Choose the appropriate sign for each of the following expressions in the table.

Question

(3 points)
< > =

8.341 × 10^−6 ? 2.15 × 10^−2

2.14 × 10^5 ? 2.14 × 10^3

1.98 × 10^5 ? 8.91 × 10^5

Answer 1

To compare the numbers in scientific notation, we need to convert them to the same order of magnitude or directly compare their coefficients:

1. 8.341 × 10^−6 ? 2.15 × 10^−2

   • Convert 2.15 × 10^−2 to the same exponent as 8.341 × 10^−6:
     • 2.15 × 10^−2 = 2.15 × 10^−2 * 10^−4 / 10^−4 = 21.5 × 10^−6
   • Now we compare: 8.341 × 10^−6 < 21.5 × 10^−6
   • So, the sign is: <

2. 2.14 × 10^5 ? 2.14 × 10^3

   • Since both terms have the same coefficient (2.14), we compare the exponents:
   • 10^5 > 10^3
   • So, the sign is: >

3. 1.98 × 10^5 ? 8.91 × 10^5

   • Again, we look at the coefficients and exponents:
   • The exponents are the same (10^5), now we compare the coefficients: 1.98 < 8.91
   • So, the sign is: <

Putting it all together, the signs are:

1. 8.341 × 10^−6 < 2.15 × 10^−2 ( < )
2. 2.14 × 10^5 > 2.14 × 10^3 ( > )
3. 1.98 × 10^5 < 8.91 × 10^5 ( < )

Answer 2

you sure

Answer 3

Let’s review the comparisons step by step again to ensure accuracy:

1. 8.341 × 10^−6 ? 2.15 × 10^−2

   • Convert 2.15 × 10^−2 to the same exponent as 8.341 × 10^−6:
   • 2.15 × 10^−2 = 2.15 × 10^−2 = 21.5 × 10^−3
   • Observing the values in the (−6) exponent: 8.341 × 10^−6 is much smaller than 2.15 × 10^−2 (which can be viewed as having the exponent of -2).
   • So, 8.341 × 10^−6 < 2.15 × 10^−2 (sign is <).

2. 2.14 × 10^5 ? 2.14 × 10^3

   • Both values share the same coefficient (2.14).
   • Comparison of exponents shows: \(10^5\) is much larger than \(10^3\).
   • Therefore, 2.14 × 10^5 > 2.14 × 10^3 (sign is >).

3. 1.98 × 10^5 ? 8.91 × 10^5

   • Here, we compare the coefficients as the exponents are equal (both are \(10^5\)).
   • Comparing the coefficients: \(1.98 < 8.91\).
   • Therefore, 1.98 × 10^5 < 8.91 × 10^5 (sign is <).

To summarize, the signs for each comparison are:

1. <
2. >
3. <

These comparisons are correct as stated. Thank you for ensuring clarity!