Question

Divide the following numbers, and round to the nearest hundredth. \(37.5 \div 100=\) ______

Short answer

0.38

Step-by-step solution

Understanding the Problem

We need to divide 37.5 by 100 and then round the result to the nearest hundredth.

Perform the Division

To divide 37.5 by 100, move the decimal point two places to the left. Therefore, \(37.5 \div 100 = 0.375\).

Round to the Nearest Hundredth

The number 0.375 is rounded to the nearest hundredth by looking at the thousandth place (the third digit after the decimal point). Since it is 5, we round up the second digit, resulting in 0.38.

Key concepts

Rounding Numbers

Rounding numbers is a way to simplify numbers by adjusting them to the nearest certain place value. This concept is crucial in various fields, like mathematics, finance, and everyday situations, to make numbers easier to work with or communicate. When rounding to the nearest hundredth, you focus on the second decimal place. Here's how you do it:

• Look at the third decimal place (thousandths). This will determine if you round up or stay the same.
• If the thousandth digit is 5 or more, increase the hundredth digit by one.
• If the thousandth digit is less than 5, the hundredth digit remains unchanged.

For instance, in the example of 0.375, the thousandth digit is 5. This requires us to round up the hundredth digit, changing it from 7 to 8, resulting in 0.38. Rounding helps in giving an approximate value that is simpler and more concise.

Decimal Division

Decimal division involves dividing numbers that have decimal points. It's a common mathematical operation useful for distributing quantities in smaller, precise amounts. Here's how to approach decimal division like in the exercise:

• Identify the number you are dividing (dividend) and the number you are dividing by (divisor).
• In cases where the divisor is a power of 10, like 100, simplify by moving the decimal point in the dividend to the left.
• For every zero in the power of 10, move the decimal point that many places to the left.

In the example of dividing 37.5 by 100, the decimal point moves two places since 100 has two zeros, resulting in 0.375. Decimal division allows precise calculations where fine distinctions between values matter, providing accurate results.

Mathematical Operations

Mathematical operations are foundational actions that involve numbers to solve problems and find quantities. They include addition, subtraction, multiplication, and division. In the context of the exercise, division and rounding are central.

• Division helps in breaking down a larger number into smaller, manageable parts or distributing it into equal groups.
• Rounding is employed to adjust a number to a specified level of precision, keeping results user-friendly.

Both processes depend on understanding place values and how numbers interact when shared or simplified. It's essential to conduct these operations correctly to maintain the integrity of the values and understand the relationships within a problem.