Problem 28 - Elementary Algebra

Question

$$ \text { Round } 0.38 \text { to the nearest tenth. } $$

Step-by-Step Solution

Answer

0.4

Step 1: Identify the tenths place

In the decimal number 0.38, the tenths place is the first digit to the right of the decimal point. Therefore, the tenths place is occupied by the digit 3.

Step 2: Identify the hundredths place

The hundredths place is the second digit to the right of the decimal point. In the number 0.38, the hundredths place is occupied by the digit 8.

Step 3: Determine if rounding is necessary

To round to the nearest tenth, look at the hundredths place. If the hundredths place (8) is 5 or greater, round the tenths place up by 1. If the hundredths place is less than 5, leave the tenths place as it is.

Step 4: Perform the rounding

Since the hundredths place is 8, which is greater than 5, round the tenths place up from 3 to 4.

Step 5: Write the rounded number

Therefore, 0.38 rounded to the nearest tenth is 0.4.

Key Concepts

Decimals

Decimals are numbers that include a decimal point to represent a whole number plus a fractional part. The digits following the decimal point show the parts of a whole divided into ten, hundred, thousand, etc.
A decimal number like 0.38 represents 0 whole units and 38 hundredths (or 38/100).

There are several places in a decimal number:

• Units (Ones) place: The digit just before the decimal point.
• Tenths place: The first digit after the decimal point.
• Hundredths place: The second digit after the decimal point.
• Thousandths place: The third digit after the decimal point.

Understanding decimals is crucial for tasks like rounding, adding, subtracting, and comparing these numbers.

Place Value

Place value in decimals refers to the position of a digit in a decimal number, which determines its value.
Each place carries a different weight based on its position relative to the decimal point.

• In 0.38:
  • The digit 3 is in the tenths place, meaning 3/10 or 0.3.
  • The digit 8 is in the hundredths place, meaning 8/100 or 0.08.

The value of each digit is multiplied by its place value. Correctly identifying place values is essential for rounding and other arithmetic operations involving decimals.

To illustrate, if you were to add 0.38 to 0.02, you would add the tenths and hundredths places separately:

1. Add the tenths place: (3 + 0 = 3).
2. Add the hundredths place: (8 + 2 = 10, carrying over 1 to the tenths).

This simple place value rule ensures accurate calculations.

Rounding Rules

Rounding decimals is the process of simplifying a decimal to a specific place value. It makes numbers easier to work with.
To round a decimal:

1. Identify the place you're rounding to. For example, if rounding 0.38 to the nearest tenth, we look at the tenths place (3).
2. Check the digit immediately to the right (hundredths place). In 0.38, that's 8.
3. Apply the rounding rule:

• If the digit is 5 or more, increase the rounding place digit by 1.
• If the digit is less than 5, leave the rounding place digit unchanged.

Following these steps for 0.38:
The tenths place is 3 and the hundredths place is 8 (which is greater than 5).
So, we round up the 3 to 4.
Thus, 0.38 rounded to the nearest tenth is 0.4.
These simple rules make rounding handy in daily life for estimation and simpler calculations.