Problem 161 - College Algebra

Question

If 6.2 is multiplied by \(10^{3},\) what does this multiplication do to the decimal point in \(6.2 ?\)

Step-by-Step Solution

Answer

Multiplying 6.2 by \(10^{3}\) moves the decimal point three places to the right, giving the result 6200.

Step 1: Identify the number and the power of 10

Here, the number is 6.2 and it is being multiplied by \(10^{3}\), which is the cube of 10, or 1000.

Step 2: Understand the impact of multiplication by a power of 10

When a decimal number is multiplied by a power of 10, the decimal point moves to the right. The number of places it moves is determined by the exponent in the power of 10. In this case, the exponent is 3, so the decimal point should move three places to the right.

Step 3: Perform the multiplication

Move the decimal point in 6.2 three places to the right. Since there are only numbers till the tenths place in 6.2, we place two more zeros. The multiplied result will be 6200.