Question

Which of the following decimals is smallest? 0.855,0.8,0.085 ______

Short answer

0.085 is the smallest decimal.

Step-by-step solution

Compare tenths place

Look at the first digit to the right of the decimal place in each number, which represents the tenths place. The numbers 0.855 and 0.8 both have a digit '8' in the tenths place, while 0.085 has a '0'.

Determine smallest tenths digit

Since the tenths digit for 0.085 is '0', which is smaller than '8', we can already identify that 0.085 is potentially the smallest number based on the tenths place alone.

Conclusion on smallest number

As tenths place comparison indicates 0.085 has the smallest digit there, it confirms 0.085 is smaller than the others, thus making it the smallest decimal amongst the options.

Key concepts

Tenths Place

When comparing decimal numbers, the tenths place is the crucial first step to consider. This place is found immediately to the right of the decimal point. It represents the largest part of the fractional value of the decimal number. Let’s consider the example from the exercise: 0.855, 0.8, and 0.085.

• In 0.855, the tenths place has the digit '8'.
• In 0.8, the tenths place also has the digit '8'.
• In 0.085, the tenths place has the digit '0'.

The value of the tenths place digit directly affects the size of the whole decimal number. Therefore, identifying and comparing these digits helps us immediately assess which number might be the largest or smallest. In this case, since '0' is the smallest number you can have in the tenths place, 0.085 immediately stands out as potentially the smallest among the three.

Decimal Place Value

Understanding decimal place value is essential in the accurate comparison of decimal numbers. Each digit after a decimal point signifies a fraction of a power of ten. The further right a digit is, the smaller its value. - **Tenths:** The first digit after the decimal. Each step further divides by ten. - **Hundredths:** The second digit to the right. It represents one part of a hundred. - **Thousandths, and so on:** Each successive place value is ten times smaller than the previous digit. When comparing decimals, start from the leftmost digit after the decimal and move rightward only if necessary. Spotting a smaller digit earlier means a smaller number overall, emphasizing the importance of checking digit by digit. In the example 0.855, 0.8, and 0.085, the emphasis is on starting with the tenths place since it is the first and most significant fraction of the whole number. This systematic approach helps solve these problems more accurately and quickly.

Mathematical Problem Solving

Experience in mathematical problem-solving, particularly with decimals, is founded on identifying the key differences between numbers and leveraging systematic methods. In our exercise, the logical steps were clear: identify tenths, then move to smaller place values only if needed. Here’s how you can tackle similar problems: - **Step 1:** Focus first on the most significant decimal place, often the tenths. Compare the digits in this place across all numbers. - **Step 2:** If those are identical, proceed to the next place value, such as hundredths. - **Step 3:** Once a difference is found at any place value, use that finding to draw conclusions about the number’s size. Employing this approach breaks the problem down into manageable parts, limiting confusion and errors. Whether you’re dealing with decimals like 0.855, 0.8, and 0.085, or other number concepts, such systematic problem-solving fosters clearer and quicker solutions.