Question

Identify the decimal with the largest value in the following sets. 0.1,0.05,0.2 ______

Short answer

0.2 is the largest decimal.

Step-by-step solution

List the Decimals

The given decimals in the set are 0.1, 0.05, and 0.2. Our task is to find which of these has the largest value.

Compare Digits after the Decimal Point

First, look at the digits immediately after the decimal point for each number. For 0.1, this is 1. For 0.05, this is 0, and for 0.2, this is 2.

Determine the Largest Decimal

Comparing the first digit after the decimal point (tenths place), we have 1 for 0.1, 0 for 0.05, and 2 for 0.2. Since 2 is the largest among these, 0.2 is the largest decimal in this set.

Key concepts

Decimal Places

When we talk about decimal numbers, understanding decimal places is crucial. Decimal places refer to the numbers that appear after the decimal point. Each digit has a place value, and these are crucial for determining a number's size.
For example, in the number 0.1, the digit '1' is in the first position to the right of the decimal point. In contrast, in 0.05, the digit '5' is in the second position, and '0' is in the first. This positioning affects their value significantly.

• The first position after the decimal is the tenths place.
• The second is the hundredths place.
• Subsequent positions include the thousandths, ten-thousandths, and so on.

The further to the right a digit is, the smaller its contribution to the overall value of the number.

Tenths Place

The tenths place is the very first digit to the right of the decimal point. This is a fundamental concept when comparing decimals, as it can often determine the larger or smaller value when the whole numbers are equal.
In our given set of numbers, 0.1, 0.05, and 0.2, identifying the tenths place is straightforward. In 0.1, the digit in the tenths place is 1. For 0.05, this digit is 0, while for 0.2, it is 2. Observing these numbers, the tenths place gives us enough information to determine which decimal is larger or smaller without scrutinizing further decimal places when the tenths digits differ.
If two numbers have the same tenths digit, only then do we look at the next digit, or the hundredths place, to make a more subtle comparison. In our exercise, 0.2 clearly stands apart because of its '2' in the tenths place.

Understanding Decimals

Comprehending how decimals work is essential, especially considering that decimals are an extension of our common number system. They provide precision where whole numbers fall short.
Decimals are often used in financial, scientific, and other practical applications where detailed measurement is important. For example, money is often handled in decimals (like dollars and cents), and scientific data is frequently recorded in decimals for accuracy.
Here are some tips to better understand decimals:

• Each move to the right in a decimal decreases the place value by a factor of ten.
• Comparing decimals is similar to whole numbers—start comparing from the leftmost digit.
• Remember that a zero can pad the decimal at the end without changing the value (e.g., 0.20 is the same as 0.2).

As seen in the exercise, understanding these concepts helps us easily compare decimals and know when one is larger than another. This knowledge is an important part of everyday math literacy.