Digits, Grade 8, Volume 2, Homework Helper

### 15-5: Operations with Numbers Expressed in Scientific Notation

#### Part 1

Intro

Adding, subtracting, multiplying, or dividing large or small numbers in scientific notation is easier and more efficient than operating on the same numbers in standard form.

To add or subtract numbers in scientific notation, they must have the same power of 10. Add or subtract the first factors of the numbers and keep the same power of 10.

table with 2 rows and 2 columns , row1 column 1 , open . 6 times , 10 to the fourth . close . plus . open . 2 times , 10 to the fourth . close . , column 2 equals . open . 6 plus 2 . close . times , 10 to the fourth , column 2 equals 8 times , 10 to the fourth , end table

Sometimes sums or differences of numbers in scientific notation are numbers that are not in scientific notation. In those cases, you need to rewrite the sum or difference in the correct form. To add or subtract numbers in scientific notation, make sure they have the same power of 10, then add or subtract the first factors.

Addition of Numbers in Scientific Notation

Arithmetic: open . 6 times , 10 to the fourth . close . plus . open . 2 times , 10 to the fourth . close . equals . open . 6 plus 2 . close . times , 10 to the fourth , equals 8 times , 10 to the fourth

Algebra: open . a times , 10 to the n . close . plus . open . b times , 10 to the n . close . equals . open . a plus b . close . times , 10 to the n , comma

where 1≤a < 10 and 1≤b < 10 and n is an integer.

Subtraction of Numbers in Scientific Notation

Arithmetic: open . 9 times , 10 super negative 2 end super . close . minus . open . 3 times , 10 super negative 2 end super . close . equals . open . 9 minus 3 . close . times , 10 super negative 2 end super , equals 6 times , 10 super negative 2 end super

Algebra: open . a times , 10 to the n . close . minus . open . b times , 10 to the n . close . equals . open . eh minus b . close . times , 10 to the n , comma

where 1≤a < 10 and 1≤b < 10 and n is an integer.

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