Decimals Unfolded: How to Switch Between Standard and Expanded Forms

Converting Decimals Between Standard and Expanded Form

Example 1:

Standard Form: \(3.42\)

Expanded Form: To convert this into expanded form:

– The digit \(3\) is in the ones place: \(3 \times 1\)

– The digit \(4\) is in the tenths place: \(4 \times 0.1\)

– The digit \(2\) is in the hundredths place: \(2 \times 0.01\)

Combine these values: \(3 + 0.4 + 0.02\)

Detailed Answer:

The expanded form of \(3.42\) is \(3 + 0.4 + 0.02\).

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Example 2:

Standard Form: \(5.067\)

Expanded Form:

– The digit \(5\) is in the ones place: \(5 \times 1\)

– The digit \(0\) is in the tenths place: \(0 \times 0.1\)

– The digit \(6\) is in the hundredths place: \(6 \times 0.01\)

– The digit \(7\) is in the thousandths place: \(7 \times 0.001\)

Combine these values: \(5 + 0 + 0.06 + 0.007\)

Detailed Answer:

The expanded form of \(5.067\) is \(5 + 0.06 + 0.007\).

Switching between the standard and expanded forms of decimals provides a clearer understanding of the value of each digit. This skill is academically important and practical when dealing with money, measurements, and more. Keep practicing to master this conversion!

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Practice Questions:

1. Convert the decimal \(2.35\) into its expanded form.

2. Convert the decimal \(0.914\) into its expanded form.

3. Convert the expanded form \(4 + 0.5 + 0.08\) into its standard form.

4. Convert the expanded form \(7 + 0.004\) into its standard form.

5. Convert the decimal \(6.001\) into its expanded form.

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Answers:

1. \(2 + 0.3 + 0.05\)

2. \(0.9 + 0.01 + 0.004\)

3. \(4.58\)

4. \(7.004\)

5. \(6 + 0.001\)

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