Arrange the following number in the ascending order of thir order of magnitude
(I) 7853
(II) 0.187
(III) 0.05

Options

A. III, II, I
B. I, II, III
C. II, III, I
D. I, III, II

Answer

To arrange the given numbers in ascending order based on their order of magnitude, we will follow these steps:

### Step 1: Identify the numbers
The numbers given are:
1. \( 7853 \)
2. \( 0.187 \)
3. \( 0.05 \)

### Step 2: Convert each number to scientific notation
We will express each number in the form \( a \times 10^n \), where \( a \) is a number between 1 and 10, and \( n \) is an integer.

1. **For \( 7853 \)**:
- In scientific notation:
\[ 7853 = 7.853 \times 10^3 \]
- Order of magnitude: \( 3 \)

2. **For \( 0.187 \)**:
- In scientific notation:
\[ 0.187 = 1.87 \times 10^{-1} \]
- Order of magnitude: \( -1 \)

3. **For \( 0.05 \)**:
- In scientific notation:
\[ 0.05 = 5.00 \times 10^{-2} \]
- Order of magnitude: \( -2 \)

### Step 3: List the orders of magnitude
Now we have the orders of magnitude for each number:
- \( 7853 \): Order of magnitude = \( 3 \)
- \( 0.187 \): Order of magnitude = \( -1 \)
- \( 0.05 \): Order of magnitude = \( -2 \)

### Step 4: Arrange the orders of magnitude in ascending order
To arrange the numbers in ascending order of their order of magnitude:
- The smallest order of magnitude is \( -2 \) (for \( 0.05 \))
- Next is \( -1 \) (for \( 0.187 \))
- The largest order of magnitude is \( 3 \) (for \( 7853 \))

Thus, the ascending order of the numbers based on their order of magnitude is:
1. \( 0.05 \)
2. \( 0.187 \)
3. \( 7853 \)

### Final Answer
The numbers arranged in ascending order of their order of magnitude are:
\[ 0.05 < 0.187 < 7853 \]

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