Scientific Notation Practice

Question

1.) 8,000,000 x 140/ 0.04=

2.) 640 x 0.072 x 4/ 160,000 x 0.00036=

3.) 30/60,000 x 0.05=

4.) 42 x 0.00070/ 0.35 x 30,000 x 140=

5.) 450 x 0.008 x 0.2/ 20,000 x 40 0.18=

Answer 1

To convert to scientific notation, count the number of decimal places to go from what the number is, to get to a number greater than 1 but less than 9. Example: For the number 123,456 the decimal is to the right of the "6", counting left to get to the number 1.23456 you count:

5 places to the left means this will be 1.23456 x 10⁵

For the number 0.000123456 you must move the decimal 4 places to the right to get to 1.23456 so this number becomes 1.23456 x 10^-4 (moving left makes a positive exponent, moving right makes a negative exponent.

Problem 1) 8,000,000 x 140/ 0.04

Converting 8,000,000 into scientific notation makes it 8.0 x 10⁶

Converting 140 into scientific notation makes it 1.4 x 10²

Converting 0.04 into scientific notation makes it 4.0 x 10^-2

1) Now, to do the math, (8.0 x 10⁶)(1.4 x 10²)/(4.0 x 10^-2) you use this rule: Multiply and/or divide the regular numbers like regular, so (8)(1.4)/4 = 2.8

2) Convert this number into scientific notation if it's not greater than 1 or less than 10. In this case it is so you can skip this step.

3) For all number being multiplied, add the exponents. For numbers being divided, subtract the exponents.

In this case, the numbers being multiplied have exponents of 6 and 2 so add them to get 8. The number being divided has a exponent of -2 so subtract: 8 - -2 = 10. You must also include any exponents you get from step 2 (but again, in this problem, step 2 was not needed)

4) Put the numbers and exponents together: 2.8 x 10¹⁰

Problem 2) 640 x 0.072 x 4/ 160,000 x 0.00036 - This problem isn't clear because parentheses were not used. I'm going to assume it is supposed to be (640)(0.072)(4)/[(160,000)(0.00036)] so:

Converting 640 into scientific notation makes it 6.4 x 10²

Converting 0.072 into scientific notation makes it 7.2 x 10^-2

4 is already greater than 1 and less than 10 so it's OK. You can officially convert it into scientific notation by calling it 4.0 x 10⁰

Converting 160,000 into scientific notation makes it 1.6 x 10⁵

Converting 0.00036 into scientific notation makes it 3.6 x 10^-4

That results in: (6.4 x 10²)(7.2 x 10^-2)(4.0 x 10⁰)/[(1.6 x 10⁵)(3.6 x 10^-4)]

1. Multiply/divide the numbers: (6.4 • 7.2 • 4)/(1.6 • 3.6) = 184.32/5.76 = 32. Convert this to scientific notation to be 3.2 x 10¹
2. Then add/subtract the exponents: The numerator has 2 + -2 + 0 = 0. The denominator has 5 + -4 = 1. The number from step 1 has an exponent of 1. So 0 - 1 + 1 = 0
3. The final answer in scientific notation is 3.2 x 10⁰ or JUST 3.2

You can do the other problems just the same.