Question

Express the following decimals to the nearest tenth. 0.13 ______

Short answer

0.13 rounded to the nearest tenth is 0.1.

Step-by-step solution

Understanding Decimal Place Values

Decimals are numbers that contain a decimal point. In the number 0.13, the digit after the decimal point, '1', is in the tenths place, and the digit '3' is in the hundredths place.

Rounding to the Nearest Tenth

To round a number to the nearest tenth, we look at the hundredths place. If the digit in the hundredths place is 5 or more, we round up. If it is less than 5, we keep the tenths place the same and drop all digits to the right.

Applying the Rounding Rule

The number 0.13 has '3' in the hundredths place, which is less than 5. So, we do not round up '1' in the tenths place. The number rounded to the nearest tenth remains 0.1.

Key concepts

Understanding the Tenths Place

The tenths place is the first digit you encounter immediately after the decimal point in a number. It represents one part out of ten and is crucial for determining the value of a decimal number. For example, in the number 0.13, the digit '1' is in the tenths place. This means that there is one-tenth or 0.1. The tenths place helps us understand fractions and decimals in everyday contexts, such as money or measurements. By recognizing the tenths place, we can accurately represent and compare decimal numbers.

Getting to Know the Hundredths Place

The hundredths place is the second digit after the decimal point. It shows one part out of one hundred. In 0.13, the digit '3' is in the hundredths place, meaning three-hundredths or 0.03.
This position is more precise than the tenths place and is important when details matter, like in measurements or financial calculations. Understanding the hundredths place helps us see smaller differences in decimal numbers, which can be crucial for precision. When rounding decimals, knowing the hundredths place is key to applying rounding rules correctly.

Grasping the Basics of Rounding Rules

Rounding rules help simplify numbers but still keep them as accurate as possible. When we round decimals, specifically to the nearest tenth, we look at the hundredths place.

• If the hundredths digit is 5 or more, round up the tenths place by one.
• If it is less than 5, keep the tenths digit the same and drop all digits to the right.

For example, in 0.13, since the hundredths digit is 3, which is less than 5, we do not change the tenths digit. Therefore, the number rounded to the nearest tenth is 0.1.
This process helps in estimating and makes numbers easier to work with for practical purposes. Understanding these rules allows us to apply them effectively across various situations.