To solve the problem [tex]\( \frac{4.37 \times 10^8}{7.13 \times 10^{-3}} \)[/tex], we need to follow these steps:
1. Understand the problem: We are given a division of two numbers expressed in scientific notation. The numerator is [tex]\( 4.37 \times 10^8 \)[/tex] and the denominator is [tex]\( 7.13 \times 10^{-3} \)[/tex].
2. Rewrite the expression: We want to divide [tex]\( 4.37 \times 10^8 \)[/tex] by [tex]\( 7.13 \times 10^{-3} \)[/tex]. Mathematically, this is represented as:
[tex]\[
\frac{4.37 \times 10^8}{7.13 \times 10^{-3}}
\][/tex]
3. Separate the coefficients and the powers of 10: We can rewrite the fraction as:
[tex]\[
\left( \frac{4.37}{7.13} \right) \times \left( \frac{10^8}{10^{-3}} \right)
\][/tex]
4. Divide the coefficients: Using a calculator to divide 4.37 by 7.13:
[tex]\[
\frac{4.37}{7.13} \approx 0.613
\][/tex]
5. Divide the powers of 10: We use the properties of exponents. Note that dividing by [tex]\( 10^{-3} \)[/tex] is equivalent to multiplying by [tex]\( 10^3 \)[/tex]:
[tex]\[
\frac{10^8}{10^{-3}} = 10^8 \times 10^3 = 10^{8+3} = 10^{11}
\][/tex]
6. Combine the results: Now multiply the coefficient by the power of 10 we calculated:
[tex]\[
0.613 \times 10^{11} = 6.13 \times 10^{10}
\][/tex]
7. Convert to 3 significant figures in standard form: The coefficient [tex]\( 0.613 \times 10^{11} \)[/tex] can be expressed as [tex]\( 6.13 \times 10^{10} \)[/tex].
So the final answer is:
[tex]\[
6.13 \times 10^{10}
\][/tex]
Therefore, [tex]\( \frac{4.37 \times 10^8}{7.13 \times 10^{-3}} \)[/tex] is [tex]\( 6.13 \times 10^{10} \)[/tex] in standard form to 3 significant figures.
