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

Question

Choose one of the scientific numbers from the list and subtract it from 1,845.19 (or subtract 1,845.19 from the number you choose). Show your work.

Answer 1

Let's choose the number \( 1.95 \times 10^6 \) for this operation and subtract it from \( 1,845.19 \).

Step 1: Convert Numbers to the Same Format

Before performing the subtraction, we need to convert \( 1,845.19 \) into scientific notation.

To convert \( 1,845.19 \) to scientific notation:

1. Move the decimal point left until only one non-zero digit remains to its left.
2. This gives us \( 1.84519 \times 10^3 \).

Step 2: Values in Scientific Notation

We have:

• \( 1,845.19 = 1.84519 \times 10^3 \)
• \( 1.95 \times 10^6 \)

Step 3: Prepare for Subtraction

To perform the subtraction, both numbers need to be in the same exponent. We can express \( 1.84519 \times 10^3 \) in terms of \( 10^6 \):

• \( 1.84519 \times 10^3 = 1.84519 \times 10^3 \times \frac{10^3}{10^3} = 1.84519 \times 10^6 \times 10^{-3} \)

Now, both numbers can be expressed with \( 10^6 \) as the power of 10:

• \( 1.84519 \times 10^6 \times 10^{-3} \)
• \( 1.95 \times 10^6 \)

Step 4: Perform the Subtraction

Now we can subtract: \[ (1.84519 \times 10^6 \times 10^{-3}) - (1.95 \times 10^6) = (1.84519 - 1.95) \times 10^6 \] Calculating \( 1.84519 - 1.95 \): \[ 1.84519 - 1.95 = -0.10481 \]

So the subtraction results in: \[ -0.10481 \times 10^6 \]

Step 5: Convert Back to Scientific Notation

Now, we will convert \( -0.10481 \times 10^6 \) into proper scientific notation: \[ -0.10481 \times 10^6 = -1.0481 \times 10^5 \]

Final Result

Thus, the result of subtracting \( 1.95 \times 10^6 \) from \( 1,845.19 \) is: \[ \boxed{-1.0481 \times 10^5} \]

Answer 2

Put it in Plain Language please

Answer 3

Sure! Here’s a simple step-by-step explanation of how we subtracted the scientific number from 1,845.19:

1. Choose a Number: We chose \( 1.95 \times 10^6 \) to subtract from \( 1,845.19 \).

2. Convert 1,845.19 to Scientific Notation:

   • Move the decimal point left until we have one non-zero digit to the left. This gives us \( 1.84519 \).
   • Since we moved the decimal point three places to the left, we write this as \( 1.84519 \times 10^3 \).

3. Align the Numbers:

   • We have \( 1.84519 \times 10^3 \) (from \( 1,845.19 \)) and \( 1.95 \times 10^6 \).
   • To subtract these, we need to have the same exponent (power of 10). So we express \( 1.84519 \times 10^3 \) in terms of \( 10^6 \) by recognizing \( 10^3 = 0.001 \times 10^6 \). This makes it \( 1.84519 \times 10^6 \times 10^{-3} \).

4. Perform the Subtraction:

   • Now, we can subtract:
   • \( 1.84519 \) (from \( 1,845.19 \)) minus \( 1.95 \) gives us \( -0.10481 \), and since we still have \( \times 10^6 \) in the equation, we write this as:
   • \( -0.10481 \times 10^6 \).

5. Convert Back to Scientific Notation:

   • Finally, to express \( -0.10481 \times 10^6 \) in proper scientific notation, we move the decimal point one place to the right, which turns it into \( -1.0481 \times 10^5 \).

Final Result: The result of subtracting \( 1.95 \times 10^6 \) from \( 1,845.19 \) is \( -1.0481 \times 10^5 \).

In simple words, when you subtract the larger scientific number from \( 1,845.19 \), the answer becomes a negative number in scientific notation.

Answer 4

explain it in 8th grade style

Answer 5

Sure! Here’s how we can think about subtracting \(1.95 \times 10^6\) from \(1,845.19\) in a way that an 8th grader can understand:

Step 1: Pick a Number

We are going to subtract \(1.95 \times 10^6\) from \(1,845.19\).

Step 2: Change 1,845.19 to Scientific Notation

1. What is Scientific Notation?
   It’s a way to write very big or very small numbers. We write it as a number between \(1\) and \(10\) multiplied by a power of \(10\).

2. Convert 1,845.19:
   We want to change \(1,845.19\) into scientific notation. To do this:

   • We move the decimal point to the left until there's only one number before the decimal.
   • So, \(1,845.19\) becomes \(1.84519\) when we move the decimal point 3 places to the left.
   • This means we write it as \(1.84519 \times 10^3\) because we moved it 3 places.

Step 3: Put the Numbers in the Same Format

Now we have two numbers:

• \(1.84519 \times 10^3\) (from \(1,845.19\))
• \(1.95 \times 10^6\) (from the scientific number)

To subtract them, they need to have the same exponent (the power of \(10\)).

Adjust the First Number:

We can rewrite \(1.84519 \times 10^3\) so it has the same exponent as the second number:

• We need to express \(10^3\) in terms of \(10^6\).
• We know that \(10^6\) is much larger than \(10^3\), so: \[ 1.84519 \times 10^3 = 1.84519 \times 10^3 \times 10^{3} = 1.84519 \times 10^6 \times 10^{-3} \]

Step 4: Do the Subtraction

Now we can perform the subtraction:

• We have \(1.84519 \times 10^6 \times 10^{-3}\) and \(1.95 \times 10^6\).
• We can simplify it to: \[ (1.84519 - 1.95) \times 10^6 \] Now, subtract \(1.95\) from \(1.84519\): \[ 1.84519 - 1.95 = -0.10481 \]

So we end up with: \[ -0.10481 \times 10^6 \]

Step 5: Write it in Scientific Notation

To put this into proper scientific notation:

• We need to adjust the number. Since we have \( -0.10481\), we can move the decimal point to the right, which gives us: \[ -1.0481 \times 10^5 \]

Final Result

So the final answer after subtracting \(1.95 \times 10^6\) from \(1,845.19\) is: \[ \boxed{-1.0481 \times 10^5} \]

In simple terms, after doing all the math, we find out that \(1,845.19\) is much smaller than \(1.95 \times 10^6\), which is why our answer turns out to be a negative number!

Answer 6

I meant that stop explaining it like THIS

### Step 1: Convert Numbers to the Same Format
Before performing the subtraction, we need to convert \( 1,845.19 \) into scientific notation.

To convert \( 1,845.19 \) to scientific notation:
1. Move the decimal point left until only one non-zero digit remains to its left.
2. This gives us \( 1.84519 \times 10^3 \).

### Step 2: Values in Scientific Notation
We have:
- \( 1,845.19 = 1.84519 \times 10^3 \)
- \( 1.95 \times 10^6 \)

### Step 3: Prepare for Subtraction
To perform the subtraction, both numbers need to be in the same exponent. We can express \( 1.84519 \times 10^3 \) in terms of \( 10^6 \):
- \( 1.84519 \times 10^3 = 1.84519 \times 10^3 \times \frac{10^3}{10^3} = 1.84519 \times 10^6 \times 10^{-3} \)

Now, both numbers can be expressed with \( 10^6 \) as the power of 10:
- \( 1.84519 \times 10^6 \times 10^{-3} \)
- \( 1.95 \times 10^6 \)

### Step 4: Perform the Subtraction
Now we can subtract:
\[
(1.84519 \times 10^6 \times 10^{-3}) - (1.95 \times 10^6) = (1.84519 - 1.95) \times 10^6
\]
Calculating \( 1.84519 - 1.95 \):
\[
1.84519 - 1.95 = -0.10481
\]

So the subtraction results in:
\[
-0.10481 \times 10^6
\]

### Step 5: Convert Back to Scientific Notation
Now, we will convert \( -0.10481 \times 10^6 \) into proper scientific notation:
\[
-0.10481 \times 10^6 = -1.0481 \times 10^5
\]

### Final Result
Thus, the result of subtracting \( 1.95 \times 10^6 \) from \( 1,845.19 \) is:
\[
\boxed{-1.0481 \times 10^5}
\]

Answer 7

Got it! Let me explain the problem in a simpler and more straightforward way, just like a conversation.

---

Let's subtract \( 1.95 \times 10^6 \) from \( 1,845.19 \).

1. Convert 1,845.19 to Scientific Notation:
   First, we need to rewrite \( 1,845.19 \) in scientific notation. This means we express it as a number between 1 and 10 multiplied by a power of 10.

   • \( 1,845.19 \) becomes \( 1.84519 \times 10^3 \) because we moved the decimal point 3 places to the left.

2. Now We Have Two Numbers:

   • \( 1.84519 \times 10^3 \) (from \( 1,845.19 \))
   • \( 1.95 \times 10^6 \)

3. Make Their Exponents the Same:
   The numbers need to have the same power of 10 for us to subtract them. It’s easier if we express everything in terms of \( 10^6 \).

   • To do this, we can rewrite \( 1.84519 \times 10^3 \) as \( 0.00184519 \times 10^6 \) (because \( 10^3 \) is smaller than \( 10^6 \)).

4. Now We Can Subtract:
   So, we subtract: \[ 0.00184519 \times 10^6 - 1.95 \times 10^6 \] To do this, we first change \( 1.95 \times 10^6 \) to have a decimal to help with the subtraction: \[ 0.00184519 - 1.95 = -1.94815481 \]

5. Combine It:
   Now, it becomes: \[ -1.94815481 \times 10^6 \]

6. Convert Back to Scientific Notation:
   We need to express \( -1.94815481 \) in proper scientific notation:

   • We move the decimal point one place to the right, which means we have: \[ -1.94815481 \times 10^6 = -1.94815 \times 10^5 \] (We adjust the exponent down because we moved the decimal.)

7. Final Result:
   So after all that, the answer is: \[ \boxed{-1.94815 \times 10^5} \]

---

That’s how we subtract \( 1.95 \times 10^6 \) from \( 1,845.19 \). The result is a negative number since \( 1.95 \times 10^6 \) is much larger than \( 1,845.19 \). Hope that makes it clearer!

Answer 8

make it so people can understand what you are saying, right now you are making no sense with those robotic like characters

Answer 9

Got it! Let's break it down in a more casual and straightforward way without all the symbols and complex explanations.

---

Problem: Subtract \( 1.95 \times 10^6 \) from \( 1,845.19 \)

1. Changing \( 1,845.19 \) into Scientific Notation:
   First, we want to change \( 1,845.19 \) into scientific notation. To do this, we move the decimal point so there’s just one digit before it. So:

   • \( 1,845.19 \) becomes \( 1.84519 \) and since we moved the decimal 3 places to the left, we write it as \( 1.84519 \times 10^3 \).

2. Now We Have Two Numbers:

   • \( 1.84519 \times 10^3 \) (from \( 1,845.19 \))
   • \( 1.95 \times 10^6 \) (the other number)

3. Aligning the Exponents:
   To subtract these two numbers, they need to have the same power of ten. Since \( 10^6 \) is much larger than \( 10^3 \), we can adjust \( 1.84519 \times 10^3 \).

   • We can rewrite \( 1.84519 \times 10^3 \) in terms of \( 10^6 \). This means it becomes \( 0.00184519 \times 10^6 \).

4. Performing the Subtraction:
   Now we can subtract:

   • \( 0.00184519 \) from \( 1.95 \).
   • So, we do the math: \( 0.00184519 - 1.95 \) gives us about \( -1.94815481 \).

5. Final Result in Scientific Notation:
   We need to put our answer back in scientific notation. Since our result is negative, we’ll express it like this:

   • We write \( -1.94815481\) multiplied by \( 10^6 \) because that’s from our original scale. But to keep it in proper scientific notation, we shift the decimal one place to the right, which makes our number \( -1.94815\) and adjusts the exponent down to \( 10^5 \).

Conclusion

So, the final answer when you subtract \( 1.95 \times 10^6 \) from \( 1,845.19 \) is:

• \(-1.94815 \times 10^5\)

This shows that \( 1.95 \times 10^6\) is much larger than \( 1,845.19\), resulting in a negative value!

Hope this is clearer!

Answer 10

ok better but make it into a paragraph

Answer 11

Sure! Here’s the explanation in a single paragraph:

To subtract \(1.95 \times 10^6\) from \(1,845.19\), we first need to change \(1,845.19\) into scientific notation. This is done by moving the decimal point three places to the left, which gives us \(1.84519 \times 10^3\). Now we have two numbers: \(1.84519 \times 10^3\) and \(1.95 \times 10^6\). Since the powers of ten are different, we convert \(1.84519 \times 10^3\) into a form that uses \(10^6\) as the base, changing it to \(0.00184519 \times 10^6\). Next, we perform the subtraction by taking \(0.00184519\) away from \(1.95\), which results in approximately \(-1.94815481\). To express this final answer in proper scientific notation, we shift the decimal one place to the right, resulting in \(-1.94815 \times 10^5\). This shows us that \(1.95 \times 10^6\) is significantly larger than \(1,845.19\), resulting in a negative answer. The final result is \(-1.94815 \times 10^5\).