To determine the correct comparison between [tex]\(1.45 \times 10^{15}\)[/tex] and [tex]\(8.97 \times 10^{16}\)[/tex], let's consider the magnitudes and values of these numbers in scientific notation.
1. Understand the Exponents:
- The first number is [tex]\(1.45 \times 10^{15}\)[/tex], which means 1.45 multiplied by 10 raised to the 15th power.
- The second number is [tex]\(8.97 \times 10^{16}\)[/tex], which means 8.97 multiplied by 10 raised to the 16th power.
2. Compare the Exponents:
- The exponent of [tex]\(10^{15}\)[/tex] indicates that the number is large, in the quadrillion range.
- The exponent of [tex]\(10^{16}\)[/tex] is one order of magnitude higher, indicating that the number is in the tens of quadrillions range.
3. Scale of the Numbers:
- Since [tex]\(10^{16}\)[/tex] is ten times larger than [tex]\(10^{15}\)[/tex], we can immediately infer that [tex]\(8.97 \times 10^{16}\)[/tex] should be significantly larger than [tex]\(1.45 \times 10^{15}\)[/tex].
4. Visualize the Numbers:
- [tex]\(1.45 \times 10^{15} = 1,450,000,000,000,000\)[/tex]
- [tex]\(8.97 \times 10^{16} = 89,700,000,000,000,000\)[/tex]
5. Compare the Quantities:
- Clearly, 1,450,000,000,000,000 is much smaller than 89,700,000,000,000,000.
So the comparison between [tex]\(1.45 \times 10^{15}\)[/tex] and [tex]\(8.97 \times 10^{16}\)[/tex] reveals that [tex]\(1.45 \times 10^{15}\)[/tex] is less than [tex]\(8.97 \times 10^{16}\)[/tex].
Therefore, the correct choice to complete the statement is:
[tex]\[ 1.45 \times 10^{15} \ < \ 8.97 \times 10^{16} \][/tex]
Hence, the answer is:
a. <
