Answer :
To determine the expanded form of the number five hundred twenty-seven and thirty-six thousandths (527.036), let's break it down step-by-step:
1. Hundreds place: The digit in the hundreds place is 5. This part of the number can be represented as:
[tex]\[ 5 \times 100 = 500 \][/tex]
2. Tens place: The digit in the tens place is 2. This can be represented as:
[tex]\[ 2 \times 10 = 20 \][/tex]
3. Units place: The digit in the units place is 7. This can be represented as:
[tex]\[ 7 \times 1 = 7 \][/tex]
4. Tenths place: The digit in the tenths place is 0. This can be represented as:
[tex]\[ 0 \times \frac{1}{10} = 0 \][/tex]
5. Hundredths place: The digit in the hundredths place is 3. This can be represented as:
[tex]\[ 3 \times \frac{1}{100} = 0.03 \][/tex]
6. Thousandths place: The digit in the thousandths place is 6. This can be represented as:
[tex]\[ 6 \times \frac{1}{1000} = 0.006 \][/tex]
Adding these up, we get:
[tex]\[ 500 + 20 + 7 + 0.03 + 0.006 = 527.036 \][/tex]
Now, let's compare this step-by-step breakdown with the given options:
Option (A)
[tex]\[ (5 \times 100) + (2 \times 10) + (7 \times 1) + (36 \times \frac{1}{10}) \][/tex]
This is incorrect because \(36 \times \frac{1}{10} = 3.6\), not \(0.036\).
Option (B)
[tex]\[ (5 \times 100) + (2 \times 10) + (7 \times 1) + (3 \times \frac{1}{10}) + (6 \times \frac{1}{100}) \][/tex]
This is the correct option based on our breakdown:
- \(5 \times 100 = 500\)
- \(2 \times 10 = 20\)
- \(7 \times 1 = 7\)
- \(3 \times \frac{1}{10} = 0.3\)
- \(6 \times \frac{1}{100} = 0.06\)
- Sum = 527.036
Option (C)
[tex]\[ (5 \times 100) + (2 \times 10) + (7 \times 1) + (3 \times \frac{1}{100}) + (6 \times \frac{1}{1,000}) \][/tex]
This is incorrect because \( 3 \times \frac{1}{100} = 0.03\) and \(6 \times \frac{1}{1,000} = 0.006\), which does not equate to \(0.036\).
Option (D)
[tex]\[ (5 \times 100) + (2 \times 10) + (7 \times 1) + (3 \times \frac{1}{1,000}) + (6 \times \frac{1}{1,000}) \][/tex]
This is incorrect because \((3 \times \frac{1}{1,000}) + (6 \times \frac{1}{1,000}) = 0.009\).
Therefore, the correct answer is:
(B) [tex]\((5 \times 100) + (2 \times 10) + (7 \times 1) + (3 \times \frac{1}{10}) + (6 \times \frac{1}{100})\)[/tex]
1. Hundreds place: The digit in the hundreds place is 5. This part of the number can be represented as:
[tex]\[ 5 \times 100 = 500 \][/tex]
2. Tens place: The digit in the tens place is 2. This can be represented as:
[tex]\[ 2 \times 10 = 20 \][/tex]
3. Units place: The digit in the units place is 7. This can be represented as:
[tex]\[ 7 \times 1 = 7 \][/tex]
4. Tenths place: The digit in the tenths place is 0. This can be represented as:
[tex]\[ 0 \times \frac{1}{10} = 0 \][/tex]
5. Hundredths place: The digit in the hundredths place is 3. This can be represented as:
[tex]\[ 3 \times \frac{1}{100} = 0.03 \][/tex]
6. Thousandths place: The digit in the thousandths place is 6. This can be represented as:
[tex]\[ 6 \times \frac{1}{1000} = 0.006 \][/tex]
Adding these up, we get:
[tex]\[ 500 + 20 + 7 + 0.03 + 0.006 = 527.036 \][/tex]
Now, let's compare this step-by-step breakdown with the given options:
Option (A)
[tex]\[ (5 \times 100) + (2 \times 10) + (7 \times 1) + (36 \times \frac{1}{10}) \][/tex]
This is incorrect because \(36 \times \frac{1}{10} = 3.6\), not \(0.036\).
Option (B)
[tex]\[ (5 \times 100) + (2 \times 10) + (7 \times 1) + (3 \times \frac{1}{10}) + (6 \times \frac{1}{100}) \][/tex]
This is the correct option based on our breakdown:
- \(5 \times 100 = 500\)
- \(2 \times 10 = 20\)
- \(7 \times 1 = 7\)
- \(3 \times \frac{1}{10} = 0.3\)
- \(6 \times \frac{1}{100} = 0.06\)
- Sum = 527.036
Option (C)
[tex]\[ (5 \times 100) + (2 \times 10) + (7 \times 1) + (3 \times \frac{1}{100}) + (6 \times \frac{1}{1,000}) \][/tex]
This is incorrect because \( 3 \times \frac{1}{100} = 0.03\) and \(6 \times \frac{1}{1,000} = 0.006\), which does not equate to \(0.036\).
Option (D)
[tex]\[ (5 \times 100) + (2 \times 10) + (7 \times 1) + (3 \times \frac{1}{1,000}) + (6 \times \frac{1}{1,000}) \][/tex]
This is incorrect because \((3 \times \frac{1}{1,000}) + (6 \times \frac{1}{1,000}) = 0.009\).
Therefore, the correct answer is:
(B) [tex]\((5 \times 100) + (2 \times 10) + (7 \times 1) + (3 \times \frac{1}{10}) + (6 \times \frac{1}{100})\)[/tex]
