Problem 60 - Fundamentals of Mathematics

Question

Write this number in decimal form using digits: "fifty-two three-thousandths"

Step-by-Step Solution

Answer

0.052

Step 1: Understand the Structure of the Number

The given number is "fifty-two three-thousandths." This means we have the number fifty-two (52) as the numerator over one thousand (1000) as the denominator.

Step 2: Write the Fraction

The phrase "three-thousandths" tells us that the number 52 is out of 1000. Therefore, we first write 52/1000 as a fraction.

Step 3: Convert Fraction to Decimal Form

To convert the fraction \( \frac{52}{1000} \) to decimal form, perform the division: 52 divided by 1000.

Step 4: Perform the Division

Divide 52 by 1000. This will involve moving the decimal point in 52 three places to the left, resulting in 0.052.

Step 5: Final Step: Verify the Decimal Form

Check if the decimal form, 0.052, corresponds to fifty-two three-thousandths. The digit 5 is in the thousandths place, confirming the conversion.

Key Concepts

Fractions

Fractions represent parts of a whole. They are written in the form of two numbers separated by a slash, like this: \( \frac{a}{b} \). The number on top, known as the numerator, specifies how many parts of the whole we have. The number on the bottom, known as the denominator, indicates the total number of equal parts the whole is divided into.
Example: In the fraction \( \frac{3}{5} \), the 3 is the numerator and 5 is the denominator, meaning we have 3 parts out of a total of 5.
Fractions can represent values less than 1 or more than 1. When the numerator is smaller than the denominator, it represents a part of a total, i.e. \( \frac{3}{5} \) represents less than a whole. If the numerator is larger, it represents more, such as \( \frac{7}{5} \).

Understanding fractions is essential when converting them into decimals, which helps in various math operations.

Numerators and Denominators

The terms "numerator" and "denominator" are fundamental in understanding fractions.

• Numerator: This number tells us how many parts of the whole or group we are discussing. It's the top part of the fraction. In our example of \( \frac{52}{1000} \), 52 is the numerator, representing fifty-two parts.
• Denominator: This number indicates into how many parts the whole is divided. It's the bottom part of the fraction. Here, 1000 is the denominator, suggesting the whole is divided into one thousand equal parts.

Understanding these allows us to grasp the idea of how fractions signify portioning of quantities. For example, sometimes problems will involve changing these quantities to get forms of numbers that are easier to work with, such as decimals.

Decimal Place Value

In decimals, place value plays a crucial role in determining the value of a number. Each digit in a decimal number has a specific place value depending on its position.
For example, in the number 0.052, each number is placed differently:

• The digit '0' is in the tenths place.
• The digit '5' is in the hundredths place.
• The digit '2' is in the thousandths place.

This means 0.052 is equivalent to fifty-two thousandths because the '2' occupies the thousandths slot.
Understanding decimal place value helps during conversion. When moving from a fraction to a decimal, like \( \frac{52}{1000} \), knowing where to place each digit after the decimal point ensures that the number you end up with correctly represents the actual value, which, in our case, is 0.052.