Write True (T) or False (F) against each of the following statements :
`0.9 : 0.36 :: 10 : 4 `

Answer

To determine whether the statement `0.9 : 0.36 :: 10 : 4` is true or false, we need to check if the two ratios are equal. We will do this by simplifying both ratios.

**Step 1: Write down the ratios.**
We have two ratios:
- The first ratio is \(0.9\) and \(0.36\).
- The second ratio is \(10\) and \(4\).

**Step 2: Set up the proportion.**
We need to check if:
\[ \frac{0.9}{0.36} = \frac{10}{4} \]

**Step 3: Simplify the second ratio.**
The second ratio \(\frac{10}{4}\) can be simplified:
\[ \frac{10}{4} = \frac{5}{2} \]

**Step 4: Calculate the first ratio.**
Now, we will calculate \(\frac{0.9}{0.36}\):
\[ \frac{0.9}{0.36} = \frac{9}{3.6} = \frac{9 \times 10}{3.6 \times 10} = \frac{90}{36} \]
Now simplify \(\frac{90}{36}\):
\[ \frac{90 \div 18}{36 \div 18} = \frac{5}{2} \]

**Step 5: Compare the two ratios.**
Now we have:
\[ \frac{0.9}{0.36} = \frac{5}{2} \quad \text{and} \quad \frac{10}{4} = \frac{5}{2} \]
Since both ratios are equal, we conclude that:
\[ 0.9 : 0.36 :: 10 : 4 \quad \text{is True (T)}. \]

**Final Answer:**
The statement is True (T).

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