6th Class Mathematics Decimals Place value and Conversion of Like and Unlike Decimals

Place value and Conversion of Like and Unlike Decimals  

Place Value of Decimals

Place value of whole part of decimal numbers is read from extreme right to left from decimal point and decimal part is read from first right from decimal point to extreme right. In a decimal number 56.98, whole part of the number is 56 (Fifty six) and decimal part is 98 (Nine eight). The number 6 is at unit place and 5 at tens place. In the decimal part the number 9 is at tenth place and 8 is at hundredth place. Read the following place value of decimals:                

What is the place value of 6 in the decimal 3787.367?

(a) Hundredths                                

(b) Thousandths

(c) Six hundredths          

(d) None of these

(e) All of these

Answer: (c)

Explanation

Place value of 6 in 3787.367 is six hundredths.  

Conversion of Fractions into Decimals

Conversion of fractions into decimal is the division of numerator by denominator. If numerator is greater than denominator then mixed (Some part of whole and decimal) decimal is obtained. If numerator is smaller than denominator then decimal form of resulting decimal is obtained. In the fraction \[\frac{2}{5},\] numerator is greater than denominator, therefore, on division of 5 by 2, 2.5 is a decimal number, whereas 2 is whole and 0.5 is decimal part. In another fraction with smaller numerator 4, resulting decimal is 0.444, it has decimal parts only. Decimal number is considered up to three decimal places. The conversion of \[\frac{2}{9}\] into decimal is 0.222222 ....infinite, its up to three digits as 0.222 are considered.  

Convert the fraction g into its decimal form.

(a) 0.777                                              

(b) 0.555

(c) 0.666                                              

(d) None of these

(e) All of these

Answer: (c)

Explanation

Decimal form of the fraction, \[\frac{6}{9}=0.666.\]

Conversion of Decimals into Fractions

The following methods are used for conversion of decimals into fractions:

1.Rewrite decimal numbers into whole number by omitting decimal point.

2.Write 1 under converted whole number and put one zero for each decimal places.

3.Simplify them into its lowest term.

Let the number is 78.65, by omitting decimal, the number becomes 7865. There are two digits after the decimal, therefore, 7865 should be divided by \[100=\frac{7865}{100},\] on  simplification or reducing to its lowest term, number becomes \[\frac{1573}{20}.\]  

Convert the 0.100 into fraction.

(a) \[\frac{1}{100}\]                       

(b) \[\frac{1}{10}\]

(c) \[\frac{1}{1000}\]                     

(d) None of these

(e) All of these  

Answer: (b)                

Explanation  

Like and Unlike Decimals

The decimals whose number of digits from decimal point is same are called like decimals. If total number of digits is not same then called unlike decimals. The following decimals have two digits at right hand side from decimal point 0.22, 0.29, 0.01, thus these are called like decimals. Number of digits from decimal point towards right side of the following decimals 0.345, 0.32, 0.45677 are not same, therefore, called unlike decimals.  

Choose the like decimals from the following decimals: 23.01,12.23,14.9, 22.234.

(a) 14.9 and 22.234                           

(b) 23.01 and 12.23

(c) 23.01 and 14.9                            

(d) None of these

(e) All of these  

Answer: (b)

Explanation

Number of digit at decimal place of 23.01 and 12.23 is 2. Hence, these are like decimals.  

Comparison of Decimals

Comparison of decimals is used to denote the greater and smaller decimals among two or more decimals. The greater decimal has greater whole part and smaller has smaller whole part. If two decimals have equal whole part then by comparing its first digit from right of decimal, the greater and smaller decimals can be obtained. If first digit of a decimal number is greater than the first digit of another decimal number then the greater decimal has greater digit and smaller has smaller digit. If first digit of decimal part is equal then by comparing second digit, greater and smaller number is obtained. If a decimal number has all parts equal to the same part of another decimal except second digit from right of decimal point is greater than the same place of other decimal number then the greater decimal has greater digit. The decimal numbers are 34.56 and 45.67, the whole part (34) of 34.56 is smaller than the whole part o 45.67, therefore, 34.56issmallerthan45.67. In the decimal numbers 56.78 and 56.79, the whole and first digit of decimal part of both the decimal numbers are equal therefore, by comparing its second digit from decimal parts, greater and smaller decimals can be obtained, thus the greater decimal is 56.79 because second digit or hundredths place of decimal part, 9 is greater than the hundredths place, 8 of decimal number, 56.78.  

Compare the following two decimals 34.45, 34.35 and choose the correct option from the options given below?

(a) 34.35 = 34.45                              

(b) 34.45 > 34.35

(c) 34.45 < 34.35                               

(d) None of these

(e) All of these  

Answer: (b)

Explanation

All the digits of both the decimal numbers, 34.45 and 34.35 are equal except digits at tenths place. Hence, the greater decimal has greater digit at tenths place.  

Conversion of Unlike Decimals into Like Decimals

All operations on the decimals are performed by converting unlike decimals into like decimals. Two unlike decimals are 45.67 and 35.7. The decimal 45.67 cannot be converted just like the decimal 35.7 but the decimal 35.7 is converted by putting one zero after 7, therefore, the number 35.7 is converted into 35.70. The value of the number does not change on putting 0 after the decimal. Now both the numbers 45.67 and 35.70 are like decimals.  

Remember the following on putting 0 in decimals numbers:

1. Zero cannot be placed before the digits in the decimal part of the decimal number, it should be placed just after the digits.

2. Zero cannot be placed after the digits in the whole part of decimal number. It should be placed before the digits.  

Convert the following unlike decimals 23.34, 34.4, 67.456 and 99.1 into like decimals:

(a) 23.340,34.040,67.456,99.100                

(b) 23.340,34.040,67.456,99.001

(c) 23.340,34.400,67.456,99.100                

(d) None of these                

(e) All of these  

Answer: (c)                

Explanation

There are three decimal places of 67.456. Therefore, every decimal should be changed into three decimal places.