Standard Form
Just like how whole numbers have a standard form, word form and expanded form, even decimals also have the same type of terminology associated with them. The standard form is how numbers are usually written in which digits are placed one after the other according to their place values.
We have a number in the decimal format, such as 87.67.
We then have the word form where the numbers are written in the form of letters, which is eighty-seven point six seven.
Expanded Form
In the expanded form the numbers are expressed as the sum of its digits.
This can be written as: 87 . 67 = 80 + 7 + 0.6 + 0.07
The place values of decimals are slightly different from the place value of whole numbers. The value of the digits decreases from the decimal point to the right of the decimal number. The numbers to the right of the decimal number is called the fractional part. The digit immediately after the decimal point is the tenths place, followed by the hundredths place, the thousandths place, the ten thousandths and hundred thousandths place.
The values of each of these digits are placed in the following order.
As we can observe, the fractional part can also be depicted as decimals and the other way around. But why not use only one form and not the other?
There are a few forms that the fractional form has over the decimal form and vice-versa. There are some scenarios like when ten is divided by three, the quotient is 3.3333.
In such scenarios when the result stretches to infinity, using fractions is more advantageous than using decimals. In other scenarios where we need a precise number, like when measurements are taken, 0.5 is a more precise result as compared to \(\frac{1}{2}\). So, the form of the number depends on the circumstance.
Solved Decimal Place Value Examples
Example 1: Determine the place value of the underlined digits.
1. 9.576
2. 8.89495
Solution:
1. 9.576
The value of \(7=\frac{1}{100}\)
The value of 7 at hundreth place.
2. 8.89495
The value of \(5=\frac{1}{100000}\)
The value of five is at the hundred thousandths place.
Example 2: Determine which number is greater in value.
1. 3.15467 or 3.15476
2. 2.898 or 2.988
Solution:
1. From the given pair of numbers, the value of the first three numbers after the decimal place as well as that of the number before the decimal place is the same. The ten thousandths place of the first number is “6” and that of the second number is “7”. The value of the number in the ten thousandths place is ”7”. This shows us that 3.15467 is greater than 3.15476.
2. The number 2.898 is smaller than 2.988. This is because the value of the digit in the tenths place is greater for 2.988.
Example 3: The distance covered by three athletes for a competition of long jump is as follows:
A- 4.56 m
B- 4.06 m
C- 4.11 m
Determine the winner among the three athletes.
Solution:
If one observes the tenths place of each of these numbers, we can see that the “A” covered the longest distance, followed by “C” and then “B”.
So, the winner among the three athletes is athlete A.
There isn’t a way to determine if a number having more number of digits after the decimal place is greater than the number with lesser number of digits after the decimal place. That being said, the number of digits after the decimal place, no matter how large it is does not determine the greatness of the value. This is because the value of the digits lessens as they move to the right of the decimal point.
This depends entirely on the situation. When measuring something, the fractional form may be of lesser use than the decimal form. However, there are circumstances when the decimal form stretches upto infinity. Here, the fractional form is more convenient.