Problem 75 - Prealgebra

Question

Round 89.3033 to the nearest thousandth.

Step-by-Step Solution

Answer

89.303

Step 1: Identify the thousandth place

In the number 89.3033, the digit '3' in '3033' represents the thousandth place. Thus, we underline or highlight the third digit after the decimal point: 89.30_3_3.

Step 2: Determine which digit impacts the rounding

The rule for rounding is to look at the digit immediately to the right of the place value we are rounding to. In this case, we need to look at the digit in the ten-thousandth place, which is the last '3' in 89.30_3_3.

Step 3: Apply the rounding rule

If the digit in the ten-thousandth place (which is 3 in this case) is less than 5, we do not change the digit in the thousandth place. If it were 5 or more, we would increase the thousandth place by 1.

Step 4: Result of rounding

Since the ten-thousandth digit is 3, we do not round up the thousandth place digit. Therefore, the rounded number is 89.303.

Key Concepts

Understanding Decimal Places

When dealing with decimal numbers, it's essential to comprehend what decimal places are. Decimal places refer to the digits that come after the decimal point in a number. These digits represent values less than one and are part of what we call a decimal fraction. For seeing the importance of these positions, imagine the number 89.3033. Here, '3033' are the decimal places.

• The first digit '3' after the decimal is in the tenths place. It holds a value of 0.3.
• The second digit '0' is in the hundredths place, representing 0.00 as it doesn't add any value.
• The third digit '3' is in the thousandths place, which adds 0.003 to the number.
• The fourth digit '3' is in the ten-thousandths place, a tiny fraction of 0.0003.

Recognizing these decimal places allows us to decide how precise our number should be based on what is significant or necessary for a specific situation.

Place Value Significance

Place value is crucial in understanding the worth of each digit in the number, depending on its position. When rounding numbers, knowing this helps us focus on the correct digit to change.
For the number 89.3033, the digits after the decimal point no longer represent whole numbers but parts of one. The place value system works the same way as it does for whole numbers, only in reverse:

• The thousandth place is where you'll find the third digit after the decimal point, which is significant when rounding to this place.
• This place value directly aligns with how much of one unit it represents, in this case, 0.003.

In practicality, knowing which digits stand at what place value means knowing exactly what part of the whole number each digit represents. This basic understanding is important for effective math skills, especially when accuracy is vital, such as in mathematics, science, and engineering.

Rounding Rules Simplified

Rounding numbers might seem challenging at first, but it's quite straightforward once you grasp the basic rules. The purpose of rounding is to simplify numbers, making them easier to work with by eliminating less significant digits.
To round a number like 89.3033 to the nearest thousandth, follow these steps:

• Locate the thousandth digit, which in this case is '3'.
• Look at the digit directly to the right, in the ten-thousandth place - another '3'.
• If this ten-thousandth digit is 5 or greater, you round the thousandth place up by adding one. Otherwise, stay put.
• Since the ten-thousandth is 3 (less than 5), we don't add anything to the thousandth place.

Therefore, the rounded number remains 89.303. Understanding and applying these rounding rules makes dealing with lengthy decimal numbers more manageable, leaving us with cleaner, more concise figures to work with.