Problem 5 - Prealgebra

Question

Write out the name of each number in words. $$3.4$$

Step-by-Step Solution

Answer

3.4 in words is "three point four."

Step 1: Understanding the Whole Number Part

The number given is 3.4. Start by identifying the whole number part, which is 3. The word for the whole number 3 is "three." This is the first part of writing the number in words.

Step 2: Identifying the Decimal

The number 3.4 has a decimal point after the whole number. This decimal point is read as "point" or "decimal." It's important to indicate that you are moving from whole numbers to decimal fractions.

Step 3: Understanding the Fractional Part

The number after the decimal point is 4. Since it is a single digit in the tenths place, we write it as "four tenths" or simply "point four."

Key Concepts

Decimal Numbers

Decimal numbers are numbers that have a whole number part and a fractional part, separated by a decimal point. The decimal point is pivotal in distinguishing the two. For instance, in the number 3.4, the '3' is the whole number part while the '.4' is the fractional part. This fractional part is read after saying the word "point."

• Decimal numbers provide a way to express values between two whole numbers. For example, 3.4 is between the whole numbers 3 and 4.
• They are often used to represent quantities such as money, measurements, and scientific data.
• The position of a number after the decimal determines its size, with the first position to the right of the decimal point representing tenths, followed by hundredths, and so on.

Understanding decimal numbers is crucial for both everyday life and advanced mathematical concepts, as they provide precision when whole numbers are not detailed enough.

Whole Numbers

Whole numbers are the building blocks of the number system, including all positive integers starting from zero. They are the numbers without any fractional or decimal part, like 0, 1, 2, 3, etc. These numbers are fundamental in counting and basic arithmetic.

• Whole numbers are easy to understand as they represent complete units without any division or parts.
• They are always non-negative. There are no whole numbers between two consecutive whole numbers, such as 2 and 3.
• Used in real life to count objects, people, and to measure discreet quantities.

When reading decimal numbers like 3.4, it's essential to first recognize the whole number part, here being '3'. Writing whole numbers in words, such as 3 as "three," is often the first step in numeracy.

Fractions

Fractions are numbers that represent parts of a whole. They consist of a numerator, which is the top part of the fraction, and a denominator, which is the bottom part. In the context of decimal numbers, the fractional part follows the decimal point and introduces divisions of unity into tenths, hundredths, etc.

• A simple example of a fraction is \( \frac{1}{2} \), which means one part of a whole that is divided into two equal parts.
• In decimal numbers, fractions are expressed in a linear form. For instance, in the number 3.4, the '.4' is equivalent to \( \frac{4}{10} \), which means four parts of ten equal divisions or "four tenths."
• Understanding fractions allows more flexibility and precision in expressing non-whole quantities.

Reading decimals like '3.4' involves transforming these decimal fractions into words, deriving the concept of fractions in a straightforward manner.