Respuesta :
Explanation:
Scientific notation is defined as the representation of the numbers that are too big or too small and are represented in the form of decimal with one digit before the decimal point times 10 raise to the power.
Significant figures from scientific notation:
- Count the digits in number coming before the 10 raise to the power.
- Zero after decimal are significant.
- Zero before decimal are not significant.
- Zero in between two digits are significant
A)[tex](5.3\times 10^4) + (1.3\times 10^4)[/tex]
[tex]10^4(5.3+1.3)=10^4(6.6)=6.6\times 10^4[/tex]
Number of significant figures = 2
B)[tex]\frac{(7.2\times 10^-4)}{(1.8\times 10^3)}[/tex]
[tex]\frac{7.2\times 10^{-4-3}}{1.8}=4.0\times 10^{-7}[/tex]
Number of significant figures = 2
C).[tex] 10^4\times 10^{-3}\times 10^6 [/tex]
[tex]10^{4-3+6}=10^7=1\times 10^7[/tex]
Number of significant figures = 1
D). [tex](9.12\times 10^{-1}) - (4.7\times 10^{-2})[/tex]
[tex]10^{-1}(9.12-0.47)=8.65\times 10^{-1}[/tex]
Number of significant figures = 3
E). [tex](5.4\times 10^4)\times (3.5\times 10^9)[/tex]
[tex]5.4\times 3.5\times 10^{4+9}=18.9\times 10^{13}=1.89\times 10^{14}[/tex]
Number of significant figures = 3
Scientific notation always have a decimal part multiplied by 10 raised to the exponent of a positive or negative integer.
a) [tex](5.3 x 10^4) + (1.3 x 10^4) = 6.6 * 10^4[/tex]
b) [tex](7.2 x 10^-4) /(1.8 x 10^3) = 4.0 * 10^-7[/tex]
c) [tex]10^4 x 10^-3 x 10^6 = 1.0 * 10^7[/tex]
d) [tex](9.12 x 10^-1) - (4.7 x10^-2) = 8.65 * 10^-1[/tex]
e) [tex](5.4 x 10^4) x (3.5 x 10^9) = 2.1 * 10^14[/tex]
When working on multiplication and division of numbers in scientific notation, the laws of indices are applied as shown in the results above.
For addition and subtraction, the both numbers in scientific notation must be made to have a common exponent before the operation can be carried out successfully.
Also note that the correct number of significant figure must be maintained in the results obtained from each operation.
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