Solve the following mathematics problems: 1. Round 2,748,595 to the nearest 10,000. 2. Multiply 0.0409 by 0.0021 in standard form. 3. A student spent 1/4 of her money on books and 1/3 on transport. Wh

Here are the solutions to the problems:

3. Write 2,748,595 correct to the nearest 10,000.

Step 1: Identify the digit in the ten thousands place.
The number is 2,748,595. The digit in the ten thousands place is 4.

Step 2: Look at the digit to the right of the ten thousands place.
The digit to the right is 8 (in the thousands place).

Step 3: Round based on the digit identified in Step 2.
Since 8 is 5 or greater, we round up the digit in the ten thousands place. The 4 becomes 5. All digits to the right become zeros.

Step 4: Write the rounded number.

$$2,748,595 \approx 2,750,000$$

The correct option is C.

$$\boxed{\text{C. } 2,750,000}$$

4. Find the product of 0.0409 and 0.0021, leaving the answer in standard form.

Step 1: Convert each number to standard form (scientific notation).

$$0.0409 = 4.09 \times 10^{-2}$$ $$0.0021 = 2.1 \times 10^{-3}$$

Step 2: Multiply the numbers in standard form.

$$(4.09 \times 10^{-2}) \times (2.1 \times 10^{-3})$$

Step 3: Multiply the numerical parts and the powers of 10 separately.

$$(4.09 \times 2.1) \times (10^{-2} \times 10^{-3})$$ $$8.589 \times 10^{(-2) + (-3)}$$ $$8.589 \times 10^{-5}$$

The correct option is B.

$$\boxed{\text{B. } 8.589 \times 10^{-5}}$$

5. A student spent $\frac{1}{4}$ of her money on books and $\frac{1}{3}$ on transport. What fraction of the money was left?

Step 1: Calculate the total fraction of money spent.
Fraction spent on books $= \frac{1}{4}$
Fraction spent on transport $= \frac{1}{3}$
Total fraction spent $= \frac{1}{4} + \frac{1}{3}$

Step 2: Find a common denominator for the fractions and add them.
The least common multiple of 4 and 3 is 12.

$$\frac{1}{4} = \frac{1 \times 3}{4 \times 3} = \frac{3}{12}$$ $$\frac{1}{3} = \frac{1 \times 4}{3 \times 4} = \frac{4}{12}$$

Total fraction spent $= \frac{3}{12} + \frac{4}{12} = \frac{3+4}{12} = \frac{7}{12}$$

Step 3: Calculate the fraction of money left.
The total money is represented by 1 (or $\frac{12}{12}$).
Fraction left $= 1 - \text{Total fraction spent}$
Fraction left $= \frac{12}{12} - \frac{7}{12} = \frac{12-7}{12} = \frac{5}{12}$
The correct option is B.

$$\boxed{\text{B. } \frac{5}{12}}$$