Question

Tell the nearest tenths of a centimeter that each given measurement is between. For example, 3.66 is between 3.6 and 3.7 \(5.75 \mathrm{cm}\)

Short answer

5.75 cm is between 5.7 cm and 5.8 cm.

Step-by-step solution

Identify the given measurement

The given measurement is 5.75 cm.

Determine the tenths place

Look at the first digit after the decimal point. In this case, the digit in the tenths place is 7.

Identify the boundaries

Since the tenths place is 7, the measurement 5.75 cm is between 5.7 cm and 5.8 cm.

Key concepts

tenths place identification

When dealing with decimals, it's important to identify the correct place value. For tenths place identification, you should look at the first digit to the right of the decimal point. Let's break this down:

If you have a decimal number like 5.75, the tenths place is the 7. This is because it is the first digit after the decimal which determines the tenths unit.

Identifying the tenths place helps you understand how the number is divided into smaller parts, making it easier to round accurately and compare measurements.

number boundaries

Number boundaries represent the range within which a specific decimal value falls. In our example, the measurement is 5.75 cm. After identifying the tenths place as 7, our boundaries are the nearest tenths it could round to, which are 5.7 cm and 5.8 cm.

Here’s a simple way to determine boundaries:

• First, identify the tenths place.
• Then, the lower boundary will be the same number as the tenths digit followed by 0. (e.g., 5.7)
• The upper boundary will be this digit plus one, followed by 0. (e.g., 5.8)

This makes it clear within which two tenths the original decimal lies.

decimal place value

Understanding decimal place value is essential for accurate measurements and rounding. In decimals, each place to the right of the decimal point represents a fraction of ten. Let’s break them down quickly:

• The first place is the tenths.
• The second place is the hundredths.
• The third place is the thousandths, and so forth.

For instance, in 5.75, the digit 7 is in the tenths place, and the digit 5 is in the hundredths place. Knowing the place value helps you figure out by how much the tenths differ from each other and it’s crucial for precise calculations and comparisons.