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How to convert scientific notation to decimal form

Convert to decimal form: 6.2 × 10 3 .

Solution

This figure is a table that has three columns and three rows. The first column is a header column, and it contains the names and numbers of each step. The second column contains further written instructions. The third column contains math. On the top row of the table, the first cell on the left reads “Step 1. Determine the exponent, n, on the factor 10.” The second cell reads “The exponent is 3.” The third cell contains 6.2 times 10 cubed. In the second row, the first cell reads “Step 2. Move the decimal n places, adding zeros if needed. If the exponent is positive, move the decimal point n places to the right. If the exponent is negative, move the decimal point absolute value of n places to the left.” The second cell reads “The exponent is positive so move the decimal point 3 places to the right. We need to add two zeros as placeholders.” The third cell contains 6.200, with an arrow showing the decimal point jumping places to the right, from between the 6 and 2 to after the second 00 in 6.200. Below this is the number 6,200. In the third row, the first cell reads “Step 3. Check to see if your answer makes sense.” The second cell is blank. The third reads “10 cubed is 1000 and 1000 times 6.2 will be 6,200.” Beneath this is 6.2 times 10 cubed equals 6,200.
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Convert to decimal form: 1.3 × 10 3 .

1,300

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Convert to decimal form: 9.25 × 10 4 .

92,500

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The steps are summarized below.

Convert scientific notation to decimal form.

To convert scientific notation to decimal form:

  1. Determine the exponent, n , on the factor 10.
  2. Move the decimal n places, adding zeros if needed.
    • If the exponent is positive, move the decimal point n places to the right.
    • If the exponent is negative, move the decimal point | n | places to the left.
  3. Check.

Convert to decimal form: 8.9 × 10 −2 .

Solution

8.9 times 10 to the power of negative 2.
Determine the exponent, n , on the factor 10. The exponent is negative 2.
Since the exponent is negative, move the decimal point 2 places to the left. 8.9, with an arrow the decimal place showing the decimal point being moved two places to the left.
Add zeros as needed for placeholders. 8.9 times 10 to the power of negative 2 equals 0.089.
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Convert to decimal form: 1.2 × 10 −4 .

0.00012

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Convert to decimal form: 7.5 × 10 −2 .

0.075

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Multiply and divide using scientific notation

Astronomers use very large numbers to describe distances in the universe and ages of stars and planets. Chemists use very small numbers to describe the size of an atom or the charge on an electron. When scientists perform calculations with very large or very small numbers, they use scientific notation. Scientific notation provides a way for the calculations to be done without writing a lot of zeros. We will see how the Properties of Exponents are used to multiply and divide numbers in scientific notation.

Multiply. Write answers in decimal form: ( 4 × 10 5 ) ( 2 × 10 −7 ) .

Solution

( 4 × 10 5 ) ( 2 × 10 −7 ) Use the Commutative Property to rearrange the factors. 4 · 2 · 10 5 · 10 −7 Multiply. 8 × 10 −2 Change to decimal form by moving the decimal two places left. 0.08

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Multiply ( 3 × 10 6 ) ( 2 × 10 −8 ) . Write answers in decimal form.

0.06

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Multiply ( 3 × 10 −2 ) ( 3 × 10 −1 ) . Write answers in decimal form.

0.009

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Divide. Write answers in decimal form: 9 × 10 3 3 × 10 −2 .

Solution

9 × 10 3 3 × 10 −2 Separate the factors, rewriting as the product of two fractions. 9 3 × 10 3 10 −2 Divide. 3 × 10 5 Change to decimal form by moving the decimal five places right. 300,000

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Divide 8 × 10 4 2 × 10 −1 . Write answers in decimal form.

400,000

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Divide 8 × 10 2 4 × 10 −2 . Write answers in decimal form.

20,000

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Access these online resources for additional instruction and practice with integer exponents and scientific notation:

Key concepts

  • Property of Negative Exponents
    • If n is a positive integer and a 0 , then 1 a n = a n
  • Quotient to a Negative Exponent
    • If a , b are real numbers, b 0 and n is an integer , then ( a b ) n = ( b a ) n
  • To convert a decimal to scientific notation:
    1. Move the decimal point so that the first factor is greater than or equal to 1 but less than 10.
    2. Count the number of decimal places, n , that the decimal point was moved.
    3. Write the number as a product with a power of 10. If the original number is:
      • greater than 1, the power of 10 will be 10 n
      • between 0 and 1, the power of 10 will be 10 n
    4. Check.

  • To convert scientific notation to decimal form:
    1. Determine the exponent, n , on the factor 10.
    2. Move the decimal n places, adding zeros if needed.
      • If the exponent is positive, move the decimal point n places to the right.
      • If the exponent is negative, move the decimal point | n | places to the left.
    3. Check.

Questions & Answers

how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Two sisters like to compete on their bike rides. Tamara can go 4 mph faster than her sister, Samantha. If it takes Samantha 1 hours longer than Tamara to go 80 miles, how fast can Samantha ride her bike? Got questions? Get instant answers now!
Seera Reply
how do u solve that question
Seera
Two sisters like to compete on their bike rides. Tamara can go 4 mph faster than her sister, Samantha. If it takes Samantha 1 hours longer than Tamara to go 80 miles, how fast can Samantha ride her bike?
Seera
Speed=distance ÷ time
Tremayne
x-3y =1; 3x-2y+4=0 graph
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Brandon has a cup of quarters and dimes with a total of 5.55$. The number of quarters is five less than three times the number of dimes
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app is wrong how can 350 be divisible by 3.
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Susanna if the first cooler holds five times the gallons then the other cooler. The big cooler holda 40 gallons and the 2nd will hold 8 gallons is that correct?
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@Susanna that person is correct if you divide 40 by 8 you can see it's 5 it's simple
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@Geogie my bad that was meant for u
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Can you all help me I don't get any of this
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4^×=9
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Practice Key Terms 2

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Source:  OpenStax, Elementary algebra. OpenStax CNX. Jan 18, 2017 Download for free at http://cnx.org/content/col12116/1.2
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