Write 5 x 10^-3 as an ordinary number.
The Correct Answer and Explanation is:
To write ( 5 \times 10^{-3} ) as an ordinary number, we need to understand how powers of 10 work and apply the negative exponent.
Step-by-step Explanation:
- Understanding the Exponent:
The expression ( 5 \times 10^{-3} ) uses scientific notation, where the number ( 5 ) is multiplied by ( 10 ) raised to the power of ( -3 ). A negative exponent means we need to move the decimal point to the left, rather than the right. - Moving the Decimal Point:
In scientific notation, the exponent indicates how many places we need to shift the decimal point. A negative exponent of ( -3 ) tells us to move the decimal point three places to the left from its original position. - Writing 5 as a Decimal:
The number ( 5 ) is equivalent to ( 5.0 ) in decimal form, so the decimal point is at the right of the number. To convert ( 5 \times 10^{-3} ) into a regular number, we move the decimal point three places to the left. - Shifting the Decimal Point:
- Start with ( 5.0 ).
- Moving the decimal three places to the left:
- The first move places the decimal between the 5 and the 0 (i.e., ( 0.5 )).
- The second move places it before the 5 (i.e., ( 0.05 )).
- The third move places it at the far left (i.e., ( 0.005 )).
Thus, ( 5 \times 10^{-3} ) as an ordinary number is ( 0.005 ).
Conclusion:
The number ( 5 \times 10^{-3} ) is equivalent to ( 0.005 ) when written as an ordinary number. The negative exponent indicates that the decimal point should be moved to the left, resulting in a smaller value.