Multiplying Decimals by 100 Using Expanded Form

Question

345 × 100
3.45 × 100
(3×100) + (4×10) + (5x1) ×100
x 100
(3x1) +(4x01) +(5x0.01)
30,000 +
+ 500
300 +
+ 5
x 100
Compare to the original number.
34,500.00
345.00
Compare to the original number.
345.00
3.45
The digits 3, 4, and 5 each shifted two places to the left. This is because now
their value is
times more
than what it was before.
Again, each digit shifted two places to
the

Answer 1

right when we multiply the original numbers by 100.

Let's break down the two examples you've provided.

1. For the number 345 multiplied by 100:

   • We can express 345 in expanded form as: \[ 345 = (3 \times 100) + (4 \times 10) + (5 \times 1) \]
   • When we multiply by 100, we need to multiply each part by 100: \[ (3 \times 100 \times 100) + (4 \times 10 \times 100) + (5 \times 1 \times 100) \]
   • Simplifying, we get: \[ 30000 + 4000 + 500 = 34500 \]
   • So, \( 345 \times 100 = 34500 \).

2. For the number 3.45 multiplied by 100:

   • We can express 3.45 in expanded form as: \[ 3.45 = (3 \times 1) + (4 \times 0.1) + (5 \times 0.01) \]
   • When we multiply by 100, we multiply each part by 100: \[ (3 \times 1 \times 100) + (4 \times 0.1 \times 100) + (5 \times 0.01 \times 100) \]
   • Simplifying, we get: \[ 300 + 40 + 5 = 345 \]
   • So, \( 3.45 \times 100 = 345 \).

Observations:

• In both examples, the original value is multiplied by 100.
• In the first example, the value shifts two places to the right to become 34,500. This means that the position of each digit in 345 moved 2 places to the right.
• In the second example, the decimal moves two places to the right, turning 3.45 into 345.

Thus, we see that multiplying by 100 shifts the digits two places to the right, effectively increasing their value.

Conclusion:

• When a decimal is multiplied by 100, the digits shift two places to the right, and their value becomes 100 times more than what it was before.