Problem 79 - Prealgebra

Question

Round 19.854 to the nearest hundredth.

Step-by-Step Solution

Answer

19.85

Step 1: Identify the Hundredth Place

The hundredth place in the number 19.854 is the second digit to the right of the decimal point. So, in 19.854, the digit '5' is in the hundredth place.

Step 2: Look at the Next Digit

Check the digit right after the hundredth place, which is the thousandth place. In 19.854, the thousandth place is occupied by the digit '4'.

Step 3: Apply Rounding Rules

According to rounding rules, if the digit in the thousandth place is 5 or more, you increase the hundredth place by 1. If it's less than 5, like in this case, you keep the hundredth place unchanged.

Step 4: Write the Rounded Number

Since the thousandth digit is 4, which is less than 5, we keep the hundredth digit as 5. Therefore, 19.854 rounded to the nearest hundredth is 19.85.

Key Concepts

Hundredth Place

When dealing with decimals, understanding the hundredth place is essential. This is the second digit to the right of the decimal point. For instance, in the number 19.854, the digit that resides in the hundredth place is '5'. This position is crucial because it determines the level of precision to which you will round the number. Identifying the hundredth place correctly ensures you apply rounding rules to the correct digits. This knowledge is particularly helpful in various scenarios such as balancing finances, conducting experiments, or when an exact numerical representation is required for a calculation.

Thousandth Place

The thousandth place is the third digit to the right of the decimal point. For the number 19.854, the digit '4' occupies the thousandth place. It plays an important role when rounding to the nearest hundredth. Understanding the value in the thousandth place is vital since it influences whether you adjust the hundredth digit. In practical terms, knowing how these decimal places work can help in measurements and calculations where precision at this level affects outcomes, such as in engineering or scientific data.

Rounding Rules

Rounding rules are simple guidelines that help us determine how to round numbers to a desired level of precision. In rounding decimals:

• If the digit in the place after your rounding position (like the thousandth place when rounding to the hundredths) is 5 or greater, you increase the rounding position by 1.
• If it is less than 5, you leave the rounding position as it is.

These rules ensure that numbers are represented in a way that's both practical and reflective of their actual value. Applying these rounding rules correctly is essential in daily tasks such as financial estimates, statistical data interpretation, and academic assessments.