WRITING A NUMBER IN SCIENTIFIC NOTATION

To translate between standard notation and scientific notation, you can count the number of places the decimal point moves.

To write a number which is greater than 1 in scientific notation, move the decimal point left and use a positive exponent.

It has been illustrated in the picture given below.

To write a number which is less than 1 in scientific notation, move the decimal point right and use a negative exponent.

It has been illustrated in the picture given below.

Solved Examples

Example 1 : 

The distance from Earth to the Sun is about 93,000,000 miles. Write this distance in scientific notation.

Solution : 

Step 1 :

Move the decimal point in 93,000,000 to the left until you have a number that is greater than or equal to 1 and less than 10.

Move the decimal point 7 places to the left.

Remove extra zeros.

9.3

Step 2 :

Divide the original number by the result from Step 1.

That is, divide 93,000,000 by 9.3.

10,000,000

Write your answer as a power of 10.

10⁷

Step 3 :

Write the product of the results from Steps 1 and 2.

Write a product to represent 93,000,000 in scientific notation.

93,000,000  =  9.3 × 10⁷ miles

Example 2 : 

The average size of an atom is about 0.00000003 centimeter across. Write the average size of an atom in scientific notation.

Solution : 

Step 1 :

Move the decimal point as many places as necessary to find a number that is greater than or equal to 1 and less than 10.

Place the decimal point after 3 and put one zero to make the decimal visible. 

3.0

Step 2 :

Count the number of places you moved the decimal point.

8

Step 2 :

Multiply 3.0 times a power of 10.

Since 0.00000003 is less than 1, you moved the decimal point to the right and the exponent on 10 is negative.

3.0 × 10^-8

The average size of an atom in scientific notation is 3.0 × 10^-8.

Reflect

When we write a number that is less than 1 in scientific notation, how does the power of 10 differ from when we write a number greater than 1 in scientific notation ?

The exponent is negative instead of positive.

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

If you have any feedback about our math content, please mail us : 

v4formath@gmail.com

We always appreciate your feedback. 

You can also visit the 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