MULTIPLYING DECIMALS

Problem 1 :

Evaluate :

4.8 x 5.2

Solution :

In 4.8 and 5.2, ignore the decimal points and consider them as if they were integers. That is, 48 and 52.

Multiply 48 and 52.

48 x 52 = 2496

In both 4.8 and 5.2, there is 1 digit to the right of the decimal point. So, in the result 2496, count 2 digits from the right and put a decimal point.

Therefore,

4.8 x 5.2 = 24.96

Problem 2 :

Evaluate :

0.25 x 6.8

Solution :

In 0.25 and 6.8, ignore the decimal points and consider them as if they were integers. That is, 25 and 68.

Multiply 25 and 68.

25 x 68 = 1700

In 0.25, there are 2 digits to the right of the decimal point and in 6.8, there is 1 digit to the right of the decimal point, total 3 digits. So, in the result 1700, count  3 digits from the right and put a decimal point.

Therefore,

0.25 x 6.8 = 1.700

= 1.7

Note :

To the right of a decimal point, zeros at the end need not be considered.

Problem 3 :

If the length of each side of a square is 3.2 cm, find its perimeter.

Solution :

All the sides of a square are equal.

Length of each side = 3.2 cm.

Perimeter of a square = 4 x length of each side

Thus, perimeter :

= 4 × 3.2

= 12.8 cm.

Problem 4 :

If the length of each side of a square is 2.8 cm, find its area.

Solution :

Area of a square = side x side

Length of each side = 2.8 cm.

= 2.8 x 2.8

= 7.84 cm²

Problem 5 :

The length of a rectangle is 5.8 cm and its width is 2.5 cm. What is the area of the rectangle?

Solution :

Area of a rectangle = length x width

Length = 5.8 cm. and width = 2.5 cm.

= 5.8 x 2.5

=  14.5 cm²

Problem 6 :

The length of a rectangle is 6.3 cm and its width is 3.2 cm. What is the perimeter of the rectangle?

Solution :

Perimeter of the rectangle = 2(length + width)

Length = 6.3 cm. and width = 3.2 cm.

= 2(6.3 + 3.2)

= 2(9.5)

= 19 cm

Problem 7 :

The radius of a circle is 6.5 cm. Find its circumference using π ≈ 3.14.

Solution :

Circumference of a circle = 2πr

Substitute π ≈ 3.14 and r = 6.5.

≈ 2 x 3.14 x 6.5

= 40.82

Circumference of the circle is about 40.82 cm.

Problem 8 :

The radius of a circle is 7.5 cm. Find its area using π ≈ 3.14.

Solution :

Area of a circle = πr²

Substitute π ≈ 3.14 and r = 7.5.

≈ 3.14 x 7.5²

= 3.14 x 56.25

= 176.625

Area of the circle is about 176.625 square cm.

Problem 9 :

What is 45% of 78.2?

Solution :

45% of 78.2 = 45% x 78.2

= (45/100) x 78.2

= 0.45 x 78.2

= 35.19

Problem 10 :

What is 2.5% of 15.6?

Solution :

2.5% of 15.6 = 2.5% x 15.6

= (2.5/100) x 15.6

= 0.025 x 15.6

= 0.39

Multiplying decimals by 10 100 and 1000

Lily observed that

1.9 = 19/10

1.97 = 197/100

1.973 = 1973/1000

Thus, she found that depending on the position of the decimal point the decimal number can be converted to a fraction with denominator 10 , 100 or 1000.

Now let us see what would happen if a decimal number is multiplied by 10 or 100 or 1000.

For example, 

2.97 x 10 = (297/100) x 10 = 297/10 = 29.7

Decimal point shifted to the right by one place, since 10 has one zero.

2.97 x 100 = (297/100) x 100 = 297

Decimal point shifted to the right by two places, since 100 has two zeros.

2.97 x 1000 = (297/100) x 1000 = 297 x 10 = 2970

Decimal point shifted to the right by three places, since 1000 has three zeros.

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