Express each of the following rational numbers in the form of a/b where a and b are integers and b != 0. g) -4.3 h) 114.97 i) 0.012 j) 0.123

Here are the solutions to the problems.

1. Express each of the following rational numbers in the form of $\frac{a}{b}$ where $a$ and $b$ are integers and $b \neq 0$.

g) $-4.3$

Step 1: Write the decimal as a fraction.

$$-4.3 = -\frac{43}{10}$$

The number is already in the form $\frac{a}{b}$.

$$\boxed{-\frac{43}{10}}$$

h) $114.\overline{97}$

Step 1: Let $x$ be the repeating decimal.

$$x = 114.979797...$$

Step 2: Multiply by 100 to shift the decimal past one repeating block.

$$100x = 11497.979797...$$

Step 3: Subtract the original equation from the new equation.

$$100x - x = 11497.979797... - 114.979797...$$ $$99x = 11383$$

Step 4: Solve for $x$.

$$x = \frac{11383}{99}$$ $$\boxed{\frac{11383}{99}}$$

i) 0.012

Step 1: Write the decimal as a fraction.

$$0.012 = \frac{12}{1000}$$

Step 2: Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which is 4.

$$\frac{12 \div 4}{1000 \div 4} = \frac{3}{250}$$ $$\boxed{\frac{3}{250}}$$

j) $0.1\overline{23}$

Step 1: Let $x$ be the repeating decimal.

$$x = 0.1232323...$$

Step 2: Multiply by 10 to shift the decimal just before the repeating block.

$$10x = 1.232323...$$

Step 3: Multiply by 1000 to shift the decimal past one repeating block and the non-repeating digit.

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