# COMPARING NUMBERS IN SCIENTIFIC NOTATION

## About "Comparing numbers in scientific notation"

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 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 "Comparing numbers in scientific notation".

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

You can also visit our following web pages on different stuff in math.

WORD PROBLEMS

Word problems on simple equations

Word problems on linear equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation

Word problems on unit price

Word problems on unit rate

Word problems on comparing rates

Converting customary units word problems

Converting metric units word problems

Word problems on simple interest

Word problems on compound interest

Word problems on types of angles

Complementary and supplementary angles word problems

Double facts word problems

Trigonometry word problems

Percentage word problems

Profit and loss word problems

Markup and markdown word problems

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

Pythagorean theorem word problems

Percent of a number word problems

Word problems on constant speed

Word problems on average speed

Word problems on sum of the angles of a triangle is 180 degree

OTHER TOPICS

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

Time, speed and distance shortcuts

Ratio and proportion shortcuts

Domain and range of rational functions

Domain and range of rational functions with holes

Graphing rational functions

Graphing rational functions with holes

Converting repeating decimals in to fractions

Decimal representation of rational numbers

Finding square root using long division

L.C.M method to solve time and work problems

Translating the word problems in to algebraic expressions

Remainder when 2 power 256 is divided by 17

Remainder when 17 power 23 is divided by 16

Sum of all three digit numbers divisible by 6

Sum of all three digit numbers divisible by 7

Sum of all three digit numbers divisible by 8

Sum of all three digit numbers formed using 1, 3, 4

Sum of all three four digit numbers formed with non zero digits

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6