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Magazine Chapter 1: Problem 459
Find the place value of the given digits. \(472,981\) (a) 8 (b) 4 (c) 1 (d) 7 (e) 2
Short Answer
Expert verified
80, 400,000, 1, 70,000, 2,000
Step by step solution
01
Identify the digit's position - for 8
In the number 472,981, the digit 8 is in the 'tens' place. The place value of a digit is determined by its position in the number.
02
Calculate place value for 8
Since 8 is in the 'tens' place, its place value is calculated by multiplying 8 by 10: \[ 8 \times 10 = 80 \]
03
Identify the digit's position - for 4
In the number 472,981, the digit 4 is in the 'hundred-thousands' place.
04
Calculate place value for 4
Since 4 is in the 'hundred-thousands' place, its place value is calculated by multiplying 4 by 100,000: \[ 4 \times 100,000 = 400,000 \]
05
Identify the digit's position - for 1
In the number 472,981, the digit 1 is in the 'units' place.
06
Calculate place value for 1
Since 1 is in the 'units' place, its place value is calculated by multiplying 1 by 1: \[ 1 \times 1 = 1 \]
07
Identify the digit's position - for 7
In the number 472,981, the digit 7 is in the 'ten-thousands' place.
08
Calculate place value for 7
Since 7 is in the 'ten-thousands' place, its place value is calculated by multiplying 7 by 10,000: \[ 7 \times 10,000 = 70,000 \]
09
Identify the digit's position - for 2
In the number 472,981, the digit 2 is in the 'thousands' place.
10
Calculate place value for 2
Since 2 is in the 'thousands' place, its place value is calculated by multiplying 2 by 1,000: \[ 2 \times 1,000 = 2,000 \]
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
place value system
The place value system is a way to determine the value of each digit in a number based on its position. In our number system, also called the decimal system or base-10, each place represents a power of 10.
The further left a digit is in a number, the greater its value. Here are some key points:
The further left a digit is in a number, the greater its value. Here are some key points:
- Each digit has a unique place value
- Place values increase by powers of 10 as you move from right to left
- Examples of place values: units (or ones), tens, hundreds, thousands, etc.
digit positions
Digit positions in a number are crucial for identifying their place values. Let鈥檚 clarify how this works in the number 472,981.
Each digit occupies a specific position:
Each digit occupies a specific position:
- The rightmost digit (1) is in the 'units' place.
- The second digit from the right (8) is in the 'tens' place.
- The third digit from the right (9) is in the 'hundreds' place.
- The fourth digit from the right (2) is in the 'thousands' place.
- The fifth digit from the right (7) is in the 'ten-thousands' place.
- The sixth digit from the right (4) is in the 'hundred-thousands' place.
multiplication in place value
To find the place value of a digit, we multiply it by the value of its position.
Let's see the number 472,981:
Let's see the number 472,981:
- For the digit 8 in the 'tens' place: \[ 8 \times 10 = 80 \]
- For the digit 4 in the 'hundred-thousands' place: \[ 4 \times 100,000 = 400,000 \]
- For the digit 1 in the 'units' place: \[ 1 \times 1 = 1 \]
- For the digit 7 in the 'ten-thousands' place: \[ 7 \times 10,000 = 70,000 \]
- For the digit 2 in the 'thousands' place: \[ 2 \times 1,000 = 2,000 \]
