Question

Identify the decimal with the largest value in the following sets. 0.8,0.7,0.12 ______

Short answer

0.8 is the largest decimal.

Step-by-step solution

Compare the Whole Numbers Part

Look at the part of the numbers before the decimal point. For our numbers, 0.8, 0.7, and 0.12, the digits before the decimal point are all 0. When this part of the decimal is the same across all numbers, proceed to the next step.

Compare the Tenths Place

Now, compare the digits in the tenths place (the first digit to the right of the decimal). For 0.8, the tenths digit is 8; for 0.7, it is 7; for 0.12, it's 1. Compare 8, 7, and 1: 8 is the largest. The decimal with the largest number in the tenths place will be the largest decimal unless the tenths digits are the same.

Identify the Largest Decimal

Since 0.8 has the highest tenths digit among the choices and the whole number parts are all the same, 0.8 is identified as the decimal with the largest value.

Key concepts

Decimal Place Value

Understanding decimal place value is essential in comparing and identifying the value of decimals. A decimal number consists of parts on either side of the decimal point: the whole number part and the fractional part.

• The digit immediately to the right of the decimal point is in the tenths place.
• The next digit is in the hundredths place, followed by the thousandths, and so on.

Each position represents a fraction of 10. For example, a digit in the tenths place is $\frac{1}{10}$, and a digit in the hundredths place represents $\frac{1}{100}$. This framework helps us know how to value each part of a decimal systematically. It’s like each digit is a soldier in an army row, and their positions determine their rank and power.

Comparison of Decimals

When comparing decimals, start by examining the digits from left to right, beginning with the whole number part before the decimal point. If these digits are equal, move to the digits after the decimal point. Here’s a simplified approach:

• Firstly, compare the tenths place.
• If they are still equal, compare the hundredths place, and so on.

For instance, when comparing 0.8, 0.7, and 0.12, we observe:

• The whole number parts are identical (all zeros).
• Thus, moving to the tenths place, where 0.8 has an 8, 0.7 has a 7, and 0.12 has a 1.

Since 8 is the largest digit amongst the tenths place, 0.8 has the highest value.

Value Identification in Decimals

Identifying the largest value among decimals involves systematic analysis rather than mere inspection.
To efficiently identify values, follow these steps:

• Firstly, examine the whole number part of the decimals. If they are the same, proceed further.
• Compare the digits in the tenths place.
• If those are identical, check the hundredths, then the thousandths, etc.
• This method ensures you compare the most significant non-zero digit first.

Practicing this skill helps in swiftly determining the largest, smallest, or equal decimals accurately without confusion.