To determine the order of magnitude of the number 1013, we want to find the exponent when the number is expressed in scientific notation, specifically as a power of 10.
1. The order of magnitude of a number is the power of 10 when the number is expressed in scientific notation. For example, 100 can be expressed as [tex]\(10^2\)[/tex], and hence its order of magnitude is 2.
2. For the number 1013, it falls between [tex]\( 10^3 \)[/tex] and [tex]\( 10^4 \)[/tex] because:
- [tex]\( 10^3 \)[/tex] is 1000
- [tex]\( 10^4 \)[/tex] is 10000
3. Since 1013 is much closer to 1000 than 10000, we observe that it is just slightly more than [tex]\( 10^3 \)[/tex].
4. Thus, the appropriate exponent that best represents 1013 when approximated using powers of 10 is 3.
Therefore, the order of magnitude of the number 1013 is:
(2) 3
