Problem 22 - Prealgebra

Question

Give the place value of the 5 in each of the following numbers. $$0.00532$$

Step-by-Step Solution

Answer

The place value of the 5 is thousandths.

Step 1: Understand Place Values

In a decimal number, the place of each digit to the right of the decimal point corresponds to different fractional parts of ten. The first digit right after the decimal point is the tenths place, the second is the hundredths place, the third is the thousandths place, and so on.

Step 2: Identify the Position of the 5

Locate the digit 5 in the number 0.00532. It is the third digit after the decimal point.

Step 3: Determine the Place Value

Since the 5 is the third digit after the decimal, it occupies the thousandths place. This means its place value is in the thousandths.

Key Concepts

Understanding Decimal Numbers

Decimal numbers are a fundamental part of mathematics, representing values that are not whole numbers. They include a decimal point which separates the whole number part from the fractional part. For example, in the number 3.14, the number 3 represents the whole part and 0.14 represents the fractional part. Dexterity with decimals enables us to handle tiny measurements or express fractions in a way that's more comprehensible in everyday life.

• The numbers to the left of the decimal point are integers, showing complete units or wholes.
• To the right of the decimal point, each digit represents a fraction of a whole, getting smaller as they spread out to the right.

Understanding how decimal numbers work is crucial because it’s this systematic placement that determines the value each digit possesses. This establishes clear communication in mathematics, finance, and sciences.

The Thousandths Place

The concept of the thousandths place is essential when dealing with finer fractions of numbers. In any decimal number, each digit after the decimal point holds a specific place value. As you travel from left to right, starting from the decimal point, we move from larger to smaller parts:

• The first position is the tenths place (1/10).
• The second is the hundredths place (1/100).
• The third is the thousandths place (1/1000).

So, when the digit 5 occupies the third slot, as in our exercise, it is within the thousandths place.
This emphasizes precision in numbers, allowing us to pinpoint exact amounts with just a few digits, which is particularly beneficial in fields like engineering and science, where minute measurements matter.

Fractional Parts of Ten

When talking about decimal numbers, the term 'fractional parts of ten' describes how each position to the right of the decimal point represents a successive division by ten. This builds a tidy hierarchy where each subsequent place is ten times smaller than the one directly to its left.

• The tenths place indicates a single part of ten, or 0.1.
• The hundredths place signifies a single part of a hundred, or 0.01.
• The thousandths place stands for a single part of a thousand, or 0.001.

Support in understanding this sequence comes from viewing the decimal system as a way to break down numbers into smaller and smaller parts, offering both flexibility and precision. This mechanism is vital when performing mathematical operations or interpreting numerical data, enabling clearer insights and reporting.