Understanding the Division Problem: 80.6 ÷ 4030

The question asks us to find the value of the expression 80.6 divided by 4030. This is a basic arithmetic operation involving a decimal number and a whole number.

How to Perform the Division 80.6 by 4030

To perform the division $80.6 \div 4030$, we are essentially asking how many times 4030 fits into 80.6. Since 80.6 is smaller than 4030, the result will be less than 1. Here's how we can perform the calculation:

We can set up the long division. When dividing a decimal number by a whole number, we divide as usual and place the decimal point in the quotient directly above the decimal point in the dividend.

Consider the division:

$$ \frac{80.6}{4030} $$

To make the division easier, we can remove the decimal from the numerator by multiplying both the numerator and the denominator by 10. This does not change the value of the fraction:

$$ \frac{80.6 \times 10}{4030 \times 10} = \frac{806}{40300} $$

Now we need to calculate $806 \div 40300$.

• 40300 does not go into 806. So, we write down 0 and add a decimal point and a zero to 806, making it 8060.
• 40300 does not go into 8060. So, we write another 0 after the decimal point in the quotient and add another zero to 8060, making it 80600.
• Now we check how many times 40300 goes into 80600. We can see that $40300 \times 2 = 80600$.
• So, 40300 goes into 80600 exactly 2 times. We write down 2 in the quotient.

The quotient is 0.02.

Let's verify the result:

$$ 4030 \times 0.02 = 4030 \times \frac{2}{100} = \frac{4030 \times 2}{100} = \frac{8060}{100} = 80.6 $$

The multiplication confirms that our division is correct.

Comparing the Result with the Options

The result of the division $80.6 \div 4030$ is 0.02.

Let's look at the given options:

• Option 1: 2
• Option 2: 0.02
• Option 3: 20
• Option 4: 0.2

Our calculated value, 0.02, matches Option 2.

Revision Table: Decimal Division Concepts

Additional Information: Understanding Division and Decimals

Division is one of the four basic arithmetic operations. It is the inverse of multiplication. When we divide a number (the dividend) by another number (the divisor), we find out how many times the divisor is contained within the dividend. The result is called the quotient.

Decimal numbers are numbers that include a fractional part represented by digits after a decimal point. Each digit after the decimal point represents a power of 10: tenths, hundredths, thousandths, and so on.

• 0.1 means 1 tenth ($\frac{1}{10}$)
• 0.01 means 1 hundredth ($\frac{1}{100}$)
• 0.001 means 1 thousandth ($\frac{1}{1000}$)

Understanding place value in decimals is crucial for performing arithmetic operations correctly, especially division where the position of the decimal point in the quotient is determined by its position in the dividend.

In our problem, $80.6 \div 4030$, the result is 0.02. This means that 4030 fits into 80.6 exactly 0.02 times. This is a small fraction of a time, as expected when a larger number divides a smaller number.