Sure! Let’s solve the division of two numbers written in scientific notation [tex]\( 7.06 \times 10^5 \)[/tex] and [tex]\( 5.3 \times 10^{-2} \)[/tex].
The general form of scientific notation is [tex]\( a \times 10^b \)[/tex], where [tex]\( a \)[/tex] is the coefficient and [tex]\( b \)[/tex] is the exponent. Here, our operation involves:
[tex]\[ \frac{7.06 \times 10^5}{5.3 \times 10^{-2}} \][/tex]
To perform this division, we can tackle it in two parts: the coefficients and the exponents.
Step 1: Divide the coefficients
First, focus on the coefficients [tex]\( 7.06 \)[/tex] and [tex]\( 5.3 \)[/tex]. We need to divide these two numbers:
[tex]\[ \frac{7.06}{5.3} \][/tex]
When we perform the division, we get:
[tex]\[ \frac{7.06}{5.3} = 1.3320754716981131 \][/tex]
Step 2: Subtract the exponents
Next, we handle the exponents. We have [tex]\( 10^5 \)[/tex] and [tex]\( 10^{-2} \)[/tex]. According to the properties of exponents, when we divide with the same base, we subtract the exponents:
[tex]\[ 5 - (-2) = 5 + 2 = 7 \][/tex]
Step 3: Combine results in scientific notation
Now we combine the results from both steps. The final answer in scientific notation combines the coefficient from Step 1 and the exponent from Step 2:
[tex]\[ 1.3320754716981131 \times 10^7 \][/tex]
Thus, the result of the operation [tex]\( \frac{7.06 \times 10^5}{5.3 \times 10^{-2}} \)[/tex] in scientific notation is:
[tex]\[ 1.3320754716981131 \times 10^7 \][/tex]
