Question

Round the following decimals to the nearest thousandth. 0.5673 ______

Short answer

0.567

Step-by-step solution

Identify the Thousandths Place

In the number 0.5673, the thousandths place is the third digit to the right of the decimal point. In this case, it's the number 7.

Identify the Digit for Rounding

Look at the digit to the right of the thousandths place to decide whether to round up or stay the same. In 0.5673, the digit in the ten-thousandths place is 3.

Apply Rounding Rule

Since the digit after the thousandths place is 3 (which is less than 5), we round down, meaning the digit in the thousandths place stays the same.

Write the Final Rounded Number

Since we did not need to round up, the final rounded number is 0.567.

Key concepts

Understanding the Thousandths Place

When dealing with decimals, understanding place value is crucial. Each digit has a specific spot that determines its value. After the decimal point, the first digit represents the tenths place, the second digit the hundredths, and the third digit represents the thousandths place. For the decimal 0.5673, the digit '7' is in the thousandths place. This means 7 is multiplied by \(0.001\) or \(\frac{1}{1000}\). Knowing which digit is in the thousandths place helps you decide how to round your decimal accurately. Remember, the thousandths place is three digits to the right of the decimal point. Keeping this in mind makes rounding much easier and more precise.

Applying Decimal Rounding Rules

Rounding decimals involves specific rules that determine whether you 'round up' or 'round down'. Here are the steps:

• Identify the digit in the place you are rounding to; in our case, it's the thousandths place.
• Look at the digit immediately to the right of this place (the ten-thousandths place).
• If the digit in the ten-thousandths place is 5 or greater, increase the digit in the thousandths place by 1 (round up).
• If it is less than 5, leave the digit in the thousandths place as it is (round down).

In the example 0.5673, the digit in the ten-thousandths place is 3, so the thousandths place remains 7. Knowing these rules ensures your rounding is both quick and correct.

Exploring the Place Value System

The place value system is fundamental to understanding why each digit in a number decreases in value as you move from left to right. Each position represents a power of ten, and as you move right past the decimal point, you are dividing by 10 each time. Here's how it works:

• Tenths (\(10^{-1}\)
• Hundredths (\(10^{-2}\)
• Thousandths (\(10^{-3}\)

This hierarchy means decimal numbers can seem complex, but it ensures precision. Knowing the place value system helps in rounding decimals because it clarifies how changing one digit impacts the entire number. For example, even a small change like rounding can significantly alter the value represented by a longer decimal.