Teaching Notes 2.11: Expressing Large Numbers
in Scientific Notation
Scientific notation is a type of mathematical shorthand for writing very large or very small
numbers without copying numerous zeros. Students often make two errors when writing large
numbers in scientific notation: either they place the decimal point incorrectly or they use an
incorrect power of ten.- Explain that scientific notation is a way of writing very large (or small) numbers as the prod-
uct of a decimal between 1 and 10 and a power of 10. This eliminates the need for copying a
lot of zeros. - Make sure that your students understand that the decimal point may be placed to the right
of any whole number. For example, for 152 the decimal point is understood to be after the 2. - Explain that to write large numbers in scientific notation, students should place the deci-
mal point to the right of the number written in standard form. They should then move the
decimal point as far to the left as possible, placing it after the first nonzero digit. Next they
should count the number of places they moved the decimal point. For example, for the num-
ber 4,230,000,000, 4 is the first nonzero digit in standard form. Because nine digits are to the
right of 4, 9 is the exponent. Written in scientific notation, 4,230,000,000= 4. 23 × 109. - Note that all zeros, except those between two nonzero digits, should be dropped.
- Review the steps for writing scientific notation and the examples on the worksheet with your
students.
EXTRA HELP:
Check that your expressions in scientific notation are numbers between 1 and 10 and that the
exponent of 10 indicates the correct number of places the decimal point was moved.ANSWER KEY:
(1) 3. 4 × 105 (2) 1. 86 × 108 (3) 2. 405 × 104 (4) 1. 672 × 104 (5) 2. 0713 × 106
(6) 4. 81 × 103 (7) 9. 0001 × 105 (8) 7. 1005 × 107 (9) 5. 142 × 106 (10) 1. 1 × 103
(11) 7. 0012 × 108 (12) 8. 915 × 107
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(Challenge)Sunil is incorrect because the number 23.5 is not between 1 and 10. The correct
answer is 2. 35 × 104.
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