6th Grade Math Textbook, Fundamentals

Lesson 4-10 for exercise sets. &KDSWHU 

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Write in scientific notation. Write in standard form.

1.4,000,000 2.7,500,000 3. 4    104 4.8.13  103

Compare. Write ,, , or ..

5.7.234     103 5.6     105 6.3.45  106 9.9     10 ^4 7.3.45   102 9.5     100

Order from least to greatest.

8.5.83  107 ; 2.22  106 ; 7.94  107 9.1.09  105 ; 7.93  106 ; 1.4   107 ; 450,000

10.Discuss and Write Explain why 0.003  103 is not scientific notation.

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There are two ways to write the standard form for numbers in scientific notation.

• Write the power of 10 in standard form, then multiply the two factors.
  5.8 106  5.8 1,000,000  5,800,000
  2.3 10 ^4  2.3 0.0001  0.00023


• To show the multiplication by the power of 10, move the decimal point
  to the right if the exponent is positive and to the left if the exponent is
  negative. Use placeholder zeros as needed.
  5.8 106 5. 8 0 0 0 0 0. The exponent is 6, so the decimal point moves right 6 places.
  2.3 10 ^4 0.000 23 The exponent is 4, so the decimal point moves left 4 places.

You can compare two numbers written in scientific notation.

• Compare: 6.7 104 6.8 106

So 6.7  104 6.8    106.

• Compare: 2.47 10 ^3 1.8 10 ^3

2.47 1. 8

So 2.47     10 ^3 1.8     10 ^3

To order numbers when some are in scientific notation and some are not,

rename numbers as needed so that all are in like form. Then compare and order.

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Compare powers

of 10: 10^3  10 ^3

Then compare decimal

factors: 2.47  1. 8

Compare the exponents:

104  106.

• Order from least to greatest:
  9.48 104 ; 5.9 105 ; 4.342 104
  5.9 105 greatest power
  4.342 104
  9.48 104

same power of 10

4.342 9.48 Compare decimal factors.

So the order from least to greatest is

4.342   104 ; 9.48  104 ; 5.9   105.

• Order from least to greatest:
  7.501 108 ; 75,100,000; 7.51 108
  75,100,000 7.51 107

7.501   108 ; 7.51  108

7.501 7.51

So the order from least to greatest is

75,100,000; 7.501   108 ; 7.51  108.

108  108 ; compare

the decimal factors.

Rename in like form;

107 is least power.

Key Concept

Compare Expressions in

Scientific Notation

To compare two expressions

in scientific notation, first

compare the powers of 10.

An expression with a greater

power of 10 is greater. If the

powers of 10 are the same,

compare the decimal factors.