Problem 22 - Fundamentals of Mathematics

Question

For following problems, give the value of the indicated digit in the given number. 9 in 29,827.

Step-by-Step Solution

Answer

The value of the digit 9 is 90,000.

Step 1: Identify the Place Value

First, look at the given number 29,827 and locate the digit 9. Observe its position relative to the decimal point.

Step 2: Determine the Place Value Category

The digit 9 is positioned in the tens of thousands place. This is the second position from the left in our number, just after the two.

Step 3: Calculate the Value

Multiply the digit 9 by the value of its place position, 10,000. Thus, the calculation is \( 9 \times 10,000 \).

Key Concepts

Tens of Thousands Place

When talking about numbers, understanding where each digit sits is key to knowing its contribution to the whole number. The tens of thousands place is crucial here. In a multi-digit number, this place is five positions from the right. In the number 29,827, the digit nine occupies this position. This spot means it carries a weight of 10,000.
For example, if you have the number 129,827, the digit one would be in the hundred thousands place, the digit two is now in the tens of thousands position.
Recognizing these places helps us interpret the size and significance of each digit and gives us the total value of a number.

• Think of it like building blocks, where the tens of thousands place is one of the bigger blocks.
• In 29,827, since nine is in this place, it contributes 90,000 to the number.
• Without understanding each position, interpreting numbers can be tricky and misleading.

Value of Digits

Every digit in a number has a value, depending not only on its face value but also heavily influenced by its position. The face value is the digit itself, while its position determines how much it's worth. Position gives it a multiplied factor.
In our example, the digit nine in 29,827 has a face value of 9, but because it's located in the tens of thousands place, its true value is 9 times 10,000, making it 90,000.
Understanding this multiplication concept is fundamental to comprehending large numbers.

• Every position in a number increases by a power of ten, compared to the position immediately to its right.
• The different positions can include ones, tens, hundreds, thousands, and more, each getting ten times larger than the previous.
• To find the total value of a digit, always multiply its face value by the value of its position.

Identify Place Value

Identifying the place value means recognizing where a digit stands in a sequence and what it represents. This helps you determine its worth in the context of the entire number.
For 29,827, identifying the place value of 9 involved locating it as the second digit from the left, confirming its standing in the tens of thousands place.

• Identify the position by counting from right to left, starting with the ones, tens, hundreds, and moving up.
• Each movement to the left increases the place's value tenfold, making correct identification crucial for calculations.
• Practice with some written exercises to spot the pattern and get faster at quickly identifying these values in various numbers.

To become proficient at identifying place value, begin with smaller numbers and work your way to more complex sequences. This attention to detail is particularly useful in finance, science, and daily life calculations.