Comparing numbers in scientific notation :

There are 2 ways to compare numbers that are in scientific notation:

- Compare the exponents.
- If one exponent is larger than the other than that scientific notation is bigger
- If the exponents are the same, compare the decimals.

**Example 1 :**

Compare 5.62 x 10⁶ and 7.39 x 10⁵

**Solution :**

Compare the exponents: 6 and 5.

Since , the number with 6 as its exponent is greater than the number with 5 as its exponent.

Hence, 5.62 x 10⁶ > 7.39 x 10⁵

**Example 2 :
**

Compare and 4.29 x 10⁻³ and 5.38 x 10⁻³

**Solution :**

Since the exponents are the same, we compare the decimals:

4.29 and 5.38

Since 4.29 < 5.38 the number with 5.38 as the decimal is greater than the number with 4.29 as its decimal.

Hence 4.29 x 10⁻³ < 5.38 x 10⁻³

**Example 3 :**

Compare and 6.0515 x 10⁶ and 6.12 x 10⁵

**Solution :**

Compare the exponents: 6 and 5.

Since , the number with 6 as its exponent is greater than the number with 5 as its exponent.

Hence, 6.0515 x 10⁶ > 6.12 x 10⁵

**Example 4 :**

Compare and 4.67 x 10⁻³ and 3.0967 x 10⁻³

**Solution :**

Since the exponents are the same, we compare the decimals:

4.67 and 3.0967

Since 4.67 < 3.0967 the number with 4.67 as the decimal is greater than the number with 3.0967 as its decimal.

Hence 4.67 x 10⁻³ > 3.0967 x 10⁻³

**Example 5 :**

Compare and 8.640 x 10⁸ and 8.64 x 10⁸

**Solution :**

Since the exponents are the same, we compare the decimals:

8.640 and 8.64

By comparing the above decimals, we can decide that they are same.

Hence, 8.640 x 10⁸ = 8.64 x 10⁸

**Example 6 : **

Compare and 5.2266 x 10⁻⁷ and 6.025 x 10²

**Solution :**

Compare the exponents: -7 and 2.

Always positive number is greater than negative number.

Since , the number with 2 as its exponent is greater than the number with -7 as its exponent.

Hence, 6.025 x 10² > 5.2266 x 10⁻⁷

**Example 7 : **

Compare and 6.93 x 10⁻⁵ and 6.93 x 10⁵

**Solution :**

Compare the exponents: -5 and 5.

Always positive number is greater than negative number.

Since , the number with 5 as its exponent is greater than the number with -5 as its exponent.

Hence, 6.93 x 10⁻⁵ < 6.93 x 10⁵

**Example 8 : **

Compare and 7.35 x 10⁻⁶ and 7.305 x 10⁻⁶

**Solution :**

Since the exponents are the same, we compare the decimals:

7.35 and 7.305

Since 7.35 > 7.305 the number with 7.35 as the decimal is greater than the number with 7.305 as its decimal.

Hence 7.35 x 10⁻⁶ > 7.305 x 10⁻⁶

After having gone through the stuff given above, we hope that the students would have understood "Comparing numbers in scientific notation".

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