When dealing with decimal numbers, each digit has a specific place value that determines its significance in the overall value of the number. The place value of a digit depends on its position relative to the decimal point. In the number 6.857, the digit 5 is in the thousandths place value.
The place value system is based on powers of 10, where each position to the left or right of the decimal point represents a power of 10. Starting from the decimal point and moving left, the first position is the tenths place, followed by the hundredths place, thousandths place, ten thousandths place, and so on.
In the given number, 6.857, the 5 is to the right of the decimal point, which indicates that it is a decimal digit. The 5 is in the thousandths place, as it is the third digit to the right of the decimal point. The place value of the 5 is 0.005, which means it represents five thousandths (0.005) of the total value of 6.857. The 5 contributes to the overall value of the number by adding 0.005 to it.
FAQs about place value:
1. What is the place value of the 8 in 6.857?
The place value of the 8 in 6.857 is the hundredths place.
2. How do you determine the place value of a digit in a decimal number?
To determine the place value of a digit in a decimal number, count the number of decimal places it is away from the decimal point.
3. What is the value of the digit 7 in 6.857?
The value of the digit 7 in 6.857 is 7 times the thousandths place value, which is 0.007.
4. How does the place value system help in understanding decimal numbers?
The place value system helps in understanding decimal numbers by providing a clear representation of the relative significance of each digit.
5. What is the place value of the digit 6 in 6.857?
The place value of the digit 6 in 6.857 is the units (or ones) place.
6. What is the place value of the digit 8 in 86.57?
The place value of the digit 8 in 86.57 is the tens place.
7. Can a digit have a negative place value?
No, a digit cannot have a negative place value. The place value system only applies to positive numbers.
8. What happens when a digit is moved one place to the left?
When a digit is moved one place to the left, its place value increases by a factor of 10.
9. How does the place value system extend to larger numbers?
The place value system extends to larger numbers by repeating the pattern of units, tens, hundreds, thousands, etc., as the digits move to the left.
10. What is the largest place value in the decimal system?
The largest place value in the decimal system is the googolplex, which is a 1 followed by a googol zeros.
11. Can a decimal digit have a place value greater than 1?
No, a decimal digit cannot have a place value greater than 1. The place values in decimal numbers decrease as you move right from the decimal point.
12. How does the place value system help perform arithmetic operations?
The place value system assists in performing arithmetic operations as it allows for alignment of digits in calculations, making addition, subtraction, multiplication, and division easier and more systematic.