To solve the problem [tex]\( 20 \times 100 \)[/tex] using the rules for multiplication by powers of 10, follow these steps:
1. Identify the base numbers and the powers of 10:
- We have the number [tex]\( 20 \)[/tex], which can be rewritten as [tex]\( 2 \times 10 \)[/tex].
- The number [tex]\( 100 \)[/tex] can be rewritten using powers of 10, specifically [tex]\( 10^2 \)[/tex], since [tex]\( 100 = 10 \times 10 \)[/tex].
2. Rewrite the multiplication expression:
- Combine the expressions: [tex]\( 20 \times 100 = (2 \times 10) \times (10 \times 10) \)[/tex].
3. Regroup the factors:
- Rearrange the factors to group the powers of 10 together: [tex]\( 20 \times 100 = 2 \times (10 \times 10 \times 10) = 2 \times 10^3 \)[/tex].
4. Simplify the expression:
- Calculate [tex]\( 10^3 \)[/tex] which equals [tex]\( 1000 \)[/tex]: [tex]\( 2 \times 1000 = 2000 \)[/tex].
Therefore, the result of multiplying 20 by 100 is [tex]\( 2,000 \)[/tex].
Based on the given options:
A. 20
B. 200
C. 20,000
D. 2,000
The correct answer is:
D. 2,000
