Write each of the following numbers in standard scientific...

Write each of the following numbers in standard scientific notation. a. 1$/ 0.00032$ b. $10^{3} / 10^{-3}$ c. $10^{3} / 10^{3}$ d. $1 / 55,000$ e. $\left(10^{5}\right)\left(10^{4}\right)\left(10^{-4}\right) /\left(10^{-2}\right)$ f. 43.2$/\left(4.32 \times 10^{-5}\right)$ g. $\left(4.32 \times 10^{-5}\right) / 432$ h. 1$/\left(10^{5}\right)\left(10^{-6}\right)$

Write each of the following numbers in standard scientific notation.
a. 1$/ 0.00032$
b. $10^{3} / 10^{-3}$
c. $10^{3} / 10^{3}$
d. $1 / 55,000$
e. $\left(10^{5}\right)\left(10^{4}\right)\left(10^{-4}\right) /\left(10^{-2}\right)$
f. 43.2$/\left(4.32 \times 10^{-5}\right)$
g. $\left(4.32 \times 10^{-5}\right) / 432$
h. 1$/\left(10^{5}\right)\left(10^{-6}\right)$

Key Concepts

Scientific Notation

Scientific notation is a method of writing very large or very small numbers as the product of a number (the coefficient) between 1 and 10 and a power of 10. This format simplifies calculations and comparison of numbers with many digits or many zeros.

Exponent Rules

Exponent rules refer to the mathematical laws that govern operations on numbers expressed as powers of 10. For example, when multiplying numbers in scientific notation, you add the exponents; when dividing, you subtract them. These rules are essential for simplifying expressions in scientific notation.

Standard Form

Standard form in the context of scientific notation means expressing a number such that the coefficient is at least 1 and less than 10, with the value adjusted by an appropriate power of 10. This convention ensures consistency and ease of interpretation.

Decimal Conversion

Decimal conversion involves rewriting a decimal number into scientific notation by moving the decimal point to create a new coefficient that fits the standard form, and then multiplying by the corresponding power of 10 to preserve the original value.

Transcript

00:01 So today we're going to be looking at writing a number of numbers in scientific notation.

00:04 And so scientific notation is just going to be a number to an x -axis to represent that number.

00:13 And so looking at our first one, we're looking at 1 divided by 0 .0032.

00:17 So 1 divided by, and if we put that into our calculator, that will get us 3 ,125.

00:29 125.

00:30 And so then if we go ahead and move our decimal place over, we can use that to calculate the exponent because our number is going to be 3 .125.

00:41 And so then to move our decimal place that many places, one, two, three.

00:46 So that'll be 10 to the third.

00:48 Then moving on into part b.

00:51 In part b, we have 10 to the third over 10 to the third.

00:57 And so to do this, we can add or subtract 10 to the negative third.

01:02 My apologies.

01:03 We can subtract our exponents when we divide.

01:06 So we wind up with 3 minus negative 3 equals 6.

01:10 So then to put that into scientific notation, we're at 1 times.

01:16 Moving on into part c.

01:18 Part c is looking at 10 to the third over 10 to the third.

01:23 And so this is the same number over itself, which is going to equal 1.

01:26 And then into our scientific notation is going to equal 1 times 10 to the 0, because any number to the 0 power is 1.

01:36 Moving into part d.

01:38 In part d, we are looking at 1 over 55 ,000.

01:42 And so once again, put that into your calculator, and you should get 0 .000018.

01:50 And so this is one of those numbers that scientific notation is really nice for, because this is kind of clunky to write and keep track of.

01:56 And so this time we're going to count over to the right.

01:58 1, 2, 3, 4, 5...

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