# 6th Class Mathematics Decimals

Decimals

Category : 6th Class

Decimals

• The number expressed in decimal form are called decimal numbers or simply decimals.

e.g., 5.8, 19.63, 7.269, 0.058, etc.,

• A decimal number has two parts, namely

(i) Whole-number part and           (ii) Decimal part

These parts are separated by a dot (.) called the decimal point. • Place value chart of a decimal number:

e.g., Write 236.784 in place value chart.

 100 10 1 0.1 0.01 0.001 Hundreds Tens Ones Tenths Hundredths Thousandths 2 3 6 7 8 4

• Representing decimals on number line: Let us represent 0.6 on the number line.

0.6 lies between 0 and 1.

0.6 is 6 tenths.

So, divide the unit length between 0 and 1 into 10 equal parts & take 6 parts as shown. • The number of digits in the decimal part of a decimal number gives the number of decimal places.

e.g., 5.39 has two decimal places and 9.368 has three decimal places.

• Decimals having the same number of decimal places are called like decimals.

e.g., 9.82, 5.03, 13.85 etc.,

• Decimals having different number of decimal places are called unlike decimals.

e.g, 3.4, 5.98, 111.035 etc.,

Note: Adding and number Zeros to the extreme right of the decimal part of a decimal number does not change its value.

e.g., 2.64 = 2.640 = 2.6400 etc.

• Comparing decimals:

Step 1 : Convert the given decimal numbers into like decimals.

Step 2 : First compare the whole-number part.

The decimal number with the greater whole number part is greater.

Step 3: If the whole number parts are equal, compare the tenths digit. The decimal number with the greater digit in the tenths place is greater.

Step 4: If the tenths digits are also equal, compare the hundredths digits, and so on.

e.g.,      (i)   63.87 > 59.87

(ii)   24.85 > 24.65

(iii) 111.035 < 111.038

• Conversion of decimals to fractions:

Express 2.35 as a fraction.

Step 1: In the numerator, write the given decimal number without the decimal point.

$2.\underset{\leftarrow }{\mathop{35}}\,=\frac{(235)}{(\,\,\,\,\,)}$

Step 2: From 'right to left' count the number of decimal places, say 'x'.

Here x = 2.

Step 3: In the denominator, write 1 followed by 'x' number of zeros.

$2.35=\frac{235}{100}$

Step 4: Simplify the obtained fraction into its lowest terms.

• Conversion of fractions to decimals:

(i) Conversion of decimal fraction to decimal.

Express $\frac{17153}{1000}$as a decimal.

Step 1: Write the numerator as it is 17153.

Step 2: Count the number of zeros in the denominator. Let it be 'x'.

Here x = 3.

• Step 3: From 'right to left' in the number, place the decimal point after 'x' places.

$\therefore \frac{17153}{1000}=17.153$

(ii) Conversion of a non-decimal fraction into a decimal.

Express$\frac{318}{7}$ as a decimal.

Step 1: Divide the number as usual.

Step 2: If dividend is less than divisor, place the decimal point in quotient.

Step 3: Place a zero in the dividend.

Step 4: Repeat the division process till remainder is zero or as per the required number of decimal places. Note: (a) Express $\frac{\mathbf{318}}{\mathbf{7}}$as a decimal (Upto 3 Decimals $\frac{\mathbf{318}}{\mathbf{7}}\mathbf{=45}\mathbf{.428}$

(b) Express $\frac{\mathbf{318}}{\mathbf{7}}$as a decimal (upto 2 decimal)$\frac{\mathbf{318}}{\mathbf{7}}\mathbf{=45}\mathbf{.42}$

(c)Express $\frac{\mathbf{318}}{\mathbf{7}}$as a decimal correct to 2 decima; places $\frac{\mathbf{318}}{\mathbf{7}}\mathbf{=45}\mathbf{.43}$(2 is rounded off to 3 as the third decimal digit is 8 which is greater than 5.)

• Addition of decimals :

e.g., Add: 27.8, 46,175.09 and 685.7.

Step 1: Convert the given decimals into like decimals. 27.80, 46.00, 175.09 and 685.70.

Step 2: Write the addends one below the other in column form, keeping the decimal points of all the addends in the same column and the digits of the same place in the same column.

Step 3: Add as in the case of whole numbers.

Step 4: In the sum, place the decimal point directly under decimal points in the addends. Hence, 934.59 is the sum of the given decimals.

• Subtraction of Decimals:

e.g., Subtract 35.87 from 63.2.

Step1: Convert the given decimals into like decimals.

• and 63.20

Step 2: Write the smaller number below the larger one in column form in such a way that the decimal points of both the numbers are in the same column and the digits of the same place lie in the same column.

Step 3: Subtract as in the case of whole numbers.

Step 4: In the difference, place the decimal point directly under the decimal points of the given numbers. Hence, 27.33 is the difference of the given decimals.

• Decimals are used in representing units of money, length and weight.

1 mm = $\frac{1}{10}$of a centimeter

i.e., 1 mm = 0.1 cm; 1 cm = 0.01 m

100 cm = 1 m

1000 mm = 1m

1000 m=1km

1000 m$l$=1 liter

1000$l$=1 k$l$

1000 mg=1g

1000 g=1kg

##### Notes - Decimals

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