/tex]
[tex]\mathrm{Multiply\:the\:numbers:}\:8.7\times \:10000000000=87000000000[/tex]
[tex]=87000000000[/tex]
Thus, the expression becomes
[tex]\left(5.91\times \:\:10^{-3}\right)-\left(8.7\times \:\:10^{10}\right)=5.91\times \:\:10^{-3}-8.7\times \:\:10^{10}[/tex]
[tex]=0.00591-87000000000[/tex]
[tex]=-86999999999.9941[/tex]
Hence,
converting -86999999999.9941 in a scientific notation
In order to make our job easier we will remove the sign "-" from number -86999999999.9941 (we will write "-" at the final solution). So after this step we have:
−86999999999.9941 ⟶ 86999999999.9941
In order to write number 86999999999.9941 in scientific notation, we need to move the decimal point from its current location (black dot) to the new position such as:
8.6999999999.9941
So, we need to move the decimal point 10 places to the right.
This means that the power of 10 will be positive 10.
Now we have that the
Number part = 8.69999999999941 and
Exponent part = 10
Thus, we conclude that:
−86999999999.9941 = − 8.69999999999941 × 10¹⁰
