CONVERT BETWEEN STANDARD AND SCIENTIFIC NOTATION

Convert between Standard and Scientific Notation :

In this section, you will learn how to do conversions between standard and scientific notation. 

Converting Standard Form into Scientific Notation

To learn how to convert a number from standard form to scientific notation, 

Please click here

Converting Standard Form into Scientific Notation - Examples

Example 1 :

Write the following number in scientific notation.

205852

Solution :

Here, we don't find decimal point in 205852. So we have to assume that there is decimal point at the end . 

Then,

205852 ---------> 205852.

Here, non zero digit comes first and decimal point comes next. 

We have to move the decimal point to the left. 

No. of digits between the 1^st non zero digit and the decimal point is 5.

So, the decimal point has to be moved 5 digits to the left and exponent of 10 should be 5 (positive integer). 

Therefore, the scientific notation of 205852 is

2.05852 x 10⁵

Example 2 :

Write the following number in scientific notation.

3449098.96

Solution :

3449098.96

Here, non zero digit comes first and decimal point comes next. 

We have to move the decimal point to the left. 

No. of digits between the 1^st non zero digit and the decimal point is 6.

So, the decimal point has to be moved 6 digits to the left and exponent of 10 should be 6 (positive integer)

Therefore, the scientific notation of 3449098.96 is

3.44909896 x 10⁶

Example 3 :

Write the following number in scientific notation.

0.00008035

Solution : 

Here, decimal point comes first and non zero digit comes next. 

We have to move the decimal point to the right. 

No. of digits from the decimal point up to the first non zero digit is 5.

So, the decimal point has to be moved 5 digits to the right and exponent of 10 should be -5 (negative integer)

Therefore, the scientific notation of 0.00008035 is

8.035 x 10^-5

Converting Scientific Notation into Standard Form

To convert a number from scientific notation to standard notation, first we have to notice the exponent of 10 in scientific notation.

If the exponent of 10 is positive, we have to move the decimal point to the right. 

For example, if you have 10³, you have to move the decimal point 3 digits to the right. 

If the exponent of 10 is negative, we have to move the decimal point to the right. 

For example, if you have 10^-5, you have to move the decimal point 5 digits to the left. 

Converting Scientific Notation into Standard Form - Examples

Example 1 :

Write the following number in standard form.  

5.236 x 10⁵

Solution :

Here, the exponent of 10 is positive 5. So we have to move the decimal point five digits to the right.

In 5.236, we have only three digits after the decimal point.

So, we have to add two zeros to move the decimal point five digits to the right.   

Therefore, the standard form of 5.236 x 10⁵ is 

523600

Example 2 :

Write the following number in standard form.  

6.415 x 10^-6

Solution :

Here, the exponent of 10 is negative 6. So we have to move the decimal point six digits to the left.

In 6.415, we have only 1 digit before the decimal point.

So, we have to add five zeros to move the decimal point six digits to the left.   

Therefore, the standard form of 6.415 x 10^-6 is 

0.000006415

Example 3 :

Write the following number in standard form.  

1.72 x 10⁹

Solution :

Here, the exponent of 10 is positive 9. So we have to move the decimal point nine digits to the right.

In 1.72, we have only two digits after the decimal point.

So, we have to add seven zeros to move the decimal point nine digits to the right.   

Therefore, the standard form of 1.72 x 10⁹ is 

1720000000

Example 4 :

Write the following number in standard form.  

0.00023 x 10⁷

Solution :

Here, the exponent of 10 is positive 7. So we have to move the decimal point seven digits to the right.

In 0.00023, we have only five digits after the decimal point.

So, we have to add two zeros to move the decimal point seven digits to the right.   

Therefore, the standard form of 0.00023 x 10⁷ is 

2300

Example 5 :

Write the following number in standard form.  

0.036 x 10^-3

Solution :

Here, the exponent of 10 is negative 3. So we have to move the decimal point three digits to the left.

In 0.036, we don't have any non zero digit before the decimal point.

So, we have to add three zeros to move the decimal point three digits to the left.   

Therefore the standard form of 0.036 x 10^-3 is 

0.000036

After having gone through the stuff given above, we hope that the students would have understood how to conversion between standard form and scientific notation. 

Apart from the stuff, 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

HCF and LCM  word problems

Word problems on simple equations 

Word problems on linear equations 

Word problems on quadratic 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