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 Question from mackenzie: How would you answer this question? Write 0.000661 in scientific notation

Hi Mackenzie,

To put numbers into scientific notation:

1. Place a decimal between the first 2 (non-zero) digits

2. Count the number of place values you have to shift to get from this new number to the original decimal number

3. Copy the digits and write the “shifting” with a base “10” in exponential form

4. If “shifting” to the RIGHT --> the exponent will be positive

5. If “shifting” to the LEFT --> the exponent will be negative

For example, change the following into scientific notation:
a) 0.000 049

• The first 2 non-zero digits are 4 and 9, so we put a decimal between them:   4.9

• To move from the new decimal to the old decimal, we had to move it 5 places to the left, so the digit 5 is in our exponent with a base of 10.  Since to get to the original decimal we must move to the left, our exponent is negative and our answer is then: 0.000 049 = 4.9 x 10-5

b) 2 930 000

• The first 2 non-zero digits are 2 and 9, so we put a decimal between them and include any other non-zero digits (after the decimal) if there are any:    2.93

• To move from the new decimal to the old decimal, we had to move it 6 places to the left, so the digit 6 is in our exponent with a base of 10.  Since to get to the original decimal we must move to the right, our exponent is positive and our answer is then:2 930 000 = 2.93 x 106

Sara

Hi Mackenzie,

Let me look at a different example.

Write 0.0000178 in scientific notation.

I know that for scientific notation I am to have exactly one digit to the left of the decimal so I know the answer is

0.000 017 8 = 1.78 10??

for some positive or negative inyeger ??. Look at 0.000 017 8 and 1.78. The decimal has moved 5 places so

0.000 017 8 = 1.78 10?5

but is ? a plus or minus sign? If it were posivive I would have

1.78 10+5 = 1.78 100 000 = 178 000

which is clearly wrong so it must be that

0.000 017 8 = 1.7 10-5

Penny

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