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# Scientific notation and significant figures

## on Aug 05, 2013

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## Scientific notation and significant figuresPresentation Transcript

• By Mikaela Mercado Gr. 7 – L. Guevara
• Scientific notation is a value written as a simple number multiplied by a power of ten. It is another way of writing numbers. It also makes calculating these numbers easier. Correct scientific notation has a coefficient that is less than 10 and greater than or equal to 1. That coefficient is then multiplied by a power of ten. Example: 46000 = 4.6 x 104
• The steps for writing scientific notation are rather simple. Let's go over them by actually changing numbers into scientific notation. Example: The distance between Earth and Neptune is 4,600,000,000,000 meters. How do we write it in Scientific Notation?
• Place the decimal point after the first whole number digit and drop the zeros. The number "4" is the first whole number. So: 4.600,000,000,000
• Find the exponent. To do this, count the number of places from the new decimal point to the end of the number. This decimal point is 12 places from the end of the number or where the decimal was originally. So: 4.600,000,000,000. New Decimal Point Original Decimal Point
• Rewrite the number by multiplying it by a power of ten. * Drop all zeros and write your number. This number must be multiplied by a power of 10. 4.600,000,000,000 = 4.6 x 10 * Your exponent will be the number of places that the decimal point was moved. Since the decimal point was moved 12 places, the exponent will be "12". 4.6 x 1012
• The term significant figures refers to the number of important single digits (0 through 9) in the coefficient of an expression in Scientific Notation.
• 1. All nonzero digits are significant: 1.234 g - has 4 significant figures, 1.2 g - has 2 significant figures. 2. Zeroes between nonzero digits are significant: 1002 kg - has 4 significant figures, 3.07 mL - has 3 significant figures.
• 3. Leading zeros to the left of the first nonzero digits are not significant; such zeroes merely indicate the position of the decimal point: 0.001 mg - has only 1 significant figure 0.012 g - has 2 significant figures. 4. Trailing zeroes that are also to the right of a decimal point in a number are significant: 0.0230 ml - has 3 significant figures 0.20 g - has 2 significant figures.
• 5. When a number ends in zeroes that are not to the right of a decimal point, the zeroes are not necessarily significant: 190 miles may be 2 or 3 significant figures 50,600 calories may be 3, 4, or 5 significant figures.
• 1. In addition and subtraction, the result is rounded off to the last common digit occurring furthest to the right in all components. Another way to state this rule is as follows: in addition and subtraction, the result is rounded off so that it has the same number of digits as the measurement having the fewest decimal places (counting from left to right). For example, 100 – 3 SF + 23.645 – 5 SF
• 2. In multiplication and division, the result should be rounded off so as to have the same number of significant figures as in the component with the least number of significant figures. For example, 12.25 – 4 SF X 3.0 – 2 SF 36.75 = 37