COMPARE NUMBERS WRITTEN IN SCIENTIFIC NOTATION

About "Compare numbers written in scientific notation"

Compare numbers written 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 10³ and 5.38 x 10³

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 10³ < 5.38 x 10³

Example 3 :

Compare and 6.0515 x 10⁶ and 6.12 x 10

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 10 > 6.12 x 10

Example 4 :

Compare and 4.67 x 10³ and 3.0967 x 10³

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 10³ > 3.0967 x 10³

Example 5 :

Compare and 8.640 x 10 and 8.64 x 10

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 10 = 8.64 x 10

Example 6 : 

Compare and 5.2266 x 10 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

Example 7 : 

Compare and 6.93 x 10 and 6.93 x 10

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  <  6.93 x 10

Example 8 : 

Compare and 7.35 x 10 and 7.305 x 10

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 > 7.305 x 10

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

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