`0. 423 ` is equivalent to the fraction `(94)/(99)` (b) `(49)/(99)` (c) `(491)/(990)` (d) `(419)/(990)`

Options

A. `(419)/(999)`
B. `(419)/(990)`
C. `(423)/(1000)`
D. `(409)/(999)`

Answer

To convert the decimal number \(0.423\) into a fraction, we can follow these steps:

### Step 1: Write the decimal as a fraction
We can express \(0.423\) as a fraction by writing it over \(1\):
\[ 0.423 = \frac{0.423}{1} \]

### Step 2: Eliminate the decimal
To convert the decimal into a fraction, we need to eliminate the decimal point. Since there are three digits after the decimal point, we can multiply both the numerator and the denominator by \(1000\):
\[ 0.423 \times \frac{1000}{1000} = \frac{423}{1000} \]

### Step 3: Simplify the fraction
Now we have the fraction \(\frac{423}{1000}\). We need to check if this fraction can be simplified. The numerator \(423\) and the denominator \(1000\) do not have any common factors other than \(1\), so this fraction is already in its simplest form.

### Step 4: Compare with the given options
Now, we need to check which of the given options is equivalent to \(\frac{423}{1000}\):
- (a) \(\frac{94}{99}\)
- (b) \(\frac{49}{99}\)
- (c) \(\frac{491}{990}\)
- (d) \(\frac{419}{990}\)

To compare, we can convert each option to a decimal or cross-multiply to see if they are equivalent.

### Step 5: Check each option
1. **Option (a)**: \(\frac{94}{99} \approx 0.9495\) (not equivalent)
2. **Option (b)**: \(\frac{49}{99} \approx 0.4949\) (not equivalent)
3. **Option (c)**: \(\frac{491}{990} \approx 0.496\) (not equivalent)
4. **Option (d)**: \(\frac{419}{990} \approx 0.423\) (equivalent)

### Conclusion
The equivalent fraction of \(0.423\) is \(\frac{419}{990}\), which corresponds to option (d).