To convert the scientific notation [tex]\( 9.3 \times 10^5 \)[/tex] to standard notation, we need to understand what the notation means.
1. Scientific notation [tex]\( 9.3 \times 10^5 \)[/tex] consists of two parts:
- The coefficient, which is [tex]\( 9.3 \)[/tex].
- The exponent, which is [tex]\( 5 \)[/tex].
2. The [tex]\( 10^5 \)[/tex] indicates that we multiply the coefficient [tex]\( 9.3 \)[/tex] by [tex]\( 10 \)[/tex] raised to the power of 5. This means we need to move the decimal point 5 places to the right. Here’s how you do it step-by-step:
- Start with the number [tex]\( 9.3 \)[/tex].
- Move the decimal point one place to the right, which gives [tex]\( 93 \)[/tex] (this accounts for [tex]\( 10^1 \)[/tex]).
- Move it another place, giving [tex]\( 930 \)[/tex] (this accounts for [tex]\( 10^2 \)[/tex]).
- Then move it another place, giving [tex]\( 9300 \)[/tex] (this accounts for [tex]\( 10^3 \)[/tex]).
- Then another place, giving [tex]\( 93000 \)[/tex] (this accounts for [tex]\( 10^4 \)[/tex]).
- Finally, move it the fifth place, giving [tex]\( 930000 \)[/tex] (this accounts for [tex]\( 10^5 \)[/tex]).
Therefore, [tex]\( 9.3 \times 10^5 = 930000 \)[/tex].
Now, let's look at the options given:
A. 9,300
B. 93,000
C. 930,000
D. 9,300,000
The correct standard notation for [tex]\( 9.3 \times 10^5 \)[/tex] matches option C: 930,000.
