how can you express a number in expanded form and in scientific notation?
Scientific Notation is a way that people use to write numbers that would be unpleasant to write out in Standard/Decimal Notation. Here are some examples that illustrate why anyone would care about how they write down a number:
Decimal Notation Scientific Notation
5,000,000,000,000 = 5 × 1012
12,000,000,000 = 1.2 × 1010
430,000,000 = 4.3 × 108
0.000000000008 = 8 × 10-12
0.0000000023 = 2.3 × 10-9
0.00000095 = 9.5 × 10-7
The carat (^) is used online to indicate a power, so 10^2 = 10 squared. Anna's answers need to be modified as shown below.
Decimal Notation Scientific Notation
5,000,000,000,000 = 5 × 10^12
12,000,000,000 = 1.2 × 10^10
430,000,000 = 4.3 × 10^8
0.000000000008 = 8 × 10^-12
0.0000000023 = 2.3 × 10^-9
0.00000095 = 9.5 × 10^-7
I hope this helps a little more. Thanks for asking.
thanks so much.. it did help. thanks for the answers!!
To express a number in expanded form, you need to break it down into each digit's place value. Here's a step-by-step guide on how to do it:
Step 1: Identify the place value of each digit in the number. The rightmost digit is in the one's place, the next digit to the left is in the ten's place, the next is in the hundred's place, and so on.
Step 2: Write down each digit multiplied by its respective place value. For example, if the number is 456, the expanded form would be: (4 x 100) + (5 x 10) + (6 x 1).
Step 3: Simplify the equation. Using the example above, it would be: (4 x 100) + (5 x 10) + (6 x 1) = 400 + 50 + 6.
Step 4: Add up all the simplified terms. In this case, 400 + 50 + 6 = 456. So, the expanded form of 456 is 400 + 50 + 6.
To express a number in scientific notation, you need to represent it as a product of two factors: a number between 1 and 10, multiplied by a power of 10. Here's how you can do that:
Step 1: Move the decimal point in the original number to the right or left until there's only one non-zero digit to its left.
Step 2: Count the number of times you moved the decimal point. If you moved it to the right, the exponent will be positive. If you moved it to the left, the exponent will be negative.
Step 3: Write the number you obtained from Step 1, followed by the letter "x" and the base 10 raised to the power of the exponent obtained in Step 2.
For example, let's express 456 in scientific notation:
Step 1: Move the decimal point to give us 4.56. We moved it two places to the left.
Step 2: Counting the movements, we know the exponent will be -2.
Step 3: The number in scientific notation is 4.56 x 10^-2.
So, the number 456 can be expressed in scientific notation as 4.56 x 10^-2.