Decimals
Category : 5th Class
LEARNING OBJECTIVES
This lesson will help you to:
Real – Life Example
QUICK CONCEPT REVIEW
(i) Decimal number is another way of representing fractions.
Amazing Facts
(ii) The decimal point goes between units and tenths place.
Place of a decimal: In a decimal number, position or "place" of each digit is important.
In the number 237,
and the "2" is in the Hundreds position, meaning 2 hundreds.
"Two Hundred Thirty Seven"
(iv) As we move left, each position is 10 times bigger,
Hundreds are 10 times bigger than Tens.
Expanded form of decimals
\[315.162=300+10+5+\frac{1}{10}+\frac{6}{100}+\frac{2}{1000}\]
(vi) Like and unlike decimals: Like decimals hove same decimal places unlike decimals have different decimal places.
Historical preview
Example: 2.56, 5.48, 0.25 etc., are like decimals and 0.2, 1.23, 2.236 etc., are unlike decimals.
(vii) Equivalent decimals; the decimals which have same value are called equivalent decimals.
(viii) Decimals on a number line: Each decimal number can be plotted on the number line using units, tenths, hundredths etc.
(ix) Decimal fractions: A decimal number can also be represented as fraction.
A decimal fraction is a fraction where the .denominator is a number such as (10, 100, 1000 etc).
i.e. a power of tens.
Following decimal number have following fraction
\[2.3=\frac{23}{10},13.76=\frac{1376}{100}.\]
Conversion of a Decimal into a Fraction
Step 1: Remove the point from the decimal and write the obtained number as the numerator.
Step 2: Write 1 as denominator and put zeroes right to it so that the number of zeroes is equal to the number of digits right to the point in the given decimal.
Example: \[23.56=\frac{2356}{100}.\]
Comparing two decimal numbers
Addition of Decimals
Step 1: Convert the given decimals into like decimals.
Step 2: Write the addends one under the other so that the decimal points of all the addends are in the same column.
Step 3: Add as in the case of whole numbers.
Step 4: In the sum, put decimal point directly under the decimal points in the addends.
Subtraction of Decimals
Step 1: Convert the given decimals into like decimals.
Step 2: Write the smaller number under the larger one so that their decimal points are in the same column.
Misconcept /Concept
Misconcept: Longer is larger misconcept: A longer decimal may not be a larger number than a shorter decimal
Concept: Shorter is larger misconcept: A Shorter decimal is a larger number than a longer decimal.
Step 3: Subtract as in the case of whole numbers.
Step 4: In the difference, put the decimal point directly under the decimal points of the given numbers.
Multiplication of a Decimal by a Whole Number
Step 1: Multiply the decimal without the decimal point by the whole number.
Step 2: Place the decimal point so as to obtain as many decimal places in the product as there are in the decimal.
Multiplication of Two Decimals
Step 1: Multiply the two decimals without the decimal points, just like whole numbers.
Step 2: In the product, place the decimal point so that the number of decimal places in the product is equal to the sum of the decimal places in the given decimals.
Division of a Decimal by a Whole Number
Step 1: Perform the division by considering the dividend a whole number.
Step 2: When the whole number part of the dividend is complete, put the decimal point in the quotient and proceed with the division as in case of whole numbers.
Division of a Decimal by a Decimal
Step 1: Convert the divisor into a whole number by multiplying the dividend and the divisor by 10, 100 or 1000 etc. depending upon the number of decimal places in the divisor.
Step 2: Now, divide the new dividend by the whole number as discussed above.
ROUNDING DECIMAL
Rounding means reducing the digits in a number while trying to keep its value similar.
Example: 73 rounded to the nearest ten is 70, because 73 is closer to 70 than to 80.
Rules to Round Numbers
Rounding Decimal
Examples |
Because |
3.1416 rounded to hundredths is 3.14 |
... the next digit (1) is less than 5 |
1.2635 rounded to tenths is 1.3 |
... the next digit (6) is 5 or more |
1.2635 rounded to 3 decimal places is 1.264 |
... the next digit (5) is 5 or more |
Rounding Whole Numbers
Examples |
Because |
134.9 rounded to tens is 130 |
... the next digit (4) is less than 5 |
12,690 rounded to thousands is 13,000 |
... the next digit (6) is 5 or more |
1.239 rounded to units is 1 |
... the next digit (2) is less than 5 |
Rounding to Significant Digits
Examples |
Because |
1.239 rounded to 3 significant digits is 1.24 |
... the next digit (9) is 5 or more |
134.9 rounded to 1 significant digit is 100 |
... the next digit (3) is less than 5 |
0.0165 rounded to 2 significant digits is 0.017 |
... the next digit (5) is 5 or more |
PLAY TIME
Divide the students in two teams. Assign the numbers (0 – 9) to both the teams. Ask two teams to make the largest and smallest decimal numbers with one decimal place and two decimal places with 1, 2, 3 digits as whole number part. The team who makes the maximum correct number wins the game.
USES OF DECIMAL SYSTEM
We have seen that 100 cm = 1 m
1000 m=1 km, 1000 ml= \[1\ell \]. 1000 g = 1 kg etc.
In money also, we use the conversion 100 paise = 1 rupee.
We can use the decimal system in all these places to convert a smaller unit to a bigger unit.
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