Adding and subtracting numbers in scientific notation:
When adding or subtracting numbers in scientific notation, the exponents of the numbers must be the same. If the exponents are not the same, the numbers should be converted to have the same power of 10 before performing the addition or subtraction. After converting, the coefficients of the numbers can be added or subtracted, while keeping the power of 10 the same.
For example, to add 3.2 x 10^5 and 6.4 x 10^4:
Step 1: Convert the numbers to the same exponent by moving the decimal point and adjusting the power of 10.
3.2 x 10^5 can be written as 32 x 10^4
Step 2: Add the coefficients, keeping the power of 10 the same.
32 x 10^4 + 6.4 x 10^4 = 38.4 x 10^4
Step 3: Simplify the result if necessary.
38.4 x 10^4 can be written as 3.84 x 10^5.
Multiplication and division in scientific notation:
When multiplying or dividing numbers in scientific notation, the coefficients of the numbers are multiplied or divided, and the powers of 10 are added or subtracted.
For example, to multiply 4.5 x 10^3 and 3.2 x 10^2:
Step 1: Multiply the coefficients.
4.5 x 3.2 = 14.4
Step 2: Add the exponents.
10^3 x 10^2 = 10^(3+2) = 10^5
Step 3: Write the answer in scientific notation.
14.4 x 10^5
For example, to divide 9.6 x 10^4 by 2.4 x 10^2:
Step 1: Divide the coefficients.
9.6 / 2.4 = 4
Step 2: Subtract the exponents.
10^4 / 10^2 = 10^(4-2) = 10^2
Step 3: Write the answer in scientific notation.
4 x 10^2
Compare and contrast adding / subtraction and multiplication/ division in scientific notation
1 answer