Decimals Unfolded: How to Switch Between Standard and Expanded Forms
Decimals can be represented in multiple ways, and two of the most common forms are the standard form and the expanded form. The standard form is how we typically write decimals, while the expanded form breaks down each digit's value based on its place. Let's delve into the art of converting between these two 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 not only academically important but also practical when dealing with money, measurements, and more. Keep practicing to master this conversion!
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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