Problem 27 - Prealgebra

Question

Write each of the following as a decimal number. Fifty-five hundredths

Step-by-Step Solution

Answer

Fifty-five hundredths is written as 0.55 as a decimal.

Step 1: Understand the Place Value

The word 'hundredths' refers to the second place to the right of the decimal point. So, we'll be dealing with the hundredth place in the decimal system.

Step 2: Convert Words to Digits

The phrase 'fifty-five' can be broken down into 55. When you hear or see a number like 'fifty-five hundredths,' it is indicating 0.55 because it is essentially 55 divided by 100.

Step 3: Write the Decimal Number

Since we determined that 'hundredths' refers to two decimal places and have 55 as numerals, the number is 0.55.

Key Concepts

Understanding Place Value

Place value is a fundamental concept in understanding numbers, especially when dealing with decimal numbers. It refers to the value of each digit in a number based on its position. In the decimal system, which is the most commonly used number system, the place value of digits is determined from right to left, starting from the decimal point.
For instance:

• The first place to the left of a decimal point is the 'ones' place.
• To the right of the decimal point, the first place is the 'tenths' place.
• The second place to the right is the 'hundredths' place.
• This continues as thousandths, ten-thousandths, and so on for more decimal places.

Grasping this concept helps you to read and write decimal numbers accurately. Understanding which digit is represented at which place value allows you to comprehend the full value of a decimal number, like 0.55, where 5 is in the tenths place and the other 5 is in the hundredths place.

Exploring Decimal Notation

Decimal notation is the representation of numbers using the base-ten system. This system includes the digits 0 through 9 and a decimal point to separate the whole number from the fractional part. Decimal numbers use this notation to express parts of a whole. For example, in the number 0.55, the digit after the decimal point represents tenths and hundredths.

• Numbers before the decimal point denote whole units.
• Digits after the decimal point represent parts of a whole divided into tenths, hundredths, thousandths, etc.

The decimal point is crucial as it indicates the division between whole numbers and fractions. This system makes performing arithmetic operations, such as addition and subtraction, straightforward and systematic. Decimals are used widely due to their simplicity compared to fractions, providing an easy way to deal with numbers less than one.

Converting Words to Numbers

Converting numbers written in words to numeric form is a key skill in mathematics. The process involves understanding both the words used and the numerical value they represent. Consider the phrase 'fifty-five hundredths':

• 'Fifty-five' translates directly into the digits 55.
• The term 'hundredths' communicates that this number is in the second decimal place, suggesting that 55 needs to be expressed in a way that ends in the hundredths position.

This means placing a decimal point before 55, making it 0.55. The number is equivalent to multiplying 55 by 0.01 or dividing it by 100, reflecting its place value in the decimal system.
Mastering conversions from words to numbers helps significantly in mathematics, where reading and writing forms of numbers interchangeably is often required. It's a skill that enhances numerical literacy and ensures accuracy in mathematical calculations and daily financial activities.