Problem 40 - Algebra A Combined Function

Question

Round each decimal to the given place value. $$ \text { 0.75, nearest tenth } $$

Step-by-Step Solution

Answer

The number 0.75 rounded to the nearest tenth is 0.8.

Step 1: Identify the Tenths Place

In the decimal 0.75, the tenths place is the first digit to the right of the decimal point. Here, the tenths digit is 7.

Step 2: Look at the Next Place Value

Look at the digit in the place immediately to the right of the tenths place, which is the hundredths place. In 0.75, the digit in the hundredths place is 5.

Step 3: Apply Rounding Rules

According to rounding rules, if the digit in the hundredths place is 5 or greater, increase the tenths place by 1. Since the digit is 5, we round up the tenths digit from 7 to 8.

Step 4: Finalize the Rounded Number

After increasing the tenths digit from 7 to 8, the final rounded number is 0.8.

Key Concepts

Tenths Place

In any decimal number, understanding what the tenths place is can significantly help with accurate rounding. The tenths place is the first digit to the right of the decimal point. In essence, this position represents the first level of precision in a decimal.
For instance, in the decimal 0.75, the digit '7' is situated in the tenths place. To put it simply, it reflects seven-tenths of a whole, or equivalent to 70 out of 100 in fraction form. Remembering this location and its significance is essential since it is the first step in the rounding process.

Hundredths Place

Following the tenths place, the hundredths place is the second position to the right of the decimal point. This position provides even more precision by representing fractions of a whole, focusing on hundredths.
In our example of 0.75, the digit '5' resides in the hundredths place. This means we have five-hundredths in this case. Understand that numbers in the hundredths place are crucial for rounding decisions, as they influence whether the tenths place digit will increase or stay the same based on rounding rules.

Rounding Rules

Rounding decimals follows specific rules, ensuring that numbers are more convenient to use or interpret while keeping them as accurate as necessary. Here is a breakdown of these rules:

• Identify the place value you need to round to, such as the tenths place.
• Look at the digit immediately to the right of this place value for guidance.
• If this digit is 5 or greater, increase the target digit by 1.
• If this digit is less than 5, leave the target digit unchanged.

In the context of 0.75, the digit in the hundredths place is '5', which means according to rounding rules, we increase the tenths place digit from 7 to 8, giving us the rounded number of 0.8. By using these rules, we simplify numbers while maintaining a level of accuracy appropriate for most practical uses.