Chapter 14
Scientific Notation
Scientific notation is an alternative to standard notation (that is, the way you normally write numbers). Standard notation can be awkward for writing very large and very small numbers, such as 19,740,000,000,000 and 0.0000000000291. Scientific notation allows you to express very large and very small numbers in a more compact way. For example: 19,740,000,000,000 = 
and 0.0000000000291 = 
.
The Problems You’ll Work On
Here are some of the scientific notation problems you’ll see in this chapter:
Converting numbers from standard notation to scientific notation
Converting numbers from scientific notation to standard notation
Multiplying numbers in scientific notation
What to Watch Out For
Keep these tips in mind as you work through the questions:
A number in scientific notation always includes two parts: A decimal no less than 1.0 but less than 10, multiplied by a power of 10.
To convert a large number from standard notation to scientific notation, begin by multiplying the number by 
, then move the decimal point one place to the left and add 1 to the exponent until the decimal portion of the number is between 1 and 10.
To convert a small number from standard notation to scientific notation, begin by multiplying the number by 
, then move the decimal point one place to the right and subtract 1 from the exponent until the decimal portion of the number is between 1 and 10.
To convert a large number from scientific notation to standard notation, move the decimal point one place to the right and subtract 1 from the exponent until the exponent reduces to 0; then drop the power of 10.
To convert a small number from scientific notation to standard notation, move the decimal point one place to the left and add 1 to the exponent until the exponent increases to 0; then drop the power of 10.
To multiply two numbers in scientific notation, multiply the two decimals and add the two exponents. If the resulting decimal is greater than 10, move the decimal point one place to the left and add 1 to the exponent.
Converting Standard Notation and Scientific Notation
561–580
561. What is 1,776 in scientific notation?
562. Express 900,800 in scientific notation.
563. What is 881.99 in scientific notation?
564. What is the equivalent of 987,654,321 in scientific notation?
565. What is ten million in scientific notation?
566. How do you translate 0.41 into scientific notation?
567. What is 0.000259 equal to in scientific notation?
568. What is the equivalent of 0.001 in scientific notation?
569. What is the value of 0.0000009 in scientific notation?
570. How do you represent one-millionth in scientific notation?
571. What is the equivalent of 
in standard notation?
572. What is the equivalent of 
in standard notation?
573. The distance from the earth to the sun is approximately 
kilometers. How many kilometers is that in standard notation?
574. Scientists estimate that the universe is approximately 
years old. How many years is that in words?
575. A parsec is a unit of astronomical distance approximately equivalent to 
miles. How many miles is this in standard notation?
576. What is the equivalent of 
in standard notation?
577. What is the equivalent of 
in words?
578. An inch is approximately equivalent to 
kilometers. What is this number equivalent to in standard notation?
579. What is the value of 
in standard notation?
580. What is the value of 
in words?
Multiplying Numbers in Scientific Notation
581–590
581. What do you get when you multiply 
by 
?
582. What is 
multiplied by 
?
583. What is the result when you multiply 
by 
?
584. What is 
times 
?
585. What do you get when you multiply 
by 
?
586. What is 
times 
?
587. What is 
?
588. What is 
?
589. What is 
?
590. What is 
?