Question

\(1.80264 \div 0.203=\)

Short answer

8.88

Step-by-step solution

Rewrite the Division

Rewrite the given division problem as a fraction: \(\frac{1.80264}{0.203}\)

Remove Decimal from Divisor

To remove the decimal from the divisor (0.203), multiply both the numerator and the divisor by 1000 (since the divisor has three decimal places):\[\frac{1.80264 \times 1000}{0.203 \times 1000} = \frac{1802.64}{203}\]

Perform the Division

Divide 1802.64 by 203 using long division or a calculator: \( \frac{1802.64}{203} \thickapprox 8.88 \)

Key concepts

Fraction

In mathematics, fractions are a way to represent numbers between whole numbers. A fraction consists of two parts: the numerator (top part) and the denominator (bottom part). For instance, \(\frac{3}{4}\) indicates 3 parts out of 4 equal parts. Fractions can represent parts of a whole, ratios, or even division.

In the exercise, we first transform the division problem into a fraction: \(\frac{1.80264}{0.203}\). This step makes it easier to handle and visualize the problem. By interpreting the division as a fraction, you set up for a more straightforward manipulation of the numbers. This transformation allows you to leverage properties of fractions to simplify and solve the problem more efficiently.

Decimal Removal

Decimals are another way to express fractions. For example, 0.25 is the same as \(\frac{1}{4}\). When working with division, particularly with decimals, it can be beneficial to eliminate the decimal points to simplify the calculation.

In our example, to get rid of the decimal in the divisor (0.203), we multiply both the numerator and the denominator by 1000. This conversion changes \(\frac{1.80264 \times 1000}{0.203 \times 1000}\) to \(\frac{1802.64}{203}\). Multiplying both parts by the same number doesn't change the value of the fraction; it only simplifies handling and clarity.

Removing the decimal simplifies our long division process, making it easier to arrive at the final answer without dealing with floating-point arithmetic, which can sometimes be tricky and error-prone.

Long Division

Long division is a method for dividing large numbers, which can be especially useful when dealing with larger decimals. It breaks down the division into a series of easier steps.

In our example, after removing the decimal, we have \(\frac{1802.64}{203}\). We then perform long division to find how many times 203 fits into 1802.64. The long division involves:

• Dividing the initial digits of the dividend by the divisor
• Finding the quotient
• Multiplying the quotient by the divisor
• Subtracting the result from the dividend
• Bringing down the next digit and repeating

Using this method, 203 fits into 1802 approximately 8.88 times, giving us the quotient. Long division is precise and eliminates the guesswork, leading to an accurate result step by step. Even in the age of calculators, understanding long division helps in grasping fundamental arithmetic concepts and enhances number sense.