Luttrell 2012
66
Name: ______________________
Date: _____
4j - Scientific Notation
Since mathematicians and scientists have tried to find ways of simplifying written expressions, scientific
notation is common for writing VERY large or small numbers. This is very useful when talking about the
distance between stars, light years, the number of molecules in an object, the people on the planet, etc.
Note how this large number is rewritten:
64000000 = 6.4∙10
7
The 6.4 is the mantissa and is always a
number between 1 and 9, inclusively. The exponent 7 is the characteristic and says what power of 10 you
are multiplying by. Some people just remember that is how many spaces to move the decimal point. A
negative moves it left and a positive moves the decimal right. A small decimal like 0.000007 is rewritten
as
0.000007 = 7∙10
-6
.
1. 0.000123
2. 2,340,000,000
3. 0.0000000345
4. 435000000000000
5. 76,000,000,000
6. 0.0000308
Express each number into scientific notation. For some you may have to round to three
significant digits in the mantissa.
7. 23,000,000,000,000
7. ______________________
8. 134,000,000,000
8. ______________________
9. 456,000,340,000,000
9. ______________________
10. 788,999,213,543,345,532,345
10. ______________________
Express each number in standard form.
11.
2 34 10
4
.
×
11. ______________________
12.
3 4 10
14
.
×
12. ______________________
13.
6 7 10
7
.
×
13. _______________________
14.
2 6 10
9
.
×
14. _______________________
15. 3.4 × 10
-5
15. _______________________
16. 1 × 10
-10
16. ______________________
17. 3.25 × 10
-6
17. ______________________
Fill in the missing spots of the equation.
18.
0 0000234
2 34 10
.
.
=
×
19.
31 10
00000031
5
.
×
=
−
20
. 0.0045 = 45∙10
-3
21
. 6.1 ∙ 10 = 610,000
