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PRE-ALGEBRA
PRE-ALGEBRA
Lesson 4-9 Warm-Up
PRE-ALGEBRA
“Scientific Notation” (4-9)
What is “scientific notation”?
How do you write a number in scientific notation?
scientific notation: a way to write very large numbers in short form using powers of 10 in the form a x 10n, where n is an integer and a is between 1 and 10 (1 ≤ a ≤ 10).
Example: 7,500,000,000,000 (“7 trillion, 500 billion”) = 7.5 x 1012
To write a number in scientific notation, move the decimal so it’s after the first nonzero (≠ 0) digit, write the rest of the nonzero numbers after the decimal, and multiply this by 10 to the power of the number of jumps it would take to make the original number (right jumps = positive exponent and left jumps = negative exponent).
Standard Notation: the usual way to write a number using commas, etc. Examples: The world’s largest tree is the General Sherman at, 2,777,000 pounds.Write this weight in scientific notation.
Move the decimal point to get a number greater than 1 but less than 10.Drop the zeros after the last nonzero digitSince you moved the decimal 6 places to the left to make a smaller number, make the exponent a positive 6
__._____ x 10 ___ decimal jumps it would take to make the number first rest of nonzero the nonzero digit digits
PRE-ALGEBRA
“Scientific Notation” (4-9)
What is “standard notation”?
How do you change scientific notation to standard notation?
Examples: Write 0.000079 in scientific notation.
Move the decimal point to get a number greater than 1 but less than 10.Drop the zeros before the first nonzero digitSince you moved the decimal 5 places to the right to make a bigger number, make the exponent a negative 5
Standard Notation: the usual way to write a number using commas, etc.
standard notation: the way you normally write numbers using place value
To change scientific notation to standard notation, move the decimal the number of places the exponent tells you to. Move the decimal to the right for positive exponents (make a bigger number) and to the left for negative exponents (make number smaller).
Scientific Notation Standard Notation
3.6 x 1012 (3.6 trillion) 3,600,000,000,000
4.36 x 10-11 0.0000000000436
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About 6,300,000 people visited the Eiffel Tower in
the year 2000. Write this number in scientific notation.
6,300,000
6.3 Drop the zeros after the 3.
6.3 106 You moved the decimal point 6 places. The original number is greater than 10.Use 6 as the exponent of 10.
Move the decimal point to get a decimal greater than 1 but less than 10.
6 places
Scientific NotationLESSON 4-9
Additional Examples
PRE-ALGEBRA
Write 0.00037 in scientific notation.
0.00037 Move the decimal point to get a decimal greater than 1 but less than 10.
4 places
3.7 10–4 You moved the decimal point 4 places. The original number is less than 1.Use –4 as the exponent of 10.
3.7 Drop the zeros before the 3.
Scientific NotationLESSON 4-9
Additional Examples
PRE-ALGEBRA
Write each number in standard notation.
a. 3.6 104
3.6000 Write zeros while moving the decimal point.
36,000 Rewrite in standard notation.
b. 7.2 10–3
007.2
0.0072 Rewrite in standard notation.
Write zeros while moving the decimal point.
Scientific NotationLESSON 4-9
Additional Examples
PRE-ALGEBRA
Write each number in scientific notation.
a. 0.107 1012
0.107 1012 = 1.07 10–1 1012 Write 0.107 as
1.07 10–1.
= 1.07 1011 Add the exponents.
b. 515.2 10–4
515.2 10–4 = 5.152 102 10–4 Write 515.2 as 5.152 102.
= 5.152 10–2 Add the exponents.
Scientific NotationLESSON 4-9
Additional Examples
PRE-ALGEBRA
“Scientific Notation” (4-9)
How do you order numbers in scientific notation?
To order numbers in scientific notation, order by the exponents only first, If there is a tie with the exponents, order by the decimal next. Examples: Order 0.064 x 108 , 312 x 10-4 , and 0.58 x 107 from least to greatest.
Step 1: Write each number in correct scientific notation.
Step 2: Order the powers of 10 from least to greatest first. Arrange the decimals with the same power of 10 from least to greatest if necessary.
Step 3: Write the original numbers in order from least to greatest.
PRE-ALGEBRA
Write each number in scientific notation.
0.035 104 0.69 102
3.5 102
710 10–1
7.1 10 6.9 10
Order the powers of 10. Arrange the decimals with the same power of 10 in order.
6.9 101 7.1 101 3.5 102
Write the original numbers in order.
0.69 102, 710 10–1, 0.035 104
Order 0.035 104, 710 10–1, and 0.69 102 from least to greatest.
Scientific NotationLESSON 4-9
Additional Examples
PRE-ALGEBRA
“Scientific Notation” (4-9)
How do multiply numbers in scientific notation?
To multiply numbers in scientific notation, multiply the decimals and powers of 10 separately. Then, put the answer in correct scientific notation form.Examples: The Great Pyramid of Giza in Egypt contains about 2.3 x 106 blocks of stone. On average, each block weighs about 5 x 103 ponds. About how heavy is the Pyramid?
(2.3 x 106)(5 x 103) Multiply the number of blocks by the weight of each block to find the total weight.
= 2.3 x 5 x 106 x 103Use the Commutative Property of Multiplication to rearrange the terms.
= 11.5 x 106 x 103 Multiply the decimals.
= 11.5 x 109 Add the exponents
= (1.15 x 101) x 109 Write 11.5 x 109 in correct scientific notation
= 1.15 x 1010 Add the exponents
The Great Pyramid of Giza weighs about 1.15 x 1010 lb.
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Multiply 4 10–6 and 7 109. Express the result in scientific notation.
Use the Commutative Property of Multiplication.
(4 10–6)(7 109) = 4 7 10–6 109
= 28 10–6 109 Multiply 4 and 7.
= 28 103 Add the exponents.
= 2.8 101 103 Write 28 as 2.8 101.
= 2.8 104 Add the exponents.
Scientific NotationLESSON 4-9
Additional Examples
PRE-ALGEBRA
Scientists find a wooly mammoth fossil that is
about 2.0 104 years old. They believe that Earth is
about 2.3 105 times as old as this fossil. How old dothey believe Earth is?
(2.0 104)(2.3 105) Multiply age of fossil by thenumber of times as old as thisfossil Earth is.
= 2.0 2.3 104 105 Use Commutative Property of Multiplication.
= 4.6 104 105 Multiply 2.0 and 2.3.
= 4.6 109 Add the exponents.
Earth is about 4.6 109 years old.
Scientific NotationLESSON 4-9
Additional Examples
PRE-ALGEBRA
Write each number in scientific notation.
1. 5,400,000 2. 0.0000867
Write each number in standard notation.
3. 3.45 106 4. 1.99 10–5
5. Order 7.2 105, 7.2 106, 7.02 106, and 7.1 10–6 from least to greatest.
6. Multiply 14 106 and 4 10–4. Express the result in scientific notation.
5.6 103
5.4 106 8.67 10–5
3,450,000 0.0000199
7.1 10–6, 7.2 105, 7.02 106, 7.2 106
Lesson Quiz
Scientific NotationLESSON 4-9
