By Henri Picciotto, The Urban School of San Francisco
- Scientific notation:
- 1200 = 1.2(103)
- 400,000 = 4.0(105)
- Super-scientific notation:
- 1200 and 400,000 can be written as powers of ten.
- Explain why 1200 must be a power of ten with the exponent between 3 and 4.
- 400,000 must be a power of ten with the exponent between what whole numbers?
- Find the power of ten that approximately equals the following numbers. Your answer should be accurate to the nearest thousandth.
a. 1200 (Hint: start with a window with xmin=3, xmax=4, ymin=1000 and ymax=1400. Solve 10x = 1200.)
You have converted 1200 and 400,000 to super-scientific notation.
Looking for Patterns
- Write the following numbers in super-scientific notation (with the exponents rounded to the nearest thousandth). Arrange the results in a table. Look for patterns as you work. Share the calculations with other students.
a. The whole numbers from 1 to 9
b. The multiples of 10 from 10 to 90
c. The multiples of 100 from 100 to 900
- What is the relationship between the exponents for 2, 20, and 200? Explain.
- What is the relationship between the exponents for 3 and 9? Explain.
- What is the relationship between the exponents for 20, 30, and 600? Explain.
- What is the relationship between the exponents for 2 and 8? Explain.
- Find other relationships between exponents, and explain them.
Calculating Without a Calculator!
- Without a calculator, write the following in super-scientific notation. (Hint: use your table.)
- Here is a calculation that uses scientific notation:
1200*400,000 = 1.2(103)*4.0(105) = 4.8(108)
What is the equivalent calculation using super-scientific notation?
- Explain the following statement: multiplying two numbers written in scientific notation involves a multiplication and an addition.
- What is the corresponding statement for multiplying two numbers written in super-scientific notation? Explain.