Scientific notation
NOTES: A quick overview of scientific notation Before working on scientific notation, you may want to review multiplying and dividing decimals by 10, 100, 1000, etc. (10=101, 100=102, 1000=103). See my overview of decimals handout.
What does a number in scientific notation look like?
4.26 108 a single non-zero digit to the left of the decimal point
any number of additional digits (may be none)
times a positive or negative power of 10
These ARE in scientific notation: 6.389 108 These are NOT in scientific notation: 0.3 105
2 106 8.3 10–3 62.5 103 4.2 24
Why use scientific notation? Scientists often need to work with very large and very small numbers. It’s easier to recognize and compare numbers when you don’t have to stop and count all the 0’s. Which is easier to read: 3.4 10–9 or .0000000034?
How do I convert standard & scientific notation? scientific standard notation big numbers
standard scientific notation
2.36 105 236,000
5,236,000,000 5.236 109
5 104 50,000
4,000,000 4 106
small numbers 3.46 10–6 0.00000346 0.0004567 4.567 10–4 7 10–5 0.00007 © D. Stark 2017
0.0009 9 10–4
10/5/2017
OVERVIEW: scientific notation
1
scientific standard notation Start at the decimal point. (If there’s just a whole number, remember that there’s an invisible decimal point at the end. THINK: $5 = $5.00) If the exponent is positive, hop right that many places. Add 0’s if needed. If the exponent is negative, hop left that many places. Add 0’s if needed. EXAMPLES:
2.36 105 2.36000 = 236,000 7 10–5 .00007 = 0.00007
standard scientific notation Make a new decimal point just to the right of the first non-zero digit. Count the hops from there to the old decimal point. (If the original number was just a whole number, remember the invisible decimal point at the end.) Add 10 and the exponent to match the number of hops. o If it’s a big number (>=1), the exponent is positive. o If it’s a small number (
What does a number in scientific notation look like?
4.26 108 a single non-zero digit to the left of the decimal point
any number of additional digits (may be none)
times a positive or negative power of 10
These ARE in scientific notation: 6.389 108 These are NOT in scientific notation: 0.3 105
2 106 8.3 10–3 62.5 103 4.2 24
Why use scientific notation? Scientists often need to work with very large and very small numbers. It’s easier to recognize and compare numbers when you don’t have to stop and count all the 0’s. Which is easier to read: 3.4 10–9 or .0000000034?
How do I convert standard & scientific notation? scientific standard notation big numbers
standard scientific notation
2.36 105 236,000
5,236,000,000 5.236 109
5 104 50,000
4,000,000 4 106
small numbers 3.46 10–6 0.00000346 0.0004567 4.567 10–4 7 10–5 0.00007 © D. Stark 2017
0.0009 9 10–4
10/5/2017
OVERVIEW: scientific notation
1
scientific standard notation Start at the decimal point. (If there’s just a whole number, remember that there’s an invisible decimal point at the end. THINK: $5 = $5.00) If the exponent is positive, hop right that many places. Add 0’s if needed. If the exponent is negative, hop left that many places. Add 0’s if needed. EXAMPLES:
2.36 105 2.36000 = 236,000 7 10–5 .00007 = 0.00007
standard scientific notation Make a new decimal point just to the right of the first non-zero digit. Count the hops from there to the old decimal point. (If the original number was just a whole number, remember the invisible decimal point at the end.) Add 10 and the exponent to match the number of hops. o If it’s a big number (>=1), the exponent is positive. o If it’s a small number (
