By how much should 17.45 be decreased to get 7.9702 ?

Answer

To find out by how much 17.45 should be decreased to get 7.9702, we can follow these steps:

### Step 1: Set up the equation
We need to find the value of \( x \) such that:
\[ 17.45 - x = 7.9702 \]

### Step 2: Rearrange the equation
To find \( x \), we can rearrange the equation:
\[ x = 17.45 - 7.9702 \]

### Step 3: Perform the subtraction
Now, we will subtract 7.9702 from 17.45. To make the subtraction easier, we can write 17.45 as 17.4500 (adding two zeros):
\[ \begin{array}{r} 17.4500 \\ - 7.9702 \\ \hline \end{array} \]

### Step 4: Subtract the decimal numbers
Now we will subtract column by column from right to left:
1. Start with the thousandths place: \( 0 - 2 \) (we cannot subtract, so we need to borrow)
- Borrow from the next column (the hundredths), making it 9 and changing the 0 to 10.
- Now we have \( 10 - 2 = 8 \).

2. Move to the hundredths place: \( 9 - 0 = 9 \).

3. Move to the tenths place: \( 4 - 7 \) (again, we need to borrow)
- Borrow from the next column (the units), making it 6 and changing the 4 to 14.
- Now we have \( 14 - 7 = 7 \).

4. Move to the units place: \( 6 - 9 \) (we need to borrow again)
- Borrow from the next column (the tens), making it 1 and changing the 6 to 16.
- Now we have \( 16 - 9 = 7 \).

5. Finally, in the tens place, we have \( 1 - 0 = 1 \).

Putting it all together, we get:
\[ \begin{array}{r} 17.4500 \\ - 7.9702 \\ \hline 9.4798 \\ \end{array} \]

### Step 5: Conclusion
Thus, \( x = 9.4798 \). Therefore, 17.45 should be decreased by **9.4798** to get 7.9702.

---