Question

Divide the following numbers, and round to the nearest hundredth. \(4 \div 4.1=\) ______

Short answer

0.98

Step-by-step solution

Setup the Division Problem

Set up the division \(4 \div 4.1\). This can be interpreted as asking how many times 4.1 goes into 4. You can also express this as the fraction \( \frac{4}{4.1} \).

Perform the Division

Divide 4 by 4.1 using manual division or a calculator. The result is approximately 0.97560975. This decimal number is the result without rounding.

Round to the Nearest Hundredth

Look at the third decimal place to round to the nearest hundredth. The number is 5, so you add 1 to the second decimal place, resulting in 0.98.

Key concepts

Rounding Numbers

Rounding numbers is a handy tool in mathematics that makes results simpler and more manageable. When you round a number, you're adjusting it to be closer to a certain level of simplicity or precision, often dropping less significant digits. In this exercise, we were tasked with rounding the division result to the nearest hundredth.

• To do this, you need to locate the hundredth place in a decimal. For a number like 0.97560975, you focus on the first two digits after the decimal point; here, these are 9 and 7.
• Look one digit beyond where you are rounding to decide what to do. If it's 5 or higher, round up. If it's less than 5, keep it the same. In this example, after the 7 is a 5, so you round up.

Remember that rounding numbers helps in estimation and presentation. It allows you to work with numbers more easily and ensures clearer communication of precision.

Fractions

Fractions are another fundamental concept in mathematics, representing parts of a whole as a ratio between two numbers. In division, such as in our original exercise where 4 is divided by 4.1, fractions provide an alternative way of expressing the problem.

• Here, the division problem \( 4 \div 4.1 \) can be expressed as the fraction \( \frac{4}{4.1} \). This fraction indicates how many times 4.1 fits into 4, which might initially seem counterintuitive as 4 is smaller than 4.1.
• Fractions can be converted to decimals, which can then be further processed or rounded, as was done in the original exercise.
• Understanding fractions also helps in realizing their connection to division, especially when tackling more complex calculations that involve mixed numbers or dividing whole numbers by decimals.

The ability to switch between fractions and divisions is a powerful skill that aids in problem-solving and mathematical reasoning.

Decimal Division

Decimal division involves dividing numbers that include a decimal point, which can sometimes be tricky because of the placement and rounding involved. This process is critical in many real-world applications where precision is important.

• First, ensure you understand the relationship between the two numbers in a decimal division problem, like 4 divided by 4.1.
• Using a calculator often makes decimal division straightforward, delivering a precise but often lengthy decimal result, as seen with 0.97560975 in our example.
• Sometimes it’s necessary to round these results to make the numbers more usable, as prolonged decimals can cause difficulty in interpretation or communication.

Grasping decimal division is important because it helps you understand how to handle numbers less than one and apply these concepts to practical scenarios, such as financial calculations or scientific measurements where exactness is key.