Problem 19 - Prealgebra

Question

Give the place value of the 5 in each of the following numbers. $$29.52$$

Step-by-Step Solution

Answer

The place value of 5 in 29.52 is five tenths or 0.5.

Step 1: Understanding Place Value in Decimals

Place value in decimals is similar to whole numbers; however, after the decimal point, the first place is tenths, the second is hundredths, and so on. In our case, we need to find the place value of the number 5 in the decimal 29.52.

Step 2: Locate the Number

In the decimal number 29.52, identify where the digit '5' is located. Here, 5 is the first digit to the right of the decimal point.

Step 3: Identify the Decimal Place

Since 5 is the first digit to the right of the decimal point, it is in the tenths place. This means the value of the digit '5' is in the tenths position.

Step 4: Determine the Place Value

Given its position, the digit 5 in 29.52 has a place value corresponding to 0.5 or \( \frac{5}{10} \) because it represents 'five tenths'.

Key Concepts

Tenths Place

When working with decimals, it's crucial to understand the importance of the tenths place. The tenths place is the first position to the right of the decimal point. This spot is significant because it represents fractions of ten.
For instance, consider the number 29.52. Here, the '5' is located right after the decimal point, putting it in the tenths place. This tells us that the number is five tenths of a complete whole, which is a core part of how decimals help us understand parts of a whole.
The tenths place allows us to measure more precisely than whole numbers. By knowing where a number like '5' falls in the sequence, we can accurately interpret it as 0.5 or \( \frac{5}{10} \). This is essential in fields requiring precision, like science or engineering.

Place Value in Decimals

Understanding place value in decimals is quite similar to whole numbers but with a twist after the decimal point. Each digit in a decimal conveys how many of a certain fraction of a whole number there are.

• The first digit after the decimal is the tenths place.
• The second is the hundredths place.
• The third is the thousandths place, and so on.

For example, in the decimal 29.52, each number represents something specific due to its place value: - '2' is in the hundredths place and represents \( \frac{2}{100} \) or 0.02. - '9' stands as a whole number in the ones place next to the decimal.- The concept helps us break down and understand numbers smaller than one, thereby giving us a clearer picture when dealing with measurements, currency, or simply when precise calculations are needed.

Decimal Representation

Decimal representation is a method that describes fractions using a base-ten system. It's a simple yet powerful method because it aligns with the overall numeric system structure most of us use every day—decimals are nothing more than fractions presented in a universally understandable way.
The decimal 29.52, for example, shows how complex numbers can be dissected:

• The '29' represents the whole number portion.
• The '.52' portion elaborates on this, showing additional parts of a whole beyond 29.

This manner of representation allows for an easily interpretable format, especially useful in mathematics and science for denoting quantities with precision. It’s important because it allows us to write numbers in parts that are easily understood by all due to their consistent structure. This clarity and simplicity make decimal representation an essential tool in everyday life.