Question

Round each number to one decimal place. $$398.36$$

Short answer

398.36 rounded to one decimal place is 398.4.

Step-by-step solution

Identify the Place Value to Round To

Determine that you need to round the number to one decimal place, which is the tenths place.

Find the Digit in the Desired Place Value

Locate the digit in the tenths place, which is 3 in the number 398.36.

Check the Digit to the Right

Look at the digit to the right of the tenths place to determine if you round up or keep the same. This is the digit 6 in the hundredths place.

Apply Rounding Rules

Since the digit in the hundredths place is 6 (which is 5 or greater), round the digit in the tenths place up by 1. So, 3 becomes 4.

Write the Rounded Number

The complete number rounded to one decimal place is 398.4.

Key concepts

Place Value

Understanding the concept of place value is fundamental to rounding decimals, as it dictates the value of digits based on their position in a number. Decimal numbers are essentially a way of expressing numbers that aren't whole, with each place to the right of the decimal point representing a fraction of 10. For instance, in the number 398.36, the digit 3 is in the tenths place, meaning it is worth 3/10 or 0.3, while the digit 6 is in the hundredths place, meaning it is worth 6/100 or 0.06. When asked to round to a specific place value, such as 'to one decimal place,' it signifies the need to look at the number in the tenths place and use the number directly to the right of it to determine whether to round up or down.

Rounding Rules

Rounding decimals involves a set of simple rules which tell us how to round numbers. These are critical for ensuring accuracy while simplifying numbers. To round a number to a certain decimal place, we look at the digit immediately to the right of the targeted place. The general rule is that if this digit is 5 or greater, we increase the value of the digit we are rounding to by one; if it is less than 5, we leave it as it is. In the example of rounding 398.36 to one decimal place, since the digit to the right (6) is more than 5, we round up the tenths place from 3 to 4, leading to a rounded number of 398.4. Understanding and applying these rounding rules precisely is essential for executing the process of rounding correctly.

Decimal Notation

The decimal notation system is a method of writing numbers that uses a decimal point to separate the whole number part from the fractional part. In this system, each position to the right of the decimal point represents progressively smaller subdivisions of the whole number. In the context of our example, 398.36 is in decimal notation, with 398 being the whole number part and .36 representing the fractional part. In everyday use, decimal notation is preferred for its precision, especially in finance, scientific measurements, and when dealing with data that requires accuracy beyond whole numbers. When you're rounding such numbers, you're essentially streamlining the decimal notation to make it simpler or to match the level of precision required for a specific context.