Problem 33 - Prealgebra

Question

Write each of the following as a decimal number. One hundred and two hundredths

Step-by-Step Solution

Answer

The decimal representation of 'one hundred and two hundredths' is 100.02.

Step 1: Determine the Whole Number

The whole number part of the expression is 'one hundred'. This means the whole number is 100.

Step 2: Understand the Fractional Part

The phrase 'two hundredths' refers to the fractional part of the number. The word 'hundredths' indicates that the fraction is over 100. Therefore, 'two hundredths' can be written as \( \frac{2}{100} \).

Step 3: Convert the Fraction to a Decimal

To convert the fraction \( \frac{2}{100} \) to a decimal, divide 2 by 100. This gives \( 0.02 \).

Step 4: Combine the Whole Number and Decimal

Combine the whole number 100 and the decimal 0.02. Adding them together gives 100.02.

Key Concepts

Decimal Conversion

Decimals play a vital role in math, allowing us to express parts of a whole number easily. Decimal conversion involves changing fractions or whole numbers into decimal format. It's essential to understand its foundational use.
In the given problem, we start with the number "one hundred and two hundredths." The whole number portion is clear, but we need to convert 'two hundredths' to decimal form.
To break it down:

• "Two hundredths" translates to a fraction of \( \frac{2}{100} \).
• Converting this fraction to a decimal requires dividing 2 by 100.
• The result is a decimal: \( 0.02 \).

Decimal conversion isn't just about calculation, though. It helps us in making comparisons, finding values, and understanding proportions in real-world scenarios.

Fractions to Decimals

The transition from fractions to decimals is a key math concept, providing a simpler form to work with. It involves dividing the fraction's numerator by its denominator.
For example, in the problem, we worked with the fraction \( \frac{2}{100} \). Converting it to a decimal helps us express the value in a more straightforward manner:

• Divide 2 by 100 step by step. Although this seems simple, it's important to remember it's foundational to understanding decimals.
• The result, \( 0.02 \), is what we call a "terminating" decimal because it has a finite number of digits.

The conversion from fractions to decimals is highly applicable, from dealing with currency to scientific measurements.

Arithmetic Operations

Arithmetic operations such as addition, subtraction, multiplication, and division are the basics of math. They are simple calculations that build the bridge for more complex mathematical concepts.
In our exercise, we combined whole numbers with decimals through addition to find the final decimal form of "one hundred and two hundredths."

• The whole number "100" and the decimal "0.02" need to be added together.
• When adding these, align the decimal points and add each column individually.
• This gives a sum of 100.02.

Understanding how to manipulate numbers through operations such as addition is fundamental. It enables us to solve more complex problems with confidence.