Question

Express the following decimals to the nearest hundredth. 0.147 ______

Short answer

0.147 rounded to the nearest hundredth is 0.15.

Step-by-step solution

Identify the Hundredth Position

In the number 0.147, the digits are arranged as follows: 1 is in the tenth position, 4 is in the hundredth position, and 7 is in the thousandth position. To round to the nearest hundredth, we focus on the digit 4.

Examine the Next Digit

To decide how to round the number at the hundredth position, look at the digit immediately to its right. In 0.147, this means looking at the digit 7 in the thousandth position.

Apply Rounding Rules

According to rounding rules, if the digit in the thousandth position is 5 or greater, you add 1 to the digit in the hundredth position. Since the digit 7 is greater than 5, you add 1 to 4, which becomes 5.

Rewrite the Number

After rounding, the number becomes 0.15 as the digits beyond the hundredth place are dropped. This means 0.147 rounded to the nearest hundredth is 0.15.

Key concepts

Decimal Places

When working with decimals, understanding decimal places is crucial for accurate calculations and rounding. A decimal number is made up of digits to the right of the decimal point, each occupying a specific place value.
The basic places to know include:

• The first digit to the right of the decimal point is the tenth position.
• The second digit is in the hundredth position.
• The third digit is in the thousandth position, and so forth.

Each place value represents a fraction of a whole, with the tenth position representing tenths (1/10), the hundredth representing hundredths (1/100), and the thousandth representing thousandths (1/1000).
Accurately identifying these places helps in rounding decimals effectively, ensuring precise mathematical operations.

Rounding Rules

Rounding aims to simplify numbers while retaining their approximate value. It is a key skill for estimates, making calculations easier without significant loss of precision. The process involves:

• Identifying the digit you need to round to; for example, rounding to the nearest hundredth involves focusing on the hundredth position.
• Checking the digit immediately to the right; this digit determines whether you round up or stay the same.

According to rounding rules, if this next digit is 5 or greater, you round up by adding 1 to the target digit. If it’s less than 5, the target digit stays the same.
For example, in the decimal number 0.147, to round to the nearest hundredth, you look at the thousandth digit, which is 7. Since 7 is greater than 5, you round the hundredth digit from 4 to 5, resulting in 0.15.

Thousandth Position

The thousandth position in a decimal number is three places to the right of the decimal point. It plays an important role in precise rounding decisions.
Let's look at an example with the number 0.147:

• The digit 7 is in the thousandth position.
• It directly influences the rounding of the hundredth place when you're rounding to two decimal places.

This position tells you whether to round the digit before it up or keep it as is. By examining the thousandth digit, you can decide how to adjust the number accurately when rounding to the nearest hundredth. Understanding its impact helps ensure you achieve precision in rounding tasks, transforming complex decimal numbers into simpler ones that are easier to use.