Question

Divide the following numbers, and round to the nearest hundredth. \(6.45 \div 10=\) ______

Short answer

0.65

Step-by-step solution

Understanding Division by 10

When a number is divided by 10, the decimal point of the number is moved one place to the left. This is a basic rule of division involving powers of ten.

Applying the Division Rule

For the number 6.45, move the decimal point one position to the left. This changes the number from 6.45 to 0.645.

Rounding to the Nearest Hundredth

The number 0.645 needs to be rounded to the nearest hundredth. Look at the third decimal place to decide how to round. Since the number 5 is in the thousandths place, round up the hundredths place from 4 to 5.

Final Solution

After rounding, the final answer to 6.45 divided by 10 is 0.65.

Key concepts

Decimal Point Placement

Decimal point placement is a significant concept when working with division, especially with powers of ten. When you divide a number by 10, you essentially shift the decimal point one place to the left. For instance, dividing 6.45 by 10 transforms it into 0.645. This rule can be expanded:

• Dividing by 100 moves the decimal point two places to the left.
• Dividing by 1000 moves it three places to the left.
• And so forth.

Understanding this rule helps to simplify the division process, making it straightforward without needing lengthy calculations. Always remember, when dividing by a power of ten, think of moving the ‘invisible’ boundary (decimal point) to adjust the value appropriately.

Rounding Decimals

Rounding decimals is an important skill when you need to simplify numbers to make them easier to work with or better fit a context, like financial calculations. To round a number to the nearest hundredth, follow these steps:
1. Identify the location of the hundredths place. For 0.645, the number in the hundredths place is 4.
2. Look at the digit immediately after (in the thousandths place). Here, it is 5.

• If this digit is 5 or greater, you round up the hundredths digit.
• If it is less than 5, you leave the hundredths digit unchanged.

In our example, because the thousandths digit is 5, we round the hundredths place up from 4 to 5, resulting in 0.65. Rounding is essential for maintaining precision where necessary, yet offering a streamlined number for easy use.

Basic Division Rules

Basic division rules are fundamental for solving mathematical problems effectively. One of the core rules, especially when dealing with decimals, is to understand how powers of ten affect division:

• Dividing by 10: Move the decimal one place to the left.
• Dividing by 100: Move the decimal two places to the left.
• Dividing by 1000: Move it three places to the left.

These rules illustrate how the position of a decimal impacts the scale of a number. In our context of dividing 6.45 by 10, the execution is simplified by merely adjusting the decimal point without manual calculations.
Moreover, understanding decimal placement directly correlates with accuracy and efficiency in mathematical operations. Keeping these division principles in mind, especially when dealing with powers of ten, makes the entire process intuitive and less error-prone.