Math 80/80A Unit 1.6
SUPPLEMENT
SCIENTIFIC NOTATION
Scientific Notation
Is written as the product of a number a and an integer power n of 10 : a 10n , where a is
1  a  10
Step1: Move the decimal point in the original number until the number has a value of 1  n  10
Step2: Count the number of decimal places the decimal point was moved in Step1. If the
original number is 10 or greater the exponent is positive. If the original number is less than 1,
the exponent is negative.
Step3: Write the product of the new number in Step 1 by 10 raised to an exponent equal to the
count found in Step2.
Example1:
Step1:
Write 740,000 in scientific notation.
Move the decimal point until the number is between 1  n  10.
740,000.
Step2: The decimal point is moved 5 places to the left and the original number is 10 or greater,
so the exponent is positive 5.
Step3:
740,000  7.4 105
Example2:
Step1:
Write .00000104 in scientific notation.
Move the decimal point until the number is between 1  n  10.
.00000104
Step2: The decimal point is moved 6 places to the right and the original number is less than 1,
so the exponent is negative 6.
Step3:
.00000104  1.04 106
[MATH 80A/80 SUPPLEMENT: UNIT 1.6]
©Cerritos College MLC
No part of this work may be reproduced without the prior written consent of the Cerritos College Math Learning Center.
PAGE 2
Write a Scientific Notation Number in Standard Notation
Move the decimal point in the number the same number of places as the exponent on 10. If the
exponent is positive, move the decimal point to the right (making the number larger since the
exponent is positive). Add zeros as needed. If the exponent is negative, move the decimal point
to the left (making the number smaller since the exponent is negative). Also, add zeros as
needed.
Example3:
6.4 108  640,000,000
2.024 106  .000002024
5.025 107   .0000005025
4.134 107   4,134,000
Problems:
Write each number in scientific notation.
1. 21, 243,000
2.
356,000
3.
0.013
4.
67,568
5. 46,700,000
6.
.00234
7.
.000378
8.
78,700,000
Write each number in standard notation.
9.
4.7 107
10.
3.8 106
11.
5.789 105
12.
1.04 108
13.
7.7 106
14.
4.2 103
15.
8.239 104
16.
6.40 105
[MATH 80A/80 SUPPLEMENT: UNIT 1.6]
©Cerritos College MLC
No part of this work may be reproduced without the prior written consent of the Cerritos College Math Learning Center.
PAGE 3
Answers:
1.
2.12 107
2.
3.56 105
3.
0.013 102
4.
6.75 104
5.
4.67 107
6.
2.34 103
7.
3.78 104
8.
7.8 107
9.
.00000047
10.
3,800,000
11.
578,900
12.
104,000,000
13.
.0000077
14.
.0042
15.
.0008239
16.
640,000
[MATH 80A/80 SUPPLEMENT: UNIT 1.6]
©Cerritos College MLC
No part of this work may be reproduced without the prior written consent of the Cerritos College Math Learning Center.