Select the option which is related to the third number in the same way as the second number is related to the first number. 0.13 : 0.0169 :: 0.09 : ?
0.0081
Solving Number Analogy with Decimals
Number analogy questions are designed to test your ability to understand the relationship between a pair of numbers and apply that same relationship to find a missing number in another pair. In this question, we are given the analogy 0.13 : 0.0169 :: 0.09 : ? We need to determine the relationship between 0.13 and 0.0169 and then apply it to 0.09 to find the missing number.
Finding the Pattern: 0.13 and 0.0169
Let's analyze the first pair of numbers: 0.13 and 0.0169. We should think about common mathematical operations that could link these two numbers.
- Could it be addition, subtraction, multiplication, or division by a constant? Probably not, as the numbers are quite different.
- Let's consider operations like squaring or cubing.
- What happens if we square 0.13? Squaring a number means multiplying it by itself.
- So, we calculate \(0.13 \times 0.13\).
Calculating the Square of 0.13
To multiply decimal numbers, we can follow these steps:
- First, multiply the numbers ignoring the decimal points: \(13 \times 13\).
- \(13 \times 13 = 169\).
- Next, count the total number of decimal places in the original numbers. 0.13 has 2 decimal places, and the other 0.13 has 2 decimal places. The total number of decimal places is \(2 + 2 = 4\).
- Finally, place the decimal point in the result (169) so that it has 4 decimal places. Starting from the right, move the decimal point four places to the left, adding leading zeros as needed.
- \(169 \rightarrow 16.9 \rightarrow 1.69 \rightarrow 0.169 \rightarrow 0.0169\)
So, \(0.13 \times 0.13 = 0.0169\). This shows that the second number is the square of the first number in the pair: \(0.13^2 = 0.0169\).
Applying the Pattern to 0.09
The relationship is that the second number is the square of the first number. We need to apply this same relationship to the third number, 0.09, to find the missing fourth number.
- We need to calculate the square of 0.09.
- This means we need to find \(0.09 \times 0.09\).
Calculating the Square of 0.09
Let's calculate \(0.09 \times 0.09\):
- Multiply the numbers ignoring the decimal points: \(9 \times 9\).
- \(9 \times 9 = 81\).
- Count the total number of decimal places in the original numbers. 0.09 has 2 decimal places, and the other 0.09 has 2 decimal places. The total number of decimal places is \(2 + 2 = 4\).
- Place the decimal point in the result (81) so that it has 4 decimal places. Starting from the right, move the decimal point four places to the left, adding leading zeros.
- \(81 \rightarrow 8.1 \rightarrow 0.81 \rightarrow 0.081 \rightarrow 0.0081\)
Therefore, \(0.09 \times 0.09 = 0.0081\).
Comparing with Options
The missing number in the analogy is 0.0081. Let's compare this with the given options:
- Option 1: 0.81
- Option 2: 0.0081
- Option 3: 0.081
- Option 4: 0.00081
Our result, 0.0081, matches Option 2.
Conclusion
The analogy follows the pattern where the second number is the square of the first number. By squaring 0.09, we get 0.0081, which is the correct missing number in the analogy.
Revision Table: Number Analogy & Decimal Squares
| Concept | Description | Example |
|---|---|---|
| Number Analogy | Identifying the relationship between two numbers and applying it to another pair. | A : B :: C : D (If B relates to A by a rule, D relates to C by the same rule) |
| Squaring a Number | Multiplying a number by itself (e.g., \(x^2\)). | \(0.5^2 = 0.5 \times 0.5 = 0.25\) |
| Decimal Multiplication | Multiply numbers without decimals, then place decimal point by summing decimal places of the multipliers. | \(0.1 \times 0.2\). \(1 \times 2 = 2\). Total decimal places = 1 + 1 = 2. Result = 0.02. |
| Applying the Rule | Once the rule (e.g., squaring) is found, apply it consistently to the third number. | If A : \(A^2\) :: C : ?, the answer is \(C^2\). |
Additional Information: More on Decimal Arithmetic
Understanding decimal operations is key to solving problems like this. When squaring decimals, the number of decimal places in the result is always double the number of decimal places in the original number. For example:
- 0.1 (1 decimal place) squared is 0.01 (2 decimal places).
- 0.01 (2 decimal places) squared is 0.0001 (4 decimal places).
- 0.001 (3 decimal places) squared is 0.000001 (6 decimal places).
This rule is a quick way to check your decimal squaring calculations.
Important Questions from Letter and Number Based
Select the related number from the given alternatives that will complete the series:
Y 2 : 4 : : V 2 : ?Select the related number from the given alternatives:
F : 216 : : L : ?In the following question, select the related number from the given alternatives.
52 : 57 ∷ 46 : ?Select the option in which the numbers are related in the same way as are the numbers of the following set.
(4, 25, 105)
Select the option that is related to the third term in the same way as the second term is related to the first term.
267 : 5 :: 549 : ?
