To determine which expression is equivalent to 1 ten, 3 ones, and 9 thousandths, let's analyze each option step by step.
1. Identify the values for each component:
- 1 ten: This is [tex]\(1 \times 10\)[/tex]
- 3 ones: This is [tex]\(3 \times 1\)[/tex]
- 9 thousandths: This is [tex]\(9 \times \frac{1}{1000}\)[/tex]
2. Evaluate each expression provided in the options:
Option A: [tex]\((1 \times 10) + (3 \times 1) + \left(9 \times \frac{1}{1000}\right)\)[/tex]
- Calculate each term separately:
- [tex]\(1 \times 10 = 10\)[/tex]
- [tex]\(3 \times 1 = 3\)[/tex]
- [tex]\(9 \times \frac{1}{1000} = 0.009\)[/tex]
- Sum these values:
- [tex]\(10 + 3 + 0.009 = 13.009\)[/tex]
Option B: [tex]\((1 \times 10) + (3 \times 1) + \left(9 \times \frac{1}{10}\right)\)[/tex]
- Calculate each term separately:
- [tex]\(1 \times 10 = 10\)[/tex]
- [tex]\(3 \times 1 = 3\)[/tex]
- [tex]\(9 \times \frac{1}{10} = 0.9\)[/tex]
- Sum these values:
- [tex]\(10 + 3 + 0.9 = 13.9\)[/tex]
Option C: [tex]\((1 \times 10) + (3 \times 1) + \left(9 \times \frac{1}{100}\right)\)[/tex]
- Calculate each term separately:
- [tex]\(1 \times 10 = 10\)[/tex]
- [tex]\(3 \times 1 = 3\)[/tex]
- [tex]\(9 \times \frac{1}{100} = 0.09\)[/tex]
- Sum these values:
- [tex]\(10 + 3 + 0.09 = 13.09\)[/tex]
3. Compare the calculated results to identify the correct expression:
- Option A results in 13.009.
- Option B results in 13.9.
- Option C results in 13.09.
Thus, when we carefully evaluate the expressions, we can conclude that the option which correctly represents 1 ten, 3 ones, and 9 thousandths is:
Option A: [tex]\((1 \times 10) + (3 \times 1) + \left(9 \times \frac{1}{1000}\right)\)[/tex]
Hence, the correct answer is (A).
