Why do we use scientific Notation?

Calculator Challenge: Part 1 Use a calculator. Experiment multiplying with very large numbers until your calculator gives an answer that is not in standard form. Multiply 2 billion by 3 billion by hand. Use the results to explain what 6 × 10 18 means. Why didn’t the calculator show answer in standard form?

Calculator Challenge: Part 2 Use a calculator. Experiment multiplying with very small numbers until your calculator gives an answer that is not in standard form. Multiply 2 billionths by 3 billionths. Use the results to explain what 6 × 10 −18 means. Why didn’t the calculator show answer in standard form?

Key Terms: A number is in scientific notation when it is represented as the product of a factor and a power of 10. The factor must be at least 1 and less than 10.

Which example represents scientific notation? Explain. 𝟓.𝟗 × 𝟏𝟎 −𝟔 𝟎.𝟗 × 𝟏𝟎 𝟖

𝟓.𝟗 × 𝟏𝟎 −𝟔 𝟓.𝟗 × 𝟏𝟎 𝟔 0.0000059 5,900,000 Scientific Notation Standard Form 𝟓.𝟗 × 𝟏𝟎 −𝟔 𝟓.𝟗 × 𝟏𝟎 𝟔 0.0000059 5,900,000

Remember When writing scientific notation in standard form If the exponent is negative, move the decimal point to the left. If the exponent is positive, move the decimal point to the right.

Write the number in scientific notation 𝟐𝟓,𝟎𝟎𝟎,𝟎𝟎𝟎 𝟎.𝟎𝟎𝟎𝟎𝟎𝟔𝟖 𝟐.𝟓 × 𝟏𝟎 𝟕 6.8 × 𝟏𝟎 −𝟔

You Try: Write the number in scientific notation 𝐂. 𝟏𝟎,𝟕𝟎𝟎,𝟎𝟎𝟎 D. 0.00000062 𝑨. 𝟎.𝟎𝟎𝟎𝟓𝟗𝟔 𝑩. 𝟓,𝟒𝟐𝟑,𝟎𝟎𝟎,𝟎𝟎𝟎

Write the number in standard form 𝟑.𝟐𝟐 × 𝟏𝟎 −𝟒 𝟎.𝟗 × 𝟏𝟎 𝟖 𝟎.𝟎𝟎𝟎𝟑𝟐𝟐 90,000,000

Remember to write standard form in scientific notation… If the number is very large, the exponent will be positive. If the number is very small, the exponent will be negative.

You Try: Write the number in Standard Form 𝑪. 𝟓 × 𝟏𝟎 −𝟏𝟐 𝑫. 𝟏.𝟔𝟔 × 𝟏𝟎 𝟗 𝑨. 𝟑.𝟖𝟓 × 𝟏𝟎 𝟕 𝑩. 𝟒𝟔 × 𝟏𝟎 −𝟓

Book Practice Activity 1: Page 586 Activity 2: Page 587

Activity: All for a walk on the moon

Multiplying numbers in scientific notation Rewrite the problem grouping the factors and the powers of ten 2. Simplify 3. Write answer in scientific notation

Let’s Try: Multiplying numbers in scientific notation 𝟐.𝟓 × 𝟏𝟎 𝟖 × (2 × 𝟏𝟎 𝟑 ) Rewrite the problem grouping the factors and the powers of ten 2. Simplify 3. Write answer in scientific notation

You Try: multiplying numbers in scientific notation (𝟓× 𝟏𝟎 𝟒 ) × (𝟓.𝟒× 𝟏𝟎 −𝟗 ) 2. (𝟕× 𝟏𝟎 𝟐 ) × (𝟑× 𝟏𝟎 𝟓 ) 3. (𝟔× 𝟏𝟎 𝟖 ) × (𝟏.𝟒× 𝟏𝟎 −𝟓 ) 𝟒. (𝟕.𝟐× 𝟏𝟎 −𝟏 ) × (𝟒× 𝟏𝟎 −𝟕 )