Question

In this problem, you will practice adding, subtracting, multiplying, and dividing numbers written in scientific notation. For each part, use the following numbers.
3.2×104
1.95×106
8.03×10−8
2.56×10−2
4.82×1012

Answer 1

Absolutely! Let’s perform the operations using the provided numbers in scientific notation.

Here are the numbers we will work with:

1. \( 3.2 \times 10^4 \)
2. \( 1.95 \times 10^6 \)
3. \( 8.03 \times 10^{-8} \)
4. \( 2.56 \times 10^{-2} \)
5. \( 4.82 \times 10^{12} \)

### **1. Addition**

Let's add \( 3.2 \times 10^4 \) and \( 1.95 \times 10^6 \):

To add numbers in scientific notation, they must have the same exponent.

- Convert \( 3.2 \times 10^4 \) to have an exponent of \( 10^6 \):
\[
3.2 \times 10^4 = 0.032 \times 10^6
\]

Now we can add:
\[
0.032 \times 10^6 + 1.95 \times 10^6 = (0.032 + 1.95) \times 10^6 = 1.982 \times 10^6
\]

### **2. Subtraction**

Now let's subtract \( 2.56 \times 10^{-2} \) from \( 8.03 \times 10^{-8} \):

Again, we need to convert these to the same exponent:
- Convert \( 8.03 \times 10^{-8} \) to have an exponent of \( 10^{-2} \):
\[
8.03 \times 10^{-8} = 0.0000803 \times 10^{-2}
\]

So now we can subtract:
\[
0.0000803 \times 10^{-2} - 2.56 \times 10^{-2} = (0.0000803 - 2.56) \times 10^{-2} = -2.5599197 \times 10^{-2}
\]

### **3. Multiplication**

Now let’s multiply \( 4.82 \times 10^{12} \) by \( 1.95 \times 10^6 \):

We multiply the coefficients and add the exponents:
\[
4.82 \times 1.95 = 9.399
\]
\[
10^{12} \times 10^6 = 10^{12 + 6} = 10^{18}
\]

So the product is:
\[
9.399 \times 10^{18}
\]

### **4. Division**

Finally, let's divide \( 1.95 \times 10^6 \) by \( 8.03 \times 10^{-8} \):

We divide the coefficients and subtract the exponents:
\[
\frac{1.95}{8.03} \approx 0.2435
\]
\[
10^{6} \div 10^{-8} = 10^{6 - (-8)} = 10^{6 + 8} = 10^{14}
\]

So the quotient is:
\[
0.2435 \times 10^{14} = 2.435 \times 10^{13} \quad (\text{after adjusting the coefficient})
\]

### **Summary of Operations:**

1. Addition: \( 1.982 \times 10^6 \)
2. Subtraction: \( -2.5599197 \times 10^{-2} \)
3. Multiplication: \( 9.399 \times 10^{18} \)
4. Division: \( 2.435 \times 10^{13} \)

If you have any more questions or need more calculations, feel free to ask!