Decimal Numbers
The word 'decimal' means based on 10'. This word has been derived from the Latin word decima meaning a tenth part.
The fractional numbers having denominators 10,100,1000, etc. are called decimal fractions or decimals.
Definition of Decimal Numbers:
We have learnt that the decimals are an
extension of our number system. We also know that decimals can be considered as
fractions whose denominators are 10, 100, 1000, etc. The numbers expressed in
the decimal form are called decimal
numbers or decimals.
For example: 5.1, 4.09, 13.83, etc.
A decimal has two parts:
(a) Whole number part
(b) Decimal part
These parts are separated by a
dot ( . ) called the decimal point.
• The digits lying to the left
of the decimal point form the whole number part. The places begin with ones,
then tens, then hundreds, then thousands and so on.
• The decimal point together
with the digits lying on the right of decimal point form the decimal part. The
places begin with tenths, then hundredths, then thousandths and so on………
For example:
(i) In the decimal number 211.35; the whole number part is 211 and the decimal part is .35
It can be arranged in the place-value chart as:
(ii) In the decimal number 57.031;
the whole number part is 57 and the decimal part is .031
(iii) In the decimal number 197.73;
the whole number part is 197 and the decimal part is .73
Some decimal fractions are expressed as given below:
(i) \(\frac{4}{10}\) is expressed as 0.4
(ii) \(\frac{7}{10}\) is expressed as 0.07
(iⅲ) 5\(\frac{17}{100}\) is expressed as 5.17
The 'dot' '.' is called the decimal point.
Therefore, decimal fraction consist of two parts
i,e. whole number part and decimal part, and they are separated by the decimal point.
Note:
1. 3.5 is read as 'three point five'
2. 5.71 is read as 'five point seven one'
3. 10.01 is read as 'ten point zero one'
4. 6.40 is read as 'six point four zero'
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Decimal numbers can be expressed in expanded form using the place-value chart. In expanded form of decimal fractions we will learn how to read and write the decimal numbers. Note: When a decimal is missing either in the integral part or decimal part, substitute with 0.
While comparing natural numbers we first compare total number of digits in both the numbers and if they are equal then we compare the digit at the extreme left. If they also equal then we compare the next digit and so on. We follow the same pattern while comparing the
Addition of decimal numbers are similar to addition of whole numbers. We convert them to like decimals and place the numbers vertically one below the other in such a way that the decimal point lies exactly on the vertical line. Add as usual as we learnt in the case of whole
The rules of subtracting decimal numbers are: (i) Write the digits of the given numbers one below the other such that the decimal points are in the same vertical line. (ii) Subtract as we subtract whole numbers. Let us consider some of the examples on subtraction
Word problems on decimals are solved here step by step. The product of two numbers is 42.63. If one number is 2.1, find the other. Solution: Product of two numbers = 42.63 One number = 2.1
Decimal place value chart are discussed here: The first place after the decimal is got by dividing the number by 10; it is called the tenths place.
Concept of like and unlike decimals: Decimals having the same number of decimal places are called like decimals i.e. decimals having the same number of digits on the right of the decimal
In conversion of unlike decimals to like decimals follow the steps of the method. Step I: Find the decimal number having the maximum number of decimal places, say (n). Step II: Now, convert each
In converting decimals to fractions, we know that a decimal can always be converted into a fraction by using the following steps: Step I: Obtain the decimal. Step II: Remove the decimal points from the given decimal and take as numerator.
In converting fractions to decimals, we know that decimals are fractions with denominators 10, 100, 1000 etc. In order to convert other fractions into decimals, we follow the following steps:
Practice different types of math questions given in the worksheet on decimal numbers, these math problems will help the students to review decimals number concepts.
Representing decimals on number line shows the intervals between two integers which will help us to increase the basic concept on formation of decimal numbers.
In ordering decimals we will learn how to compare two or more decimals. (i) Convert each of them as like decimals. (ii) Compare these decimals just as we compare two whole numbers ignoring
Practice the questions given in the worksheet on word problems on addition and subtraction of decimals. Read the questions carefully to add or subtract the decimals as required.
Practice the questions given in the worksheet on use of decimals in calculating money, in measuring the length, in measuring the distance, in measuring the mass and in measuring the capacity.
● Related Concept
● Decimals
● Decimal Numbers
● Decimal Fractions
● Like and Unlike
Decimals
● Comparing Decimals
● Decimal Places
● Conversion of
Unlike Decimals to Like Decimals
● Decimal and
Fractional Expansion
● Terminating Decimal
● Non-Terminating
Decimal
● Converting Decimals
to Fractions
● Converting
Fractions to Decimals
● H.C.F. and L.C.M.
of Decimals
● Repeating or
Recurring Decimal
● Pure Recurring
Decimal
● Mixed Recurring
Decimal
● BODMAS Rule
● BODMAS/PEMDAS Rules
- Involving Decimals
● PEMDAS Rules -
Involving Integers
● PEMDAS Rules -
Involving Decimals
● PEMDAS Rule
● BODMAS Rules -
Involving Integers
● Conversion of Pure
Recurring Decimal into Vulgar Fraction
● Conversion of Mixed
Recurring Decimals into Vulgar Fractions
● Simplification of
Decimal
● Rounding Decimals
● Rounding Decimals
to the Nearest Whole Number
● Rounding Decimals
to the Nearest Tenths
● Rounding Decimals
to the Nearest Hundredths
● Round a Decimal
● Adding Decimals
● Subtracting
Decimals
● Simplify Decimals
Involving Addition and Subtraction Decimals
● Multiplying Decimal
by a Decimal Number
● Multiplying Decimal
by a Whole Number
● Dividing Decimal by
a Whole Number
● Dividing Decimal by
a Decimal Number
7th Grade Math Problems
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