To solve the problem [tex]\( 5.8 \cdot 10^1 - 7.4 \cdot 10^0 \)[/tex], follow these steps:
1. Interpret the numbers in standard form:
- [tex]\( 5.8 \cdot 10^1 \)[/tex] means [tex]\( 5.8 \)[/tex] multiplied by [tex]\( 10 \)[/tex] raised to the power of [tex]\( 1 \)[/tex]. This is [tex]\( 5.8 \times 10 \)[/tex], which gives [tex]\( 58.0 \)[/tex].
- [tex]\( 7.4 \cdot 10^0 \)[/tex] means [tex]\( 7.4 \)[/tex] multiplied by [tex]\( 10 \)[/tex] raised to the power of [tex]\( 0 \)[/tex]. Any number raised to the power of [tex]\( 0 \)[/tex] is [tex]\( 1 \)[/tex], so this is [tex]\( 7.4 \times 1 \)[/tex], which gives [tex]\( 7.4 \)[/tex].
2. Subtract the numbers:
- Now, subtract [tex]\( 7.4 \)[/tex] from [tex]\( 58.0 \)[/tex]:
[tex]\[
58.0 - 7.4 = 50.6
\][/tex]
3. Express the result in scientific notation:
- The result [tex]\( 50.6 \)[/tex] can be written in scientific notation. To do this, express [tex]\( 50.6 \)[/tex] as a number between 1 and 10 multiplied by a power of 10.
- [tex]\( 50.6 \)[/tex] is [tex]\( 5.06 \times 10 \)[/tex]. Therefore, in scientific notation, this is written as:
[tex]\[
5.06 \times 10^1
\][/tex]
So, the final result of [tex]\( 5.8 \cdot 10^1 - 7.4 \cdot 10^0 \)[/tex] expressed in scientific notation is:
[tex]\[
\boxed{5.06 \times 10^1}
\][/tex]
