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Chapter 4: Problem 27

Subtract. $$ 34.07-30.7 $$

Short Answer

Expert verified
3.37

Step by step solution

01

Align the numbers

Write the numbers one below the other, aligning the decimal points: \[\begin{array}{r} 34.07 \- 30.70 \end{array}\]
02

Subtract the hundredths place

Subtract the numbers in the hundredths place: 7 - 0 = 7.
03

Subtract the tenths place

Subtract the numbers in the tenths place: 0 - 7. Since 0 is less than 7, borrow 1 from the units place: 10 - 7 = 3.
04

Subtract the units place

After borrowing, the remaining value in the units place is 3 (4 becomes 3 after borrowing). Subtract 3 - 0 = 3.
05

Subtract the tens place

Subtract the numbers in the tens place: 3 - 3 = 0.

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Key Concepts

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

Align Decimal Points
When performing decimal subtraction, it is crucial to align the decimal points of the numbers. This ensures each digit is in its correct place value column, which helps avoid mistakes.

Write the smaller number directly under the larger one, aligning the decimal points. This will make subtracting each digit from the corresponding place value straightforward.

  • Write the numbers so their decimal points are in a column.
  • Add extra zeros if necessary to make the number of decimal places equal.
Following these steps sets a strong foundation for an error-free subtraction process.
Borrow in Subtraction
Subtracting might need borrowing if the top digit is smaller than the bottom digit. Borrowing involves taking 1 from the next left place value.

For example, in subtracting 34.07 - 30.70, you need to borrow 1 from the units place to manage the tenths place as follows:

  • Original tenths place: 0 - 7.
  • Borrow 1 unit from the units column: 10 (tenths) - 7 = 3.
After borrowing, the digit in the units place decreases by one. Continue subtracting digits in their new borrowed values column-wise.
Place Value
Understanding place value is essential in decimal subtraction. Each digit in a number represents a different place value, such as units, tenths, hundredths, etc.

  • Units: The digit immediately to the left of the decimal point.
  • Tenths: The digit immediately to the right of the decimal point.
  • Hundredths: The second digit to the right of the decimal point.
In subtraction, handle each place value independently while maintaining alignment. Start from the rightmost digit (hundredths) and proceed to the left (tenths, units, tens, etc.), ensuring that borrowing is managed properly when necessary.

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Most popular questions from this chapter

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 \(\frac{6}{7}\).

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