Question

When multiplying a decimal by a power of 10, the product

Answer 1

the answers are stays the same increases decreases

Answer 2

When multiplying a decimal by a power of 10, the product can be found by shifting the decimal point to the right for positive powers of 10 and to the left for negative powers of 10.

For example:
- If you multiply by \(10^2\) (which is 100), you shift the decimal point two places to the right.
- \(2.5 \times 100 = 250\)

- If you multiply by \(10^{-1}\) (which is 0.1), you shift the decimal point one place to the left.
- \(2.5 \times 0.1 = 0.25\)

In summary, the general rule is:
- **For a positive integer \(n\):**
\[
\text{Decimal} \times 10^n \quad \text{(shift the decimal point } n \text{ places to the right)}
\]

- **For a negative integer \(n\):**
\[
\text{Decimal} \times 10^n \quad \text{(shift the decimal point } |n| \text{ places to the left)}
\]

Answer 3

When multiplying a decimal by a power of 10, the product **increases** if you multiply by a positive power of 10, and **decreases** if you multiply by a negative power of 10.

Here’s a summary:

- **If you multiply by a positive power of 10 (e.g., \(10^1, 10^2\)):** the decimal increases.
- **If you multiply by a negative power of 10 (e.g., \(10^{-1}, 10^{-2}\)):** the decimal decreases.

So, the answers for your question would be:

- **Increases** (for positive powers of 10)
- **Decreases** (for negative powers of 10)

If the context of your question is asking whether the value changes, then when multiplying by powers of 10 the answer would imply that the numerical value itself stays the same in terms of value shifting, but physically represented as larger or smaller based on the direction of decimal movement.