The document NCERT Solutions(Part- 2)- Exponents and Powers Class 8 Notes | EduRev is a part of the Class 8 Course Class 8 Mathematics by VP Classes.

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**USE OF EXPONENTS TO EXPRESS**

Small Numbers in Standard Form

We know that” a number is said to be in the standard form, if it is expressed as the product of a number between 1 and 10 and integral power of 10.’’

So far, we have learnt to express large numbers in standard form. For example,

180,000,000,000 = 1.8 * 1011 [Decimal point is moved to left for 11 places]

We can also express very small numbers in standard form by moving the decimal point to the right.**Example: **Express 0.000009 in standard form.**Solution: **0.000009 [Decimal point is moved to right for 6 places]

Note: Writing a number in standard form means expressing it in scientific notation.**TRY THESE ****Question 1.** Write the following numbers in standard form.

(i) 0.000000564

(ii) 0.0000021

(iii) 15240000**Solution:**

(iii) 15240000 = 1524 * 10000

= 1.524 * 1000 * 10000

= 1.524 * 103 * 104 = 1.524 * 107

∴ 15240000 = 1.524 * 107**Question 2.** Write all the facts given in the standard form.**Solution:** A number is said to be in the standard form when it is written as k * 10^{n}, where

1 __<__ k < 10

and ‘n’ is an integer.

A number expressed as the product of a number between 1 and 10 and an integral power of 10.**Example:** Compare the size of a red blood cell which is 0.000007 m to that of a plant cell which is 0.0000129 m.**Solution:** Size of red blood cell = 0.000007 m

Thus, the size of a red blood cell is half of the plant cell size.**EXERCISE 12.2**

Question 1. Express the following numbers in standard form.

(i) 0.0000000000085

(ii) 0.00000000000942

(iii) 6020000000000000

(iv) 0.00000000837

(v) 31860000000**Solution:****(v)** 31860000000 = 3186 * 10000000 = 3186 * 10^{7}

= 3.186 * 10^{3} * 10^{7}

= 3.186 * 10^{3+7} = 3.186 * 10^{10}**Question 2.** Express the following numbers in usual form.

(i) 3.02 * 10^{–6}

(ii) 4.5 * 10^{4 }

(iii) 3 * 10^{–8}

(iv) 1.0001 * 10^{9 }

(v) 5.8 * 10^{12 }

(vi) 3.61492 * 10^{6}**Solution:**

(i) 3.02 * 10^{–6} = 302 * 10^{–2} * 10^{–6}

= 302 * 10^{–8}**Question 3.** Express the number appearing in the following statements in standard form.

(i) 1 micron is equal to

(ii) Charge of an electron is 0.000,000,000,000,000,000,16 coulomb.

(iii) Size of a bacteria is 0.0000005 m.

(iv) Size of a plant cell is 0.00001275 m.

(v) Thickness of a thick paper is 0.07 mm.**Solution:**

∵ 1 micron = 1 * 10^{–6}

(ii) ∵ 0.000,000,000,000,000,000,16

∴ Thickness of a thick paper is 7 * 10^{–2} mm.**Question 4.** In a stack there are 5 books each of thickness 20 mm and 5 paper sheets each of thickness 0.016 mm. What is the total thickness of the stack?**Solution:**

∵ Thickness of one book = 20 mm

∴ Thickness of 5 books = 5 * 20 mm = 100 mm

Again,

Thickness of 1 paper sheet = 0.016 mm

∴ Thickness of 5 paper sheets = 5 * 0.016 mm

= 0.080 m

∴ Total thickness = 100 mm + 0.080 mm

= 100.08 mm = 1.0008 * 10^{2} mm

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