Scientific Notation

Do you remember the rule for powers of ten? What does 105 equal?? 10•10•10•10•10 Multiply by ten adds a zero, so multiplying by five tens adds five zeros! 105 = 100000 103 = 1000 109 = 1000000000

Multiplying by Tens How do we multiply other numbers by ten? What does 57 x 10 equal?? To multiply by 10, add a zero to the number, so 57 x 10 = 570 What about multiply by 1000? By 1000000? 57 x 1000 = 57000 57 x 1000000 = 57000000

Multiplying Decimals by Tens How do we multiply decimals by ten? What does 5.47 x 10 equal?? This number is close to 5, what number is ten times larger than 5? 50 So 5.47 x 10 should be close to 50 ... 5.47 x 10 = 54.7 For each power of ten (zero), move the decimal one place to the right (this makes the number have a larger place value). 8.934 x 10000 = 8.9.3.4. . = 89340

Scientific Notation The following is a number written in scientific notation: Since the first number can only have one digit to the left of the decimal, multiplying by a power of ten allows us to write larger numbers. In scientific notation, this number is always at least 1.000 and less than 10.000.

So, how big IS this number?? 360 million one hundred thousand Scientific Notation So, how big IS this number?? 108 means we multiply by 8 tens. Move the decimal 8 places to right. Since there are only 3 numbers after the decimal, we need to add 5 more zeros! 360 million one hundred thousand

Scientific Notation to Normal Write these numbers without scientific notation:

Writing Scientific Notation Write this number in scientific notation: 12,030,000 Step 1: If the number greater than or equal to 10, move the decimal point to after the first digit. 2030000 1 . Step 2: Count how many places you moved the decimal point to the left. This is the exponent for 10. 1.203 x 107 You do not need to write zeros after the last digit.

Writing Scientific Notation Write these numbers in scientific notation: