To write the number [tex]\( 6.43 \times 10^{-4} \)[/tex] in standard notation, follow these steps:
1. Understand Scientific Notation:
- The expression [tex]\( 6.43 \times 10^{-4} \)[/tex] is in scientific notation.
- The number [tex]\( 6.43 \)[/tex] is the coefficient and [tex]\( 10^{-4} \)[/tex] is the power of ten.
2. Interpret the Exponent:
- The exponent [tex]\(-4\)[/tex] means that we move the decimal point in the coefficient [tex]\( 6.43 \)[/tex] four places to the left.
3. Move the Decimal Point:
- Start with the number 6.43.
- Move the decimal point four places to the left:
- First move: 0.643.
- Second move: 0.0643.
- Third move: 0.00643.
- Fourth move: 0.000643.
4. Result:
- After moving the decimal point four places to the left, the number [tex]\( 6.43 \times 10^{-4} \)[/tex] becomes 0.000643 in standard notation.
Next, compare this result to the given options:
- Option 1: 0.000643
- Option 2: 0.00643
- Option 3: 0.0000643
- Option 4: -257.2
The number 0.000643 matches option 1.
### Final Answer:
The number [tex]\( 6.43 \times 10^{-4} \)[/tex] in standard notation is [tex]\( 0.000643 \)[/tex], which corresponds to Option 1.
