Problem 31 - Prealgebra

Question

Write each of the following as a decimal number. Eleven and eleven hundredths

Step-by-Step Solution

Answer

The decimal number is 11.11.

Step 1: Understanding the Words

First, break down the phrase 'Eleven and eleven hundredths.' The word 'Eleven' gives us the whole number part.

Step 2: Identifying the Decimal Portion

The phrase 'eleven hundredths' tells us the part of the number after the decimal point. The hundredths place is the second position after the decimal point.

Step 3: Converting to Decimal

Combine the whole number and the decimal portion. Eleven is written as 11, and eleven hundredths as 0.11. Together, you have 11.11.

Key Concepts

Place Value

Place value is a fundamental concept in understanding numbers and their structure. It tells us the value of each digit in a number based on its position. This helps us read and write numbers correctly, especially when dealing with decimals. In a decimal number, the place value changes as you move from left to right according to a specific pattern.
To understand place value better, consider the number 123.45. Each digit has a place value:

• 1 is in the hundreds place, which means its value is 100.
• 2 is in the tens place, contributing a value of 20.
• 3 is in the units place, adding 3.
• The decimal point separates the whole numbers from the decimals.
• 4 is in the tenths place, making its value 0.4.
• 5 is in the hundredths place, giving it a value of 0.05.

Understanding place value allows us to accurately convert words into decimal numbers, knowing exactly which digit belongs where after the decimal point.

Whole Numbers

Whole numbers are the set of numbers without any fractional or decimal components. Simply put, they are entirely complete numbers with nothing following a decimal point. They include all the positive integers starting from zero, like 0, 1, 2, 3, and so on.
In the exercise given, "Eleven" represents the whole number 11 in the decimal number 11.11. Whole numbers are crucial when dealing with decimals, as they form the base from which the fractional part extends. When converting phrases to decimal form, identifying the whole number is the first step, as it comprises the portion of the number before the decimal point.

Decimal Places

Decimal places refer to the position of numbers following a decimal point in a decimal number. Each position after the decimal point represents a different fractional part of 10:

• The first place is the tenths place, equal to 1/10 of a unit.
• The second place is the hundredths place, equal to 1/100 of a unit.
• The third place is the thousandths place, equal to 1/1000 of a unit, and so on.

In our initial exercise, when interpreting 'eleven hundredths,' we identify that the word "hundredths" correlates to the second position after the decimal. Thus, 11 hundredths translates to 0.11 in decimal form. Understanding decimal places helps correctly form numbers where the value diminishes with each step right of the decimal. They enable precise representation of numbers less than one and ensure accurate calculations.