Write The Value Of The Underlined Digit

Mastering Place Value: How to Write the Value of an Underlined Digit

Understanding the value of an underlined digit is a foundational skill in mathematics that unlocks a clear comprehension of our number system. It moves beyond simply recognizing a numeral to understanding its actual worth based on its position. Think about it: this seemingly simple exercise is a critical stepping stone to performing arithmetic operations, working with decimals, and developing dependable numerical literacy. Whether you are a student building confidence or an adult revisiting core concepts, mastering this skill provides clarity and precision in all future mathematical endeavors.

The Foundation: What is Place Value?

Our number system is a decimal system, meaning it is based on the number ten. The value of any digit is determined entirely by its position within a number. This position is called its place value. Each place represents a power of ten: ones, tens, hundreds, thousands, and so on to the left of the decimal point, and tenths, hundredths, thousandths to the right.

Take this: in the number 4,582:

• The digit 4 is in the thousands place, so its value is 4 × 1,000 = 4,000.
• The digit 5 is in the hundreds place, so its value is 5 × 100 = 500.
• The digit 8 is in the tens place, so its value is 8 × 10 = 80.
• The digit 2 is in the ones place, so its value is 2 × 1 = 2.

The face value is the digit itself (e.Because of that, g. , the 8), but its place value is what it is actually worth in that specific spot (e.g., 80). When a digit is underlined, the question is asking for this calculated worth, not just the numeral you see.

A Step-by-Step Guide to Finding the Value

Follow this reliable, four-step process for any number, regardless of size or complexity.

Step 1: Identify the Underlined Digit

Clearly locate the digit that has been underlined. This is your starting point. To give you an idea, in the number 37,251, the underlined digit is 3.

Step 2: Determine Its Place

Look at the position of that underlined digit relative to the decimal point. Count the places from the right, starting at the ones place.

• For whole numbers: ones (1), tens (10), hundreds (100), thousands (1,000), ten thousands (10,000), etc.
• For decimals: tenths (0.1), hundredths (0.01), thousandths (0.001), etc. In 37,251, the 3 is the fifth digit from the right. The sequence is: ones (1), tens (10), hundreds (100), thousands (1,000), ten thousands (10,000). So, the 3 is in the ten thousands place.

Step 3: Write the Place Value as a Number

Express the place you identified as a numerical value. The ten thousands place is 10,000. The hundredths place is 0.01.

Step 4: Multiply the Digit by Its Place Value

This is the final calculation. Multiply the underlined digit (its face value) by the value of its position. For our example: Underlined digit = 3. Place value = 10,000. 3 × 10,000 = 30,000. That's why, the value of the underlined digit 3 in 37,251 is 30,000.

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Practical Examples Across Different Contexts

Let’s apply the steps to various number formats.

Example 1: A Large Whole Number Number: 521,089

1. Underlined digit: 2.
2. Place: Counting from the right (ones, tens, hundreds, thousands, ten thousands), the 2 is in the thousands place.
3. Place value: 1,000.
4. Calculation: 2 × 1,000 = 2,000. Value: 2,000.

Example 2: A Decimal Number Number: 84.376

1. Underlined digit: 7.
2. Place: To the right of the decimal. Positions are: tenths (0.1), hundredths (0.01), thousandths (0.001). The 7 is in the hundredths place.
3. Place value: 0.01.
4. Calculation: 7 × 0.01 = 0.07. Value: 0.07 (or 7/100).

Example 3: A Number with a Leading Zero Number: 04.5

1. Underlined digit: 4.
2. Place: It is immediately to the left of the decimal, in the ones place.
3. Place value: 1.
4. Calculation: 4 × 1 = 4. Value: 4. The zero in the tens place is a placeholder, but it does not change the 4's position.

Common Mistakes and How to Avoid Them

• Confusing Place with Face Value: The most frequent error is stating the digit itself. If the underlined digit is 5, the answer is not "5." You must state its worth (e.g., 500, 0.5, 50).
• Miscounting Places: Always count methodically from the decimal point. To the left: ones are the first digit immediately left of the decimal. To the right: tenths are the first digit immediately right.
• Forgetting the Placeholder Zero: In a number like 60,342, the zero in the thousands place is crucial. If the 3 is underlined, it is in the hundreds place (value 300), not the thousands. The zero "holds the place" but has no value itself.
• Incorrect Decimal Place Names: Remember the "-ths" suffix for decimal places (tenths, hundredths). There is no "oneths" place.

Why This Skill Matters: Beyond the Worksheet

The ability to decompose a number into its place value components is not an isolated academic task. It is the engine for:

• Arithmetic: Adding large numbers is easier when you can mentally add thousands to thousands, hundreds to hundreds, etc. Multiplication algorithms rely entirely on place value.
• Understanding Decimals and Fractions: Recognizing that 0.