Solve the following problems involving rounding and arithmetic: a) Round 1.998 to the nearest tenth. b) Find the difference of 1.0046 and 2.68 and round to the nearest hundredth. c) Round 6,755,907 to

a) Round off 1.998 to the nearest tenth.
The tenths digit is 9. The digit in the hundredths place is 9, which is 5 or greater, so we round up the tenths digit.

$$1.998 \approx 2.0$$

The answer is $\boxed{2.0}$.

b) Find the difference of 1.0046 and 2.68 and round off the result to the nearest hundredth.
First, find the difference:

$$2.68 - 1.0046 = 1.6754$$

Now, round 1.6754 to the nearest hundredth. The hundredths digit is 7. The digit in the thousandths place is 5, which is 5 or greater, so we round up the hundredths digit.

$$1.6754 \approx 1.68$$

The answer is $\boxed{1.68}$.

c) Round 6,755,907 to the nearest tens.
The tens digit is 0. The digit in the units place is 7, which is 5 or greater, so we round up the tens digit.

$$6,755,907 \approx 6,755,910$$

The answer is $\boxed{6,755,910}$.

a) Calculate the total bottles of soda produced over 4 months.
January: 10,964,229 bottles
February: 12,726,455 bottles
March: 13,612,900 bottles
April: 5,046,500 bottles
Total production:

$$10,964,229 + 12,726,455 + 13,612,900 + 5,046,500 = 42,350,084 \text{ bottles}$$

The company produced $\boxed{42,350,084 \text{ bottles}}$.

b) Calculate the remaining bottles after sales.
Total bottles produced = 42,350,084 bottles
Bottles sold = 20,892,500 bottles
Remaining bottles:

$$42,350,084 - 20,892,500 = 21,457,584 \text{ bottles}$$

There were $\boxed{21,457,584 \text{ bottles}}$ remaining.

c) Simplify the expression.

$$\frac{0.48 \times 1.6}{6.12 \times 1.6}$$

Cancel out the common factor of 1.6 from the numerator and denominator.

$$\frac{0.48}{6.12}$$

Multiply the numerator and denominator by 100 to remove the decimals.

$$\frac{48}{612}$$

Divide both the numerator and denominator by their greatest common divisor, which is 12.

$$\frac{48 \div 12}{612 \div 12} = \frac{4}{51}$$

The simplified expression is $\boxed{\frac{4}{51}}$.