The PLACE VALUE.
is a chart used to determind the position and value of a digit in a group of numbers
No. Starting with the highest place value column (the one that contains a non-zero digit) that occurs in the numbers, compare place value columns moving right if equal until either all the digits in both numbers have been exhausted (in which case the numbers are equal) or one place value column digit is greater (in which case the number with the greater digit is the greater number). If a place value column is empty in one of the numbers, its value is taken is zero (the digit 0) For 0.856 and 0.8561 the highest place value column used is the tenths, so comparing 0.856 to 0.8561: 8 = 8, so check hundredths 5 = 5, so check thousandths 6 = 6, so check ten-thousandths 0.856 has a blank ten-thousandths column, so it is taken as 0 0 < 1, so 0.856 < 0.8561
The highest digit is one less than the base used for counting. So in binary (base 2), the highest digit is 1 In octal (base 8), the highest digit is 7 In decimal (base 10), the highest digit is 9 In hexadecimal (base 16), the highest "digit" is 15. The symbols A, B, C, D, E and F represent the "digits" 10, 11, 12, 13, 14 and 15. And so on.
The precision of a number is determined by its last digit. The true value lies with a half of the place value of this last digit. In the above case it is the 6, which is in the thousandths place. So the true value lies within half-of-one-thousandths of the given number. That is, it lies in the interval [234.8955, 234.8965]. I use round-to-even, which is the default rounding mode used in IEEE 754 standard for computing functions and operators.
9
The PLACE VALUE.
The 'zero' digit is used as a place-holder.
A place value chart is used to help understand the value of each digit based on the place or position.
In the decimal number system, the largest digit that can be used in each place value is 9. Place values increase by a power of 10 as you move from right to left, so the ones place can hold digits 0-9, the tens place can hold digits 0-9, and so on. The largest digit in each place value represents the highest value that can be assigned to that position in a number.
is a chart used to determind the position and value of a digit in a group of numbers
In the decimal number system, the highest valued digit is 9. The highest digit that ever appears in any one 'place' of a number is one less than the 'base' of the number. The numbers that everyone is most familiar with ... the numbers you see around you every day ... are numbers written in the 'decimal' system, using the 'base' of 10. So the highest digit in any one place is 9. 'Binary' numbers ... the form most used to represent numbers inside digital circuits and computers ... are constructed in base 2. So the highest digit in any one place is 1, and each of these numbers is just a string of 1's and zeros. Digits can be even higher than 9 in number systems that use other bases. For example, the hexadecimal system (often used in computer science to represent binary numbers) is base 16, so in that case the highest valued digit is "F" which has a value equivalent to 15 in a decimal representation. As an example, the number "FA" hexadecimal, has decimal value 15*16 + 10 = 250.
No. Starting with the highest place value column (the one that contains a non-zero digit) that occurs in the numbers, compare place value columns moving right if equal until either all the digits in both numbers have been exhausted (in which case the numbers are equal) or one place value column digit is greater (in which case the number with the greater digit is the greater number). If a place value column is empty in one of the numbers, its value is taken is zero (the digit 0) For 0.856 and 0.8561 the highest place value column used is the tenths, so comparing 0.856 to 0.8561: 8 = 8, so check hundredths 5 = 5, so check thousandths 6 = 6, so check ten-thousandths 0.856 has a blank ten-thousandths column, so it is taken as 0 0 < 1, so 0.856 < 0.8561
The highest digit is one less than the base used for counting. So in binary (base 2), the highest digit is 1 In octal (base 8), the highest digit is 7 In decimal (base 10), the highest digit is 9 In hexadecimal (base 16), the highest "digit" is 15. The symbols A, B, C, D, E and F represent the "digits" 10, 11, 12, 13, 14 and 15. And so on.
The use of the digit 0 in a number is to indicate place value. It enables you to distinguish between 405 and 45, for example.
To compare any two numbers:Start with the highest place value column used by one or both of the numbers.If a place value column is empty, its value is zero (0)Whichever has the greater digit is the greater number.If the two digits are the same, move right a columnif at least one number has a digit there repeat from step 2if no more digits exist in either number then the numbers are the same.In this case the first used place value column is the tenths column (the first column to the right of the decimal point).0.666 has a 6 whereas 0.8 has an 8;8 > 6 → 0.8 > 0.666No, 0.666 is not greater than 0.8
The precision of a number is determined by its last digit. The true value lies with a half of the place value of this last digit. In the above case it is the 6, which is in the thousandths place. So the true value lies within half-of-one-thousandths of the given number. That is, it lies in the interval [234.8955, 234.8965]. I use round-to-even, which is the default rounding mode used in IEEE 754 standard for computing functions and operators.