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Chapter 4: Problem 23

Subtract. $$ \begin{array}{r} 3.4 \\ -0.003 \\ \hline \end{array} $$

Short Answer

Expert verified
3.397

Step by step solution

01

- Align the decimal points

Make sure to align the two numbers by their decimal points: \( 3.4 \begin{array}{r} \ -0.003 \ \hline \ \end{array} \).
02

- Add zeros for same decimal places

Add zeros to the number 3.4 to have the same number of decimal places as 0.003, resulting in: \( 3.400 \begin{array}{r} \ -0.003 \ \hline \ \end{array} \).
03

- Subtract starting from rightmost digit

Subtract each digit starting from the rightmost column: 0 - 3 (you need to borrow) \( 3.400 \begin{array}{r} \ -0.003 \ \hline \ 3.397 \end{array} \).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Subtracting Decimals
Subtracting decimals might look a bit tricky at first, but it can be simple if you follow a few basic steps. When you subtract decimals, you are essentially performing the same steps as you would for whole numbers, with the addition of dealing with the decimal point. This means focusing on each digit and keeping track of the borrowing if needed. Remember to always subtract starting from the rightmost digit and moving left.
Aligning Decimal Points
The key to subtracting decimals correctly is aligning the decimal points. This ensures that each digit is in its correct place value (ones, tenths, hundredths, etc.). To align the decimal points, write each number in a column so that their decimal points line up vertically. For example, with the numbers 3.4 and 0.003, you need to rewrite them for subtraction:

3.400
鈭�0.003
-------
This alignment is crucial because it allows you to correctly add or subtract digits of the same place value.
Borrowing in Subtraction
When subtracting decimals, sometimes you will need to borrow, just as with whole numbers. Borrowing happens when the digit in the minuend (the top number) is smaller than the corresponding digit in the subtrahend (the bottom number). Here鈥檚 how you do it:

  • If you need to subtract 3 from 0, you can't do it directly. You need to borrow from the next higher place value.
  • Reduce the next digit of the minuend by 1, and add 10 to the current digit you need to subtract from (in this case, the tenths place).
  • Continue the subtraction as usual with these adjustments.

In our example, you would subtract like this:
3.4 becomes 3.400
鈭�0.003
-------
Start from the rightmost digit:
0 (borrow from the next higher value)->10 - 3 = 7
Next column: 9 - 0 = 9
Next column: 3 - 0 = 3

So, 3.400 - 0.003 = 3.397
Understanding and practicing borrowing in subtraction will make the process of subtracting decimals a lot easier!

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Most popular questions from this chapter

Estimate. Indicate which of the choices is an appropriate estimate. \(78 \times 5.3\) a) 400 b) 800 c) 40 d) 8

Add. $$ \begin{array}{r} 641.803 \\ +\quad 14.935 \\ \hline \end{array} $$

Estimate by rounding as directed. $$ \begin{aligned} &52.367+1.307+7.324 ;\\\ &\text { nearest one } \end{aligned} $$

Find decimal notation for \(\frac{1}{7}, \frac{2}{7}, \frac{3}{7}, \frac{4}{7},\) and \(\frac{5}{7} .\) Observe the pattern and guess the decimal notation for \(\frac{6}{7}\).

Subtract. $$ 3.801-2.81 $$
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