The number of red blood cells per cubic millimetre of blood is approximately 5.5 million. If the average body contains 5 litres of blood, what is the total number of red cells in the body? Write the standard form. (1 litre = 1,00,000 mm³)

Solution:

Given, the number of red blood cells per cubic millimetre of blood is approximately 5.5 million.

The average body contains 5 litres of blood.

We have to find the total number of red cells in the body in the standard form.

Any number can be expressed as decimal numbers between 1 and 10 multiplied by a power of 10. This form of representation is termed as the standard form.

Blood contained in a body = 5 litres

= 5 × 1,00,000 mm³

= 5 × 10⁵ mm³

Number of red blood cells = 5 × 10⁵ × 5.5 × 1000000

= 5 × 10⁵ × 5.5 × 10⁶

= 5 × 5.5 × 10⁵ × 10⁶

= 27.5 × 10⁵ × 10⁶

Using law of exponents,

a^m × aⁿ = a^{m + n}

Here, a = 10

m = 5

n = 6

So, m + n = 5 + 6

= 11

So, 10⁵ × 10⁶ = 10¹¹

27.5 × 10⁵ × 10⁶ = 27.5 × 10¹¹

= 2.75 × 10¹ × 10¹¹

Using law of exponents,

a^m × aⁿ = a^{m + n}

Here, a = 10

m = 1

n = 11

So, m + n = 1 + 11

= 12

10¹ × 10¹¹ = 10¹²

So, 2.75 × 10¹ × 10¹¹ = 2.75 × 10¹²

Therefore, the required standard form is 2.75 × 10¹².

✦ Try This: The number of red blood cells per cubic millimetre of blood is approximately 6 million. If the average body contains 5 litres of blood, what is the total number of red cells in the body? Write the standard form. (1 litre = 1,00,000 mm³)

☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 12

NCERT Exemplar Class 8 Maths Chapter 8 Problem 114

The number of red blood cells per cubic millimetre of blood is approximately 5.5 million. If the average body contains 5 litres of blood, what is the total number of red cells in the body? Write the standard form. (1 litre = 1,00,000 mm³)

Summary:

The number of red blood cells per cubic millimetre of blood is approximately 5.5 million. If the average body contains 5 litres of blood, the total number of red cells in the body in standard form is 2.75 × 10¹².

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