Question

Round each number to one decimal place. $$5.6501$$

Short answer

5.6501 rounded to one decimal place is 5.7.

Step-by-step solution

Understanding Place Value

The task is to round the number to one decimal place. This means we need to look at the second decimal digit (which is in the hundredths place) to decide whether to round up or keep the digit in the tenths place as it is.

Identify the Key Digits

For the number 5.6501, the tenths place is occupied by the digit '6', and the hundredths place by the digit '5'. We need to determine if the hundredths place (5) requires us to round up the tenths place (6) or keep it the same.

Applying Rounding Rules

According to the rounding rules, if the digit in the place you are rounding to is followed by 5, 6, 7, 8, or 9, you round up. Here, the hundredths place is '5', which means we round up the digit in the tenths place from '6' to '7'.

Final Rounded Number

After rounding up, the number 5.6501 rounded to one decimal place is 5.7.

Key concepts

Place Value

Understanding place value is fundamental in mathematics, particularly when it comes to tasks such as rounding numbers. Place value refers to the value of a digit based on its position within a number. For example, in the number 1234, the digit '1' represents one thousand, '2' represents two hundred, '3' represents thirty, and '4' represents four ones.

When dealing with decimals, place value extends to the right of the decimal point. The first place after the decimal is the 'tenths' place, followed by the 'hundredths', 'thousandths', and so on. In the number 5.6501, the digit '6' is in the tenths place, '5' is in the hundredths place, '0' is in the thousandths place, and '1' is in the ten-thousandths place.

Recognizing the place value of digits in a decimal number is crucial as it determines how we round the number to a certain decimal place or whole number.

Decimal Places

Decimal places are used to represent fractions in a base ten system, without using the traditional fraction form (like 1/2 or 3/4). Instead, fractions are written as a point (called a decimal point) followed by digits which convey the magnitude of the fraction. As mentioned earlier, the first digit to the right of the decimal point is the 'tenths', the second is 'hundredths', and it continues accordingly.

The number of decimal places indicates the precision of a value. For instance, in the number 5.6501, there are four decimal places. This precision can be crucial for measurements in science or finance where exact values need to be reported. However, not all situations require such precision, and this is where the practice of rounding becomes applied, to simplify numbers while maintaining a desired level of accuracy.

Rounding Rules

Rounding numbers means adjusting them to a specified degree of accuracy by eliminating less significant digits. The rules for rounding numbers are relatively straightforward and are based on the value of the digit that follows the one you are rounding to.

• If that digit is 5 or greater, round up the desired place.
• If it is less than 5, leave the desired place as it is and drop the rest of the digits.

Using these rules, when rounding the number 5.6501 to one decimal place, you look at the second decimal digit - the hundredths place. Here, the digit is '5', so you round up the digit in the tenths place from '6' to '7'. Thus, the rounded number is 5.7. Understanding these rules is crucial to performing calculations correctly and presenting data appropriately in various contexts, from scientific notations to financial reports. Always remember that rounding can affect the accuracy of your data, so use it judiciously in accordance with the level of precision required.