### Mathematics Class IV

Numbers
The Four Operations
Multiples and Factors
HCF and LCM
Fractions
Decimals
Metric Measures
Time
Money, Profit And Loss
Geometry
Symmetry and Pattern
Perimeter and Area
Data Handling

# What is Decimals?

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Decimals

Decimal number system is a positional notation with base 10. It is used to refer to numbers that have a fractional part separated from the integer part with decimal separator. Decimals help us to write fractional numbers without writing a fraction with numerator and denominator.

Decimal place value chart

In writing any number, the position of each digit is very crucial.

 Thousands Hundreds Tens Ones Decimal point Tenths Hundredths Thousandths Ten thousandths When we move to the right in the above place value chart, the value of digit becomes ten times smaller i.e. one tenth and when we move to the left in the chart, the value of digit becomes ten times bigger. One-tenth

We can write it as .
One-tenth One part of equal parts is one-tenth and written as or .

One – hundredth

We can write it as  One-hundredth One part of equal parts is one – hundredth and written as or .

One–thousandth

We can write it as 0.001.

Reading and Writing Decimal Fractions

Every decimal number has two parts, a whole/integral part and a decimal part. A dot (.) called decimal point separates the integral and decimal part.

Example. is a decimal fraction and can be represented as Placing the above decimal fraction in decimal place value chart.

 Thousands Hundreds Tens Ones Decimal point Tenths Hundredths Thousandths       The above number read as Forty three point six seven eight or Forty three and six hundred seventy eight thousandth.

Expanded Form of Decimals

By writing decimal in its expanded form, we can show value of each digit.

Writing Decimals in Expanded Form

Step1: Place the number in decimal place value chart.

Step2: Now, write the value of each digit of decimal fraction.

Example 1. Step1: Place the number in decimal place value chart.
Decimal Place Value Chart

 Thousands Hundreds Tens Ones Decimal Point Tenths Hundredths Thousandths Ten thousandths 6 7

Step2: Now, write the value of each digit of decimal fraction. tenths hundredths.
OR Example 2. Step1: Place the number in decimal place value chart.
Decimal Place Value Chart

 Thousands Hundreds Tens Ones Decimal Point Tenths Hundredths Thousandths Ten thousandths 5 0 7

Step2: Now, write the value of each digit of decimal fraction. tenths hundredths
OR Example 3. Step1: Place the number in decimal place value chart.
Decimal Place Value Chart

 Thousands Hundreds Tens Ones Decimal Point Tenths Hundredths Thousandths Ten thousandths 4 7 8 8 3 1

Step2: Now, write the value of each digit of decimal fraction. hundred tens ones hundredths thousandths
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