Question

Express the following decimals to the nearest tenth. 1.75 ______

Short answer

1.8

Step-by-step solution

Identify the Tenths Place

Look at the number 1.75. The tenths place is the first digit to the right of the decimal point. In this number, the tenths place is occupied by the digit 7.

Examine the Hundredths Place

Look at the digit in the hundredths place, which is the second digit to the right of the decimal point. In 1.75, the hundredths place is occupied by the digit 5.

Apply Rounding Rules

According to rounding rules, if the digit in the hundredths place is 5 or more, we round up the tenths place by 1. Otherwise, we leave the tenths place as is. Since 5 is in the hundredths place, we will round 7 up to 8 in the tenths place.

Write the Rounded Number

After rounding, the number 1.75 becomes 1.8 when expressed to the nearest tenth.

Key concepts

Tenths Place

When rounding decimals, the tenths place is crucial. It is the first digit immediately following the decimal point. In the decimal 1.75, for instance, the tenths place is occupied by the number 7. Knowing how to identify the tenths place helps us to determine where to apply rounding changes. This process is a foundational skill in mathematics education, often learned in elementary school. The tenths place can especially influence how precise a number is or how it's perceived when you conduct further mathematical operations.

Hundredths Place

The hundredths place is the second digit to the right of the decimal point, immediately following the tenths place. In our example, 1.75, the hundredths place holds the digit 5. Understanding its role is vital for rounding purposes. This place helps us decide whether or not to adjust the tenths place. Knowing how to quickly locate and understand the hundredths place is essential in various math problems, especially those involving rounding and estimation.

Rounding Rules

Rounding is a method used to simplify numbers while keeping them as close as possible to the original value. The basic principle in mathematics education is that if the digit in the hundredths place is 5 or higher, we round up the tenths place. If it's lower than 5, the tenths place stays unchanged. In our example of 1.75, since the hundredths digit is 5, we apply the rounding rule to increase the tenths digit from 7 to 8.

• Digits 5 or more: Round up.
• Digits less than 5: Keep as is.

Rounding makes numbers easier to use, especially in mental math and practical applications.

Mathematics Education

Understanding decimal rounding is a fundamental part of mathematics education. It enhances students' number sense and prepares them for more complex operations involving decimals. As students progress in their education, grasping these basics is essential for successful problem solving in advanced mathematics and science disciplines. Teachers often emphasize rounding as it helps students handle calculations more efficiently and with greater accuracy. Such knowledge is also applicable in real-life scenarios, such as financial budgeting and measurements, where precision matters.