Chapter-2 Fraction and decimals

Explanation:

The area of a rectangle is given by multiplying its length by its breadth. So, if the length of the

rectangle is 5.7cm and its breadth is 3cm. then the area is:

Area = Length x Breadth

Area = 5.7cm x 3cm

Area = 17.1cm²

Therefore, the area of the rectangle is 17.1cm².

Explanation:

To simplify the expression 1.3 x 10, we need to evaluate it

Using the rules of scientific notation, we can rewrite 1.3 x 10 as:

1.3×10=1.3× 10^1

Now, we can simplify this expression by multiplying the coefficient (1.3) by 10 raised to the power of the exponent (1):

1.3 x 10^1=13

Therefore, the simplified value of 1.3 x 10 is 13.

Explanation:

To simplify the expression 36.8 x 10, we need to evaluate it using the rules of scientific notation.

When we multiply a decimal by 10, the decimal point is shifted to the right by one place. So, we can rewrite the expression as:

36.8 x 10 = 368

Now, we can see that the expression is already in its simplest form, as there are no exponents of decimals involved. 

Therefore, the simplified value of 36.8 x 10 is 368.

Explanation:

To simplify the expression 153.7 x 10, we need to evaluate it using the rules of scientific notation.

When we multiply a decimal by 10, the decimal point is shifted to the right by one place. So, we

can rewrite the expression as:

153.7 x 10 = 1537

Now, we can see that the expression is already in its simplest form, as there are no exponents or decimals involved. 

Therefore, the simplified value of 153.7 x 10 is 1537.

Explanation:

To simplify the expression 168.07 x 10, we need to evaluate it using the rules of scientific notation.

168.07 x 10 = 1680.7

When we multiply a decimal by 10, the decimal point is shifted to the right by one place. So, we can rewrite the expression as:

Now, we can see that the expression is already in its simplest form, as there are no exponents involved. 

Therefore, the simplified value of 168.07 x 10 is 1680.7.

Explanation:

To simplify the expression 31.1 x 100, we need to evaluate it using the rules of scientific notation. 

When we multiply a decimal by 100, the decimal point is shifted to the right by two places. So, we can rewrite the expression as

31.1 x 100 = 3110

Now, we can see that the expression is already in its simplest form, as there are no exponents or decimals involved. 

Therefore, the simplified value of 31.1 x 100 is 3110.

Explanation:

To simplify the expression 156.1 x 100, we need to evaluate it using the rules of scientific notation.

When we multiply a decimal by 100, the decimal point is shifted to the right by two places. So, we can rewrite the expression as

156.1 x 100 = 15610

Now, we can see that the expression is already in its simplest form, as there are no exponents or decimals involved. 

Therefore, the simplified value of 156.1 x 100 is 15610.

Explanation:

To simplify the expression 3.62 x 100, we need to evaluate it using the rules of scientific notation. 

When we multiply a decimal by 100, the decimal poins is shifted to the right by two places. So. we can rewrite the expression as

3.62 x 100 = 362

Now, we can see that the expression is already in its simplest form, as there are no exponents or decimals involved. 

Therefore, the simplified value of 3.62 x 100 is 362.

Explanation:

To simplify the expression 43.07 x 100, we need to evaluate it using the rules of scientific

notation.

When we multiply a decimal by 100, the decimal point is shifted to the right by two places. So, we can rewrite the expression as

4307 x 100=4307

Now, we can see that the expression is already in its simplest form, as there are no exponents or decimals involved. 

Therefore, the simplified value of 43.07 x 100 is 4307.

Explanation:

To simplify the expression 05 x 10, we need to evaluate it using the rules of scientific notation,

When we multiply a decimal by 10, the decimal point is shifted to the right by one place. So, we can rewrite the expression us

0.5 x 10 = 5

Now, we can see that the expression is already in its simplest form, as there are no exponents or decimals involved. 

Therefore, the simplified value of 0.5 x 10 is 5.

Explanation:

To simplify the expression 0.008 x 10, we need to evaluate it using the rules of scientific notation.

When we multiply a decimal by 10, the decimal point is shifted to the right by one place. So, we can rewrite the expression as

0.08 x 10 is 0.8

Now, we can see that the expression is already in its simplest form, as there are no exponents involved. 

Therefore, the simplified value of 0.08 x 10 is 0.8

Explanation:

To simplify the expression 0.9 x 100, we need to evaluate it using the rules of scientific notation. When we multiply a decimal by 100, the decimal point is shifted to the right by two places. So, we can rewrite the expression as 

0.9 x 100 is 90

Now, we can see that the expression is already in its simplest form, as there are no exponents or decimals involved. 

Therefore, the simplified value of 0.9 x 100 is 90.

Explanation:

We know that a two-wheeler covers a distance of 55.3 km in one litre of petrol

To find out how much distance it will cover in 10 lines of petrol, we can use the following formula: 

Distance covered Fuel efficiency x Fuel quantity

Here, the fuel efficiency is the distance covered per unit of feel, which is 55.3 km per litre. The fuel quantity is 10 litres.

Plugging in these values, we get

Distance covered = 55.3 km/litre x 10 litres = 555 km

Therefore, the two-wheeler will cover a distance of 553 km in 10 litres of petrol. 

Explanation:

To change 2.5 and 0.3 to fractions, we can write them as

2.5 = 2 +0.5 = 2+½ = 5/2

0.3 = 3/10

Therefore,

2.5x0.3 = 5/2 x 3/10

To multiply fractions, we multiply the numerators together and the denominators together.

5/2 x 3/10 = (5 x 3) / (2 x 10) = 15/20

The fraction 15/20 can be simplified by dividing both the numerator and denominator by their common factor 5:

15/20 = (15÷5)/(20÷5)= 3/4

Therefore, 2.5x0.3 = 0.75

Explanation:

To change 0.1 and 51.7 to fractions, we can write them as

0.1 = 1/10

51.7 can be written as a fraction by placing the whole number 51 over the denominator 1, and

then adding the decimal value 07 as a fraction

51.7=51+0.7=51+7/10=517/10

Therefore, 

0.1 x 51.7= 1/10 517/10

To multiply fractions, we multiply the numerators together and the denominators together:

1/10×517/10 = (1 × 517)/(10x 10)= 5170/100

The fraction 5170/100 can be simplified by dividing both the numerator and denominator by their common factor :

5170/100= (15170 ÷ 10) (100÷ 10) = 517/10

Therefore, 0.1 x 51.7 = 517/10

=0.1x51.7 =5.17

Explanation:

To change 0.2 and 316.8 to fractions, we can write them as

0.2-2/10=1/5

316.8 can be written as a fraction by placing the whole number 316 over the denominator 1, and then adding the decimal value (1.8 as a fraction 

316.8=316 +0.8 = 316+8/10=316+4/5 = (316. 5+4)/5=1584/5

Therefore,

0.2x316.8=1/5 x 1584/5

To multiply fractions, we multiply the numerators together and the denominators together

1/5 x 1584/5 = (1 × 1584)/(5x5)=1584/25

Therefore, 02x3168=1584/25 = 02x3168=63.36

Explanation:

To change 1.3 and 3.1 to fractions, we can write them as

1.3 = 1 + 0.3 = 1 + 3/10 = 13/10

3.1 = 3 +0.1 = 3+1/10 = 31/10

Therefore,

1.3x3.1=13/10x31/10

To multiply fractions, we multiply the numerators together and the denominators together:

13/10 × 31/10=(13x31)/(10x10)=403/100

Therefore, 13 x 3.1 = 403/100=4.03

= 1.3 x 3.1 = 4.03

Explanation:

To change 0.5 and 0.05 to fractions, we can write them as

0.5 =5/10 1/2

0.05 =  5/100=1/20

Therefore,

0.5x0.05=1/2 x 1/20

To multiply fractions, we multiply the numerators together and the denominators together:

1/2 x 1/2)=(1x1)/(2×20) = 1/40

Therefore, 0.5 x 0.05 = 1/40 =05x0,05=0.025

Explanation:

To change 11.2 and 0.15 to fractions, we can write them as

11.2 = 11+02=11+2/10-11 + 1/5=56/5

0.15 = 15/100 = 3/20

Therefore,

112×0.15=56/5 x 3/20

To multiply fractions, we multiply the numerators together and the denominators together.

56/5 x 3/20 = (56x3)/(5 × 20) = 336/100

The fraction 336/100 can be simplified by dividing both the numerator and denominator by their common factor 4:

336/100= (336+4)/(100-4)=84/25

Therefore, 11.2x0.15=84/25.

11.2×0.15=3.36

Explanation:

To change 1.07 and 0.02 to fractions, we can write them as:

1.07=1+0.07=1+7/100=107/100

0.02=2/100=1/50

Therefore,

107 x 0.002=107/100 x 1/50

To multiply fractions, we multiply the numerators together and the denominators together

107/10 x 1/50 (107x1)/(100 x 50)=107/5000

Therefore, 107x0.02 107/5000, =107 x 0.02 =0.0214

Explanation:

To change 10.05 and 1.05 to fractions, we can write them as

10.05 = 10+0.05 = 10+5/100 1005/100

1.05 = 1=0.05 = 1+5/100 105/100

Therefore,

10.05 × 1.05 = 1005/100 × 105/100

To multiply fractions, we multiply the minerators together and the denominates together.

1005/100 x 105/100 (1005 x 105)/(100x100) 105525/10000

The fraction 105525/10000 can be simplified by dividing both the numerator and denominator

by their courtman fischer 25;

105525/10000 = (105525+25)/(10000+25)=4221/40)

Therefore, 10.05 x 1.054221/400 = 11.05 x 1.05=10.5525

Explanation:

To change 101.01 and 0.01 to fractions, we can write them as

101.01 = 101 + 0.01 =101+ 1/100 = 10101/100

0.01 = 1/100

Therefore

101.01x 0.01 = 10101/100 × 1/100

To multiply fractions, we multiply the numerators together and the denominators together

10101/100 1/100 = 10101/10000

Therefore, 10101x0.01 = 10101/10000. =101. 01x0.01=1.0101

Explanation:

To change 100.01 and 1.1 to fractions, we can write them as

100.01 = 100 + 0.0 1 = 100+ 1/100=10001/100

1.1 =11/10

Therefore,

100.01 x 1.1=10001/100 × 11/10

To multiply fractions, we multiply the numerators together and the denominators together:

10001/100 x 11/10 = (1000111)/(100 x 10)=110011/1000

Therefore, 1000 x 1.1=110011/1000

100.01x1.1=110.011

Explanation:

First of all converting 0.4 into a fraction 0.4 = 4/10

Next, we can divide 4/10 by 2 by multiplying 4/10 by the reciprocal of 2, which is 1/2 This gives

4/10 ÷ 2 = 4/10 x 1/2

Simplifying the fraction on the right-hand side, we get

4/10 x 1/2=2/10

Finally, we can convert the fraction 2/10 back into a decimal by dividing the numerator by the denominator

2/10 0.2

Therefore, 0.4 ÷2 = 0.2 

Explanation:

First of all converting 0.35 into a fraction

0.35=35/100

Next, we can divide 35/100 by 5 by multiplying 35/100 by the reciprocal of 5, which is 1/5. This gives

35/100 ÷5 = 35/100 x 1/5.

Simplifying the fraction on the right-hand side, we get

35/100 x 3/5 = 7/100

Finally, we can convert the fraction 7/100 back into a decimal by dividing the numerator by the denominator

7/100=0.07

Therefore, 0.35 ÷ 5 = 0.07

Explanation:

First of all converting 2.48 into a fraction

2.48 = 248/100

Next, we can divide 248/200 by 4 by multiplying 248/100 by the reciprocal of 4, which is 1/4. This gives

248/100 ÷4=248/100 x 1/4

Simplifying the fraction on the right-hand side, we get

248/100 x 1/4 = 62/100

Finally, we can convert the fraction 62/100 back into a decimal by dividing the numerator by the denominator

62/100 = 0.62

Therefore, 2.48 +4=0.62

Explanation:

First convert the decimal part into a fraction.

0.4 = 4/10

Simplifying the fraction, we get:

4/10 = 2/5

Therefore, 65.4 can be written as

65.4 = 65+ 2/5

Next, we can divide 65.4 by 6 by first converting the mixed number into an improper fraction:

65.4 ÷6=  (65+2/5)÷6

=(325/5+2/5)+6

To divide by a fraction, we can multiply by its reciprocal

(327/5)+6(327/5) (1/6)

= 327/30

Therefore, 65 4÷ 6=327/30, which can also be expressed as a decimal

65.4÷ 6 = 10.9

Explanation:

Converting decimal into fraction,

651.2=6512/10

Next, we can divide 6512/10 by 4 by multiplying 6512/10 by the reciprocal of 4, which is 1/4

This gives

6512/10 +4-6812/10x 1/4

Simplifying the fraction on the right-hand side, we get:

6512/10 ¼= 1628/10

Finally, we can convert the fraction 1628/250 back into a decimal by dividing the numerator by the denominator

1628/10= 162.8

Explanation:

First convert the decimal part into a fraction

14.4 9=1449/100

To divide 1449/100 by 7, we can multiply 1449/100 by the reciprocal of 7, which is 1/7:

1449/100-71449/100 x 1/7

Multiplying the two fractions together, we get

1449/100 x 1/7 1449/700

Therefore, 14.49 ÷7 =14.49/700 = 2.07

Explanation:

Converting decimal into fraction

3.96= 396/100x1/4

This gives

396/100 ÷ 4  = 396/100 x 1/4

Next, we can divide 396/100 by 4 by multiplying 396/100 by the reciprocal of 4, which is 1/4

396/100 + 4 = 396/100 x 1/4

Simplifying the fraction on the night-hand side, we get:

396/100 x 1/4 = 99/25

Finally, we can convert the fraction 99/25 back into a decimal by dividing the numerator by the denominator

99/25 = 3.96

Therefore, 3.96 ÷ 4 =  0.99.

Explanation: 

Converting decimal into fraction, 

0.80=8/10

Simplifying 8/10 by dividing both numerator and denominator by 2, we get:

8/10=⅘

Next, we can divide 4/5 by 5 by multiplying 4/5 by the reciprocal of 5, which is 1/5. This gives

4/5÷ 5 = 4/5 x ⅕

Multiplying the two fractions together, we get

4/5 x 1/5 4/25

Finally, we can convert the fraction 4/25 back into a decimal by dividing the numerator by the denominator

4/2.5 = 0.16

Therefore, 0.80 ÷5 = 0.16.

Explanation:

We can write 4.8 as 48/10, then divide by 10:

=(48/10)+10 = (48/10)x(1/10)

=48/100

On dividing a decimal by 100, the decimal point is shifted to the left by two places.

Therefore, we have 0.48.

Explanation:

We can write 52.5 as 525/10, then divide by 10:

=(525/10)÷ 10

= (525/10)x(1/10) = 525/100

On dividing a decimal by 100, the decimal point is shifted to the left by two places. Therefore, we have 5.25 

Explanation:

We can write 0.7 as 7/10, then divide by 10

= (7/10)÷ 10 

= (7/10)x (1/10)

=7/100

On dividing a decimal by 100, the decimal point is shifted to the left by two places.

Therefore, we have =0.07

Explanation:

We can write 33.1 as 331/10, then divide by 10:

=(331/10)+10 = (331/10)x(3/10)

=331/100

On dividing a decimal by 1000, the decimal point is shifted to the left by three places. Therefore, we have:

=3.31

Explanation:

We can write 272.23 as 27223/100, then divide by 10:

=(27223/100)+10

=(27223/100) x (1/10)

=27223/1000

On dividing a decimal by 1000, the decimal point is shifted to the left by three places. Therefore, we have 27.223

Explanation:

We can write 0.56 as 56/100, then divide by 10:

(56/100)÷ 10

= (56/100) x (1/10)

= 56/1000

On dividing a decimal by 1000, the decimal point is shifted to the left by three places. Therefore, we have: =0.056

Explanation:

We can write 3.97 un 397/100, then divide by 10:

=(397/100)÷ 10

=(397/100) x (1/10)

=397/1000

On dividing a decimal by 1000, the decimal point is shifted to the left by three places. Therefore, we have:

397 ÷ 1000 = 0.397

So the answer is 0.397.

Explanation:

We can rewrite 2.7 as a fraction by putting it over 1:

2.7/1

To divide by 100, we can move the decimal point two places to the left:

27/1000

Simplifying this fraction, we can divide numerator by 100,

2.7/100= 0.027

Explanation:

0.3 can be written as 3/10:

Moving the decimal point two places to the left:

3/1000

Simplifying this fraction, we can divide numerator by 1000,

3/1000 = 0.0013

Explanation:

0.78 can be written as 78/100:

78/100

Moving the decimal point two places to the left

78/10000

Simplifying this fraction, we can divide the numerator by 10000.

78/10000 = 0.0078

Explanation:

432.6 can be written as 4326/10

4326/10

Moving the decimal point two places to the left:

4326/1000

Simplifying this fraction, we can divide the numerator by 1000.

4326/1000=4.326

Explanation:

23.6 can be written as 236/10: 

236/10

Moving the decimal point two places to the left

236/1000

Simplifying this fraction, we can divide the numerator by 1000.

236/1000 = 0.236

Explanation:

98.33 can be written as 9853/100:

9883/100

Moving the decimal point two places to the left:

9853/10000

Simplifying this fraction, we can divide numerator by 10000,

9853/10000 = 0.9853