Question
(3.2x10^5) (1.75x10^3)
Answers
Answer
how do you multiply 3.2 and 1.75
Answer
im confused
Answer
do long multiplication as decimals
Answered by
GPT-4o mini
To multiply the numbers in scientific notation \( (3.2 \times 10^5) \) and \( (1.75 \times 10^3) \), you can follow these steps:
1. Multiply the coefficients:
\[
3.2 \times 1.75 = 5.6
\]
2. Add the exponents of 10:
\[
10^5 \times 10^3 = 10^{5+3} = 10^8
\]
3. Combine the results:
\[
5.6 \times 10^8
\]
Thus, \( (3.2 \times 10^5) (1.75 \times 10^3) = 5.6 \times 10^8 \).
1. Multiply the coefficients:
\[
3.2 \times 1.75 = 5.6
\]
2. Add the exponents of 10:
\[
10^5 \times 10^3 = 10^{5+3} = 10^8
\]
3. Combine the results:
\[
5.6 \times 10^8
\]
Thus, \( (3.2 \times 10^5) (1.75 \times 10^3) = 5.6 \times 10^8 \).
Answered by
GPT-4o mini
To multiply \(3.2\) and \(1.75\), you can follow these steps:
1. **Convert to simpler numbers**: You can temporarily remove the decimal points by treating \(3.2\) as \(32\) and \(1.75\) as \(175\).
2. **Perform the multiplication**:
\[
32 \times 175
\]
This can be computed using long multiplication or by breaking it down:
\[
32 \times 175 = 32 \times (100 + 75) = (32 \times 100) + (32 \times 75) = 3200 + 2400 = 5600
\]
3. **Adjust for the decimal points**: Since \(3.2\) has 1 decimal place and \(1.75\) has 2 decimal places, the product will need to be adjusted by moving the decimal point 3 places to the left (1 from \(3.2\) + 2 from \(1.75\)):
\[
5600 \rightarrow 5.600
\]
So, the result of multiplying \(3.2\) by \(1.75\) is:
\[
5.6
\]
1. **Convert to simpler numbers**: You can temporarily remove the decimal points by treating \(3.2\) as \(32\) and \(1.75\) as \(175\).
2. **Perform the multiplication**:
\[
32 \times 175
\]
This can be computed using long multiplication or by breaking it down:
\[
32 \times 175 = 32 \times (100 + 75) = (32 \times 100) + (32 \times 75) = 3200 + 2400 = 5600
\]
3. **Adjust for the decimal points**: Since \(3.2\) has 1 decimal place and \(1.75\) has 2 decimal places, the product will need to be adjusted by moving the decimal point 3 places to the left (1 from \(3.2\) + 2 from \(1.75\)):
\[
5600 \rightarrow 5.600
\]
So, the result of multiplying \(3.2\) by \(1.75\) is:
\[
5.6
\]
Answered by
GPT-4o mini
No problem! Let's go through the multiplication of \(3.2\) and \(1.75\) step by step in a clearer way.
### Step 1: Write the numbers without decimal points
1. **Count the decimal places**:
- \(3.2\) has **1 decimal place**.
- \(1.75\) has **2 decimal places**.
### Step 2: Multiply the numbers as if they are whole numbers
Now we will multiply \(32\) and \(175\) (removing the decimal points for now).
#### Long multiplication:
```
175
x 32
-----
350 (this is 2 * 175)
+ 5250 (this is 30 * 175, or 175 shifted one position to the left)
------
5600
```
So, \(32 \times 175 = 5600\).
### Step 3: Adjust for the decimal places
Now, we need to adjust the result \(5600\) to account for the decimal places:
- Since \(3.2\) has **1 decimal place** and \(1.75\) has **2 decimal places**, we have **1 + 2 = 3 decimal places** total.
### Step 4: Place the decimal point
In \(5600\), we will place the decimal point 3 places from the right:
- **Move 3 places left** from \(5600\):
\[
5600 \rightarrow 5.600
\]
Thus, we write it as \(5.6\) (since trailing zeros after the decimal don’t affect the value).
### Final Result
So, the answer to multiplying \(3.2\) by \(1.75\) is \(5.6\).
If you still have questions or if there's a specific part that's unclear, please let me know, and I’ll help clarify!
### Step 1: Write the numbers without decimal points
1. **Count the decimal places**:
- \(3.2\) has **1 decimal place**.
- \(1.75\) has **2 decimal places**.
### Step 2: Multiply the numbers as if they are whole numbers
Now we will multiply \(32\) and \(175\) (removing the decimal points for now).
#### Long multiplication:
```
175
x 32
-----
350 (this is 2 * 175)
+ 5250 (this is 30 * 175, or 175 shifted one position to the left)
------
5600
```
So, \(32 \times 175 = 5600\).
### Step 3: Adjust for the decimal places
Now, we need to adjust the result \(5600\) to account for the decimal places:
- Since \(3.2\) has **1 decimal place** and \(1.75\) has **2 decimal places**, we have **1 + 2 = 3 decimal places** total.
### Step 4: Place the decimal point
In \(5600\), we will place the decimal point 3 places from the right:
- **Move 3 places left** from \(5600\):
\[
5600 \rightarrow 5.600
\]
Thus, we write it as \(5.6\) (since trailing zeros after the decimal don’t affect the value).
### Final Result
So, the answer to multiplying \(3.2\) by \(1.75\) is \(5.6\).
If you still have questions or if there's a specific part that's unclear, please let me know, and I’ll help clarify!
Answered by
GPT-4o mini
Sure! Let’s go through the long multiplication of \(3.2\) and \(1.75\) step by step while keeping the decimals in place.
### Step 1: Write the numbers vertically
```
3.20
× 1.75
```
### Step 2: Multiply each digit of the bottom number by the top number
1. **Multiply \(3.20\) by \(5\) (the last digit of \(1.75\))**:
- \(5 \times 0 = 0\)
- \(5 \times 2 = 10\) (write down \(0\) and carry \(1\))
- \(5 \times 3 = 15\) and add the carry: \(15 + 1 = 16\)
So, the first row of the product is:
```
3.20
× 1.75
-------
16.00 (This is 3.20 × 5)
```
2. **Multiply \(3.20\) by \(7\) (the second digit of \(1.75\))**:
- Remember to shift one position to the left because we are now multiplying by the tens place.
- \(7 \times 0 = 0\)
- \(7 \times 2 = 14\) (write down \(4\) and carry \(1\))
- \(7 \times 3 = 21\) and add the carry: \(21 + 1 = 22\)
So, the second row (shifted left) is:
```
3.20
× 1.75
-------
16.00 (This is 3.20 × 5)
+ 22.40 (This is 3.20 × 7, shifted one position)
```
3. **Multiply \(3.20\) by \(1\) (the first digit of \(1.75\))**:
- Remember to shift two positions to the left because we are now multiplying by the hundreds place.
- \(1 \times 0 = 0\)
- \(1 \times 2 = 2\)
- \(1 \times 3 = 3\)
So, the third row (shifted two positions) is:
```
3.20
× 1.75
-------
16.00 (This is 3.20 × 5)
+ 22.40 (This is 3.20 × 7, shifted one position)
+320.00 (This is 3.20 × 1, shifted two positions)
```
### Step 3: Add the results
Now, we add the three results together, making sure to line up the decimal points:
```
16.00
+ 22.40
+320.00
---------
5.6000
```
### Step 4: Placement of the decimal
Now, let's account for the decimal places:
- \(3.20\) has **2 decimal places**.
- \(1.75\) has **2 decimal places**.
- Together, they have \(2 + 2 = 4\) decimal places.
### Final Step: Write the final answer
From \(56000\), we place the decimal point 4 places from the right:
\[
5.6000 \rightarrow 5.6
\]
So, the final answer for \(3.2 \times 1.75\) is \(5.6\).
If you have any further questions or need more clarification, feel free to ask!
### Step 1: Write the numbers vertically
```
3.20
× 1.75
```
### Step 2: Multiply each digit of the bottom number by the top number
1. **Multiply \(3.20\) by \(5\) (the last digit of \(1.75\))**:
- \(5 \times 0 = 0\)
- \(5 \times 2 = 10\) (write down \(0\) and carry \(1\))
- \(5 \times 3 = 15\) and add the carry: \(15 + 1 = 16\)
So, the first row of the product is:
```
3.20
× 1.75
-------
16.00 (This is 3.20 × 5)
```
2. **Multiply \(3.20\) by \(7\) (the second digit of \(1.75\))**:
- Remember to shift one position to the left because we are now multiplying by the tens place.
- \(7 \times 0 = 0\)
- \(7 \times 2 = 14\) (write down \(4\) and carry \(1\))
- \(7 \times 3 = 21\) and add the carry: \(21 + 1 = 22\)
So, the second row (shifted left) is:
```
3.20
× 1.75
-------
16.00 (This is 3.20 × 5)
+ 22.40 (This is 3.20 × 7, shifted one position)
```
3. **Multiply \(3.20\) by \(1\) (the first digit of \(1.75\))**:
- Remember to shift two positions to the left because we are now multiplying by the hundreds place.
- \(1 \times 0 = 0\)
- \(1 \times 2 = 2\)
- \(1 \times 3 = 3\)
So, the third row (shifted two positions) is:
```
3.20
× 1.75
-------
16.00 (This is 3.20 × 5)
+ 22.40 (This is 3.20 × 7, shifted one position)
+320.00 (This is 3.20 × 1, shifted two positions)
```
### Step 3: Add the results
Now, we add the three results together, making sure to line up the decimal points:
```
16.00
+ 22.40
+320.00
---------
5.6000
```
### Step 4: Placement of the decimal
Now, let's account for the decimal places:
- \(3.20\) has **2 decimal places**.
- \(1.75\) has **2 decimal places**.
- Together, they have \(2 + 2 = 4\) decimal places.
### Final Step: Write the final answer
From \(56000\), we place the decimal point 4 places from the right:
\[
5.6000 \rightarrow 5.6
\]
So, the final answer for \(3.2 \times 1.75\) is \(5.6\).
If you have any further questions or need more clarification, feel free to ask!
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