Scientific Notation And Computing W/o A Calculator Worksheet
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1
2Name: ___________________
Scientific Notation and Computing
Period: __________________
Without a Calculator
Date:
___________________
(Unit: Measurement, Chapter 2)
Objectives
To correctly convert numbers between scientific and standard (non-scientific) form without the use of a calculator.
To correctly add, subtract, multiply, and divide numbers in scientific notation without the use of a calculator.
Background
24
In scientific notation, the Earth's mass is 5.97 × 10
kg. The 5.97 part is called the coefficient, and the 24 is called the
exponent. Remember, an exponent simply describes how many times you are multiplying a number by itself. 2³ is
4
2×2×2, which is 8, and 2
is 2×2×2×2, or 16. It's especially easy when multiplying by tens.
3
10
is 10 × 10 × 10 = 1000, or a one with three zeros (a thousand).
6
10
is 10 × 10 × 10 × 10 × 10 × 10 = 1000000, a one followed by six zeros (a million).
24
So 10
is a 1 followed by twenty-four zeros, 1000000000000000000000000. The mass of the Earth (in kilograms) is 5.97
24
times bigger than that, so that's how we write it: 5.97 × 10
kg. If you wanted to write it out not-in-scientific-notation,
(standard form) write 5.97, and then move the decimal point 24 places to the right, filling in zeros to hold the places.
Small numbers are trickier; we have to use negative exponents. Recall that a negative exponent means the inverse ("1
divided by...") of the number raised to the exponent. For instance:
-3
2
= 1/2³ = 1/8
-3
10
= 1/10³ = 1/1000 = 0.001 (one thousandth)
-6
10
= 1/106 = 1/1000000 = 0.000001 (one millionth)
-27
The mass of a proton, in scientific notation, is 1.67 × 10
kg. To write this out in standard form (not-in-scientific-
notation), write 1.67 and then move the decimal point to the left 27 places, filling in zeros as needed.
General Rules
The coefficient and exponent are always written as decimal numbers, not as fractions (for example, 1.4 × 10², rather
than 7/5 × 10²). In general, we prefer to keep the coefficient between 1 and 10 (either positive or negative) by adjusting
the exponent so that only one non-zero number is to the left of the decimal. For example, we could write the mass of a
-28
-29
proton as 16.7 × 10
kg, or 167 × 10
kg ; mathematically, they are all the same! However, we prefer to write it as
-27
1.67 × 10
kg. You don’t need to do this for intermediate results when doing a long calculation, just for “final answers”.
Practice Problems
Convert the following numbers to scientific notation or standard form without using a calculator.
1.
1,280
_______________
2.
2.56
_______________
3.
5,000
_______________
4.
0.00085
_______________
5.
0.00163
_______________
6.
3,585,000
_______________
7.
9,582,000
_______________
8.
0.0000726
_______________
9.
80,100,000
_______________
10.
6,312
_______________
-5
4
11.
6.54 x 10
_______________
12.
5.54 x 10
_______________
-7
3
13.
3.0 x 10
_______________
14.
8.184 x 10
_______________
8
-6
15.
2.5 x 10
_______________
16.
9.25 x 10
_______________
-5
2
17.
6.54 x 10
_______________
18.
7.1456 x 10
_______________
0
1
19.
2.56 x 10
_______________
20.
3.5 x 10
_______________
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