CONVERT BETWEEN SCIENTIFIC NOTATION AND STANDARD FORM

Scientific notation helps us to represent the numbers which are very huge or very tiny in a form of multiplication of single-digit numbers and 10 raised to the power of the respective exponent.

• The exponent is positive if the number is very large.
• It is negative if the number is very small.

a × 10^b ; 1 ≤ a < 10

Convert Between Scientific Notation and Standard Form

Problem 1 :

5.3 × 10⁶

Solution :

Exponent is positive, so we have to move the decimal 6 digits to the right.

But we have one digit after the decimal.  We should use zeroes for the rest of the places.

5300000.

So, the number 5.3 × 10⁶ in standard notation is 53,00,000.

Problem 2 :

4.7 × 10^-5

Solution :

= 4.7 × 10^-5

Exponent is negative, so we have to move the decimal 5 digits to the left.

= 0.000047

Problem 3 :

5 × 10⁴

Solution :

= 5 × 10⁴

Exponent is positive, so we have to move the decimal 4 digits to the right.

50000.

So, the number  5 × 10⁴ in standard notation  is 50000.

Problem 4 :

4.59 × 10¹

Solution :

= 4.59 × 10¹

Exponent is positive 1, so we have to move the decimal one digit to the right.

= 45.9

So, the number  4.59 × 10¹ in standard notation is 45.9.

Problem 5 :

6.7 × 10⁴

Solution :

= 6.7 × 10⁴

We have positive 4, so move the decimal 4 digits to the right.

So, the number  6.7 × 10⁴ in standard notation is 67000.

Problem 6 :

9.6 × 10⁴

Solution :

= 9.6 × 10⁴

We have positive 4, so move the decimal 4 digits to the right.

= 96000

Problem 7 :

8.78 × 10³

Solution :

= 8.78 × 10³

Exponent is positive 3, so we have to move the decimal 3 digits to the right.

8780.

Problem 8 :

5.82 × 10³

Solution :

= 5.82 × 10³

We have positive exponent, we have to move the decimal to the right.

= 5820

So, the number  5.82 × 10³ in standard notation is 5820.

Problem 9 :

1.3 × 10⁵

Solution :

= 1.3 × 10⁵

We have positive exponent, so we have to move the decimal 5 digits to the right.

= 130000

Problem 10 :

4.1 × 10⁴

Solution :

= 4.1 × 10⁴

= 41000

So, the number  4.1 × 10⁴ in standard notation is 41000.

Problem 11 :

6.4 × 10²

Solution :

= 6.4 × 10²

= 640

Problem 12 :

6.91 × 10^-2

Solution :

= 6.91 × 10^-2

= 0.0691