Problem 24 - Prealgebra

Question

Give the place value of the 5 in each of the following numbers. $$0.356$$

Step-by-Step Solution

Answer

The place value of 5 is the tenths place.

Step 1: Identify the Position

First, we need to identify the position of the digit 5 in the number 0.356. The decimal number is composed of the following place values after the decimal point: tenths, hundredths, thousandths, etc. Here, 5 is located in the place immediately after the decimal point.

Step 2: Determine the Place Value

Since the digit 5 is immediately after the decimal point, it holds the position of the tenths place in the number 0.356. Therefore, the place value of the digit 5 is in the tenths place.

Key Concepts

Decimal Numbers

Decimal numbers are numbers that include a decimal point to represent fractions of a whole. They are essential for expressing values that aren't whole numbers and can describe precise quantities in daily life, such as money or measurements. Behind the decimal point, each position represents a fraction of 10. For instance:

• The first place is the tenths place, representing 1 out of 10.
• The second place is the hundredths place, representing 1 out of 100.
• The third place is the thousandths place, representing 1 out of 1000.

The more places you have after the decimal, the more precise your number becomes. Let's look at the number 0.356. Here, 3 is in the tenths place, 5 is in the hundredths place, and 6 is in the thousandths place. Decimal numbers allow us to understand these fine distinctions between fractions of a unit.

Tenths Place

The tenths place is the first position immediately following the decimal point in any decimal number. It indicates how many tenths are included in that number. To figure out which digit is in the tenths place, look right after the decimal point. In our example of the number 0.356, the digit 3 occupies the tenths place. The value represented by the tenths place will always be a fraction, specifically out of 10. For the digit in the tenths place, its value is calculated by multiplying the digit by 0.1. So here, the value is 3 times 0.1, which equals 0.3. This clear positioning helps us make accurate measurements like 0.3 liters of a fluid, where the 3 represents three-tenths of a liter.

Number Positions

Understanding the different number positions is essential for correctly identifying the value each digit represents within a decimal number. This determines how we express and understand numbers in our daily lives. Number positions are like a map that helps us navigate through numbers. Here's how it works:

• Before the decimal, we have the units and tens places, etc.
• After the decimal, the positions include the tenths place, hundredths place, and so on.

In any given decimal number like 0.356, each digit is in a specific place and plays a crucial role in the value of the number. The sequence of number positions ensures that you accurately identify and calculate the value of each digit based on its position. This understanding is vital for anything from calculating math problems to dealing with currency conversions.