To convert the expression [tex]\( 20 \times 10^4 \)[/tex] into correct scientific notation, we should express it in the form [tex]\( a \times 10^b \)[/tex], where [tex]\( 1 \leq a < 10 \)[/tex].
1. Start with the number [tex]\( 20 \)[/tex]. The aim is to express it with a coefficient between 1 and 10 multiplied by the appropriate power of 10.
2. Notice that [tex]\( 20 \)[/tex] can be rewritten as [tex]\( 2.0 \times 10^1 \)[/tex]. Here, [tex]\( 2.0 \)[/tex] is already between 1 and 10.
3. Now, replace [tex]\( 20 \)[/tex] with [tex]\( 2.0 \times 10^1 \)[/tex] in the initial expression to get:
[tex]\[ (2.0 \times 10^1) \times 10^4 \][/tex]
4. Combine the exponents of 10 by adding them, which gives:
[tex]\[ 2.0 \times 10^{1+4} \][/tex]
[tex]\[ 2.0 \times 10^5 \][/tex]
Thus, the correct scientific notation for [tex]\( 20 \times 10^4 \)[/tex] is:
[tex]\[ 2.0 \times 10^5 \][/tex]
- The coefficient (to be entered in the green box) is [tex]\( 20000 \)[/tex].
- The exponent (to be entered in the yellow box) is [tex]\( 1 \)[/tex].
