The product of $1.7 imes 10^4$ and $12.5 imes 10^{-6}$ is expressed in the standard form as $k imes 10^n$. The value of(2k + n) is

Q: The product of $1.7 \times 10^4$ and $12.5\times 10^{-6}$ is expressed in the standard form as $k \times 10^n$. The value of(2k + n) is

To solve the problem of finding the product of $1.7 \times 10^4$ and $12.5 \times 10^{-6}$ and expressing it in the standard form $k \times 10^n$, we proceed as follows: 1. **Calculate the Product:** \[ (1.7 \times 10^4) \times (12.5 \times 10^{-6}) = 1.7 \times 12.5 \times 10^{4 + (-6)} \] \[ = 1.7 \times 12.5 \times 10^{-2} \] 2. **Multiply the Decimal Numbers:** \[ 1.7 \times 12.5 = 21.25 \] 3. **Combine with the Power of Ten:** \[ 21.25 \times 10^{-2} \] 4. **Express in Standard Form:** To express $21.25 \times 10^{-2}$ in standard form, we need to adjust it so that the coefficient is between 1 and 10. Thus: \[ 21.25 = 2.125 \times 10^1 \] Therefore: \[ 21.25 \times 10^{-2} = 2.125 \times 10^{1-2} = 2.125 \times 10^{-1} \] 5. **Identify $k$ and $n$:** In the expression $2.125 \times 10^{-1}$, $k = 2.125$ and $n = -1$. 6. **Calculate $2k + n$:** \[ 2k + n = 2 \times 2.125 + (-1) = 4.25 - 1 = 3.25 \] Thus, the value of $2k + n$ is 3.25, which corresponds to Option 4. **Explanation for Other Options:** - **Option 1 (2.125):** This option would imply that $2k + n = 2.125$, which is incorrect because it does not account for the correct calculation of $2k + n$ as shown above. - **Option 2 (1.125):** This option suggests a much lower value for $2k + n$, which is not possible given the calculations of $k$ and $n$. - **Option 3 (2.25):** This option is incorrect as it does not match the calculated value of $3.25$ for $2k + n$. Therefore, the correct answer is indeed Option 4, as it accurately reflects the calculated value of $2k + n$.

Question

The product of $1.7 	imes 10^4$ and $12.5	imes 10^{-6}$ is expressed in the standard form as $k 	imes 10^n$. The value of(2k + n) is

Accepted Answer

To solve the problem of finding the product of $1.7 \times 10^4$ and $12.5 \times 10^{-6}$ and expressing it in the standard form $k \times 10^n$, we proceed as follows:

1. **Calculate the Product:**
   $$
   (1.7 \times 10^4) \times (12.5 \times 10^{-6}) = 1.7 \times 12.5 \times 10^{4 + (-6)}
   $$
   $$
   = 1.7 \times 12.5 \times 10^{-2}
   $$

2. **Multiply the Decimal Numbers:**
   $$
   1.7 \times 12.5 = 21.25
   $$

3. **Combine with the Power of Ten:**
   $$
   21.25 \times 10^{-2}
   $$

4. **Express in Standard Form:**
   To express $21.25 \times 10^{-2}$ in standard form, we need to adjust it so that the coefficient is between 1 and 10. Thus:
   $$
   21.25 = 2.125 \times 10^1
   $$
   Therefore:
   $$
   21.25 \times 10^{-2} = 2.125 \times 10^{1-2} = 2.125 \times 10^{-1}
   $$

5. **Identify $k$ and $n$:**
   In the expression $2.125 \times 10^{-1}$, $k = 2.125$ and $n = -1$.

6. **Calculate $2k + n$:**
   $$
   2k + n = 2 \times 2.125 + (-1) = 4.25 - 1 = 3.25
   $$

Thus, the value of $2k + n$ is 3.25, which corresponds to Option 4.

**Explanation for Other Options:**

- **Option 1 (2.125):** This option would imply that $2k + n = 2.125$, which is incorrect because it does not account for the correct calculation of $2k + n$ as shown above.
  
- **Option 2 (1.125):** This option suggests a much lower value for $2k + n$, which is not possible given the calculations of $k$ and $n$.

- **Option 3 (2.25):** This option is incorrect as it does not match the calculated value of $3.25$ for $2k + n$.

Therefore, the correct answer is indeed Option 4, as it accurately reflects the calculated value of $2k + n$.