Question

in exercises 3-6, find the value of n.

1. 94,000,000 = 9.4 × 10ⁿ
2. 555,500,000,000 = 5.555 × 10ⁿ
3. 0.00006 = 6 × 10ⁿ
4. 0.00000000000375 = 3.75 × 10ⁿ

Explanation:

Step1: Count decimal shifts (Q3)

To get 9.4 from 94,000,000, move decimal left 7 places. So $10^7$.

Step2: Count decimal shifts (Q4)

To get 5.555 from 555,500,000,000, move decimal left 11 places. So $10^{11}$.

Step3: Count decimal shifts (Q5)

To get 6 from 0.00006, move decimal right 5 places. For small numbers, exponent is negative: $10^{-5}$.

Step4: Count decimal shifts (Q6)

To get 3.75 from 0.0000000000375, move decimal right 11 places. Exponent is negative: $10^{-11}$.

Answer:

1. $n=7$
2. $n=11$
3. $n=-5$
4. $n=-11$