Problem 42 - Calculate With Confidence

Question

Round the following decimals to the nearest thousandth. 0.5673 ___________

Step-by-Step Solution

Answer

0.567

Step 1: Identify the Thousandth Place

In the decimal 0.5673, the digits after the decimal point are 5, 6, 7, and 3. The thousandth place is the third digit after the decimal point. Here, it is the number 7.

Step 2: Identify the Ten-Thousandth Place

Now, find the digit in the ten-thousandth place, which is the fourth digit after the decimal point. In this decimal, that number is 3.

Step 3: Determine if Rounding is Needed

We use the digit in the ten-thousandth place to decide if we need to round the decimal. If this digit is 5 or greater, we round up the number in the thousandth place by 1. If it's less than 5, the number in the thousandth place remains the same. In this case, the digit is 3, which is less than 5.

Step 4: Apply Rounding

Since the ten-thousandth digit is less than 5, we do not round up the thousandth digit. Thus, the number in the thousandth place, 7, stays as it is.

Step 5: Write the Rounded Decimal

After determining that no change is needed, write the rounded decimal as 0.567.

Key Concepts

Thousandth Place

In decimal numbers, each position after the decimal point represents a fraction of ten. Understanding these positions is key when you're asked to round a number, especially to the thousandth place.
So, what is the thousandth place? When you look at a decimal like 0.5673, you can see the digits following the decimal point: 5, 6, 7, and 3.
The first position, right after the decimal, is the tenths place (5 in this case).

• Next is the hundredths place, which is 6.
• The third position is what we're interested in here—the thousandths place, which holds the digit 7 for 0.5673.

This is the numeral that you'll often "round to" when asked, because of its specific role in representing a very precise value in decimal terms.
Being able to quickly identify this place in any decimal number is an essential skill in math!

Rounding Rules

Rounding is a crucial mathematical process that simplifies numbers, making them easier to work with without drastically affecting their value.
The basic principle of rounding to a specific place, like the thousandth, involves evaluating the digit immediately to its right—this is the deciding factor.
Here's the general rule for rounding:

• Look at the digit in the place you are rounding to, here we focus on the thousandth place.
• Identify the next digit, though, in the ten-thousandth place to make your decision.
• If this digit is 5 or more, round up by adding 1 to your target place digit. If it's less than 5, keep your target place digit the same.

For our example number, 0.5673, the ten-thousandth digit is 3. Since 3 is less than 5, the digit in the thousandth place (7) remains unchanged.
Remember, rounding isn't about raising values needlessly; it's about approximation for ease of understanding or calculation.

Decimal Numbers

Decimals are numbers that represent parts of a whole, specifically powers of ten, which makes them incredibly useful in accurately depicting fractions and precise amounts.
A decimal number has two parts: the whole number part on the left of the decimal point, and the fractional part on the right.

• The digits in the fractional part represent tenths, hundredths, thousandths, and so on, moving from left to right.
• Decimal numbers allow us to perform precise calculations and measurements effortlessly.

In the context of rounding, each position or place after the decimal point becomes crucial in determining how we adjust the number to a simpler form.
This specific adjustment maintains significant figures and ensures that mathematical calculations remain accurate yet simplified for ease of use.