The decimal .1 is how many times greater than the decimal `(.001)3` ?

Options

A. `10`
B. `10^2`
C. `10^5`
D. `10^8`

Answer

To determine how many times greater the decimal 0.1 is than the decimal (0.001)³, we can follow these steps:

### Step 1: Calculate (0.001)³
First, we need to find the cube of 0.001.

\[ (0.001)^3 = 0.001 \times 0.001 \times 0.001 \]

Calculating this gives:

\[ 0.001 \times 0.001 = 0.000001 \]
\[ 0.000001 \times 0.001 = 0.000000001 = 10^{-9} \]

So,

\[ (0.001)^3 = 0.000000001 \]

### Step 2: Compare 0.1 with (0.001)³
Now we compare 0.1 with the result from Step 1.

We have:
- 0.1 = \(10^{-1}\)
- (0.001)³ = \(10^{-9}\)

### Step 3: Calculate the ratio
To find how many times greater 0.1 is than (0.001)³, we can set up the ratio:

\[ \text{Ratio} = \frac{0.1}{(0.001)^3} = \frac{10^{-1}}{10^{-9}} \]

Using the properties of exponents, we can simplify this:

\[ \frac{10^{-1}}{10^{-9}} = 10^{-1 - (-9)} = 10^{-1 + 9} = 10^{8} \]

### Step 4: Conclusion
Thus, 0.1 is \(10^{8}\) times greater than (0.001)³.

### Final Answer:
0.1 is \(10^{8}\) times greater than (0.001)³.

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