Question

Divide the following numbers, and round to the nearest hundredth. \(5 \div 14.3=\)

Short answer

The quotient rounded to the nearest hundredth is 0.35.

Step-by-step solution

Set up the Division

Start by setting up the division problem where 5 is the dividend and 14.3 is the divisor.

Perform the Division

Divide 5 by 14.3 using long division or a calculator, obtaining the result approximately equal to 0.34965034.

Round to the Nearest Hundredth

Look at the third digit after the decimal point, which is 9, to determine how to round the second digit after the decimal point. Since 9 is more than 5, increase the second digit by one. Thus, 0.34965034 rounded to the nearest hundredth is 0.35.

Key concepts

Division

Division is a fundamental mathematical operation where you split a number (called the dividend) into equal parts, based on the number of parts indicated by another number (the divisor). In the case of our example, 5 is the dividend and 14.3 is the divisor. Think of division as determining how many times the divisor can fit into the dividend. This helps in figuring out the quotient, which is the result of the division. Performing division correctly is important because it forms the basis for understanding more complex arithmetic and algebra. Breaking down numbers helps you see patterns and make calculations manageable.

Decimal Numbers

Decimal numbers are a way of representing fractions or numbers that are not whole. They use a dot, known as the decimal point, to separate the whole number part from the fractional part. For example, in 14.3, 14 is the whole number and 0.3 is the decimal part. These numbers are crucial in mathematics as they provide an easy way to express and compute fractions. Decimals are also essential for precision, especially in measurements and scientific calculations, where whole numbers won't suffice. When you're doing division with decimals, you need to consider both parts of the number, and be careful with the decimal point to ensure your answer is accurate.

Nearest Hundredth

Rounding to the nearest hundredth means you look at the hundredths place of a decimal number, which is the second digit to the right of the decimal point. In our solution, after dividing, we obtained 0.34965034. In the hundredths place, you have 4. To round, examine the next digit, which is 9. Since it's 5 or greater, you'll increase the hundredths place by one. Therefore, 0.34965034 becomes 0.35 when rounded. Rounding helps simplify numbers, making them easier to work with, or provide a sensible approximation when high precision is not necessary.

Long Division

Long division is a methodical process used for dividing larger numbers or complex divisions. It involves dividing in steps, bringing down digits, and subtracting until you've worked through the entire dividend. For decimal division, the key step is aligning the decimal points in both the dividend and divisor to ensure an accurate quotient. With our example, dividing 5 by 14.3, long division can be complex due to the decimal. By handling this systematically, step by step, you get a detailed view of how the division works. Long division is crucial for understanding the mechanics behind division even when calculators automate the process. It reinforces your skills in arithmetic operations.